light in the local universe

Light in the Local Universe

i

LIGHT IN THE LOCAL UNIVERSE

My thesis is that light, and other forms of radiant energy, are

transferred from emitting atoms to absorbing atoms instantaneously,

without traversing the space, or the time, between the two. In a pair

of earlier books I have tried to explain how this is possible, and what

difference it makes in the interpretation of experimental results.

All of the observations which have been made by physicists have

been based on what they could see, in what I have called the local

universe, unique to each observer. But, they have generally been used

as though they were made in a universe where time is the same

everywhere. In this universe light would appear to have a finite

speed. I call this model of the real world the galactic universe.

While we no doubt live in this galactic universe, what we actually see or

experience is all contained in our local universe, where we define the

present time by what we can see right now. Einstein’s theory of

Special Relativity is the preeminent example of the use of data

obtained in the local universe as though it represented measurements

made in the galactic universe.

The difference between the two models is trivial in the everyday

world, but in astronomy, nuclear physics, and in particular, where

physicists are accelerating atomic particles to unimaginably high

velocities, it makes a big difference.

Or, I could be completely wrong.

Les Hardison

Les Hardison

ii


Copyright 2013

All rights reserved

Written and Published by

Les Hardison

Arinsco, Inc.

1682 Edith Esplanade

Cape Coral, FL 33904

ISBN 978-1 -4507-6373 -8


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CONTENTS

Chapter 1 Introduction .......................................................................... 1 Chapter 2 The Two Universes .............................................................. 5

The Galactic Universe .................................................................... 7 The Local Universe ...................................................................... 12 The Choice between the Two Models ...................................... 22

Chapter 3 Relativity in the Galactic Universe ................................ 25 Use of Galactic Space-Tme ......................................................... 26 Size and Distance .......................................................................... 29 Measurement of Distance and Length ...................................... 30 Time, AND its Measurement ..................................................... 33 Velocity Measurements ................................................................ 38 Relativistic Mass ............................................................................ 41 Energy Considerations ................................................................. 42

Chapter 4 Relativity in the Local Universe ...................................... 45 Distance Measurement in the Local Universe ......................... 48 Time in the Local universe .......................................................... 52 Velocity in the Local Universe .................................................... 59 Why Light Appears to Move at 300,000 km/sec .................... 71 Mass in the Local Universe ......................................................... 78 Energy in the Local Universe ..................................................... 80 Summary ......................................................................................... 85

Chapter 5 Velocities of Objcets Moving Away ............................. 89 Speculations on the Possibility of having two Ts .................... 98 Conclusion ..................................................................................... 99

Chapter 6 Time in the Two Universes .......................................... 100 Where the Two Times Agree .................................................... 100 Where the Times Disagree ........................................................ 104 Agreement about the Speed of Clocks .................................... 110 The Influence of Time Measurement on c ............................. 123 The Significance of c .................................................................. 124 The Uniformity of Time Throughout Galactic Space .......... 126 Accomodting the Invariant Speed of Light ............................ 129

Chapter 7 Comparison of The Two Systems ................................ 132 Measurement of Time ................................................................ 136 Measurement of Distance .......................................................... 144

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Velocity in the Two Systems ..................................................... 147 Energy Consideration................................................................. 155 Comparison of Relativistic and Local Values ......................... 156 Why the Square Root Factors? ................................................. 160 A Credible Mistake ..................................................................... 163 The F correction explained ....................................................... 166

Chapter 8 Critique of Special Relativity ......................................... 172 Construction of the Basic Diagram ......................................... 172 The Meaning of t ........................................................................ 177 Which Way Does Light Travel? ............................................... 179 Seeds of Doubt ........................................................................... 182 The Speed of Light ..................................................................... 184 Transverse Motion Not Considered ........................................ 187 Pure Translation .......................................................................... 191 Summary ....................................................................................... 195

Chapter 9 Orbital Motion .................................................................. 200 Orbital Motion Around the Observer ..................................... 200 Orbital Motion Adjacent to the Observer .............................. 207 A Final Observation ................................................................... 212

Chapter 10 The Large Hadron Collider ......................................... 216 General description of the LHC at CERN ............................. 219 The Experiments at CERN ..................................................... 226 How are Mass and Velocity Measured at CERN? ................. 229 The CERN Results in Local Terms ......................................... 238 How Does the CERN LHC Funcition?.................................. 243

Chapter 11 Do Neutrinos Move Faster than Light? .................... 255 The Faster Than Light Neutrino Error ................................... 256 Are Neutrinos a Form of High Energy Radiation? ............... 259 The Opera Experiment Paper .................................................. 260

Chapter 12 Conclusions .................................................................. 301


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CHAPTER 1 INTRODUCTION

The first book, A New Light on the Expanding Universe, was an

attempt to explain a different concept of how the Universe we live

in is put together and functions. It was based on the assumption that

light really does not travel at 300,000 Km per second, but instead

goes from one place to another in no time at all. That is, the emission

of radiant energy from one atom, and the reception of that energy

by another atom, are simultaneous events. They happen at the same

time, judging from the standpoint of the local time at the observer’s

location. This is equally true for two observers moving with respect

to each other in our three dimensional world.

To make this happen requires five dimensions --- the three we

observe when we look around us, and a fourth, which is the direction

the entire Universe is moving as it expands, at the apparent speed of

light 1 , plus a fifth dimension, around which our entire four

dimensional super-universe is wound, like a vast number of strings

representing our lines of sight..

The Universe described is pretty bizarre, but not as strange in many

ways as the one espoused by current theoretical physicists.

Allowing light to move at essentially infinite speed makes many of

Albert Einstein’s deductions untenable. For example, he deduced,

and I think firmly believed, that as objects accelerated (with respect

to an arbitrarily located observer) their time passed more slowly. The

1 The apparent speed of light is italicized here, as it is a phrase used in a special

sense. In this case it denotes the velocity, approximately 300,000 Km/sec,

which is usually defined as the speed of light in a vacuum, but is, in my

view, the speed at which the universe is expanding into the fourth

dimension.

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mass of the object increased and the linear dimensions got smaller

as the speed became significant relative to the apparent speed of light,.

My world is a little bit easier to believe, because sizes and masses

don’t change with velocity. They really can’t because all velocities

have to be measured with respect to something, and one reference

point is as good as another. So, simply shifting one’s coordinate

system to the moon should make our dimensions smaller and our

mass greater (at least as seen from the moon). But, how can one see

our mass from the moon?

Other changes in outlook follow from this simple change in

viewpoint. For example, the whole concept of energy changes. There

is no longer any need for “potential energy” as a concept. Things do

not acquire potential energy as they are lifted from the earth. If they

did, they would have a maximum potential energy with respect to

the earth when they are so far away from it that there would be no

way to even tell if the earth existed.

Instead, part of the inherent energy all matter has due to its velocity

in the fourth dimensional direction is apparent to an observer when

its direction of motion through four dimensional space isn’t parallel

his own. Every observer has his own private direction, and all

observers would judge the velocity and kinetic energy of each mass

they observe differently from all others who aren’t “stationary” by

their own standards.

The way the hydrogen atom is constructed has to change from the

accepted picture based on Bohr’s model, in order for light to be

transferred instantaneously. The concept proposed by Bohr back in

the early part of the 20th century, does not appear to be applicable to

hydrogen molecules, but only to hydrogen atoms, and is impossible

to apply to elements heavier than helium. The picture which does fit

with the theory of light presented here is applicable to all atoms,

regardless of size.

Many of these subjects were covered in the first book, and a few

additional ones were dealt with in the second book. However, a vast


3

array of experimental data has been collected by physicists and

carefully fitted into the present accepted concept of the way matter

is composed, and how it behaves.

This picture, usually called The Standard Model, is based on

quantum mechanical concepts, and quantum mechanics is, in turn

based on the presumption that light consists of waves/particles

(photons) which move through a vacuum at 300,000 Km/sec. I

think the basis is wrong, and therefore much of the substance of

quantum mechanics is wrong. I don’t believe photons exist; they are

simply made up by physicists to account for some of the properties

of light they can’t explain otherwise. Likewise, the other “transfer

particles”, muons, gluons and gravitons are, to my way of thinking,

mythical.

There are innumerable measurements made by experimental

physicists which have integrated into the Standard Model, and which

must fit just as well into my model of the Universe, and a lot of

pieces and parts that aren’t necessary in my model.

Most of these I am only vaguely aware of, having not much

education in physics beyond the fundamentals. However, all of the

measurements need to fit into my picture at least as well as they do

into the Standard Model for it to be a good theory. I am not sure

they do, because I haven’t had time to learn about all of them.

I won’t pretend to cover the whole of physics in this book either,

because I don’t know the tiniest fraction of all of the experimental

results which have been produced by the thousands of physicists,

living and dead, who have made significant contributions to the

literature. But, in this book, I will try to examine some of the

additional experimental work I have become aware of. Of course, I

will do so from the view point of someone who has something to

sell (my ideas about how the Universe works), so let the reader

beware.

Even more importantly, I believe that there are two distinct ways of

looking at the physical universe, which I have called the galactic

universe and the local universe. Modern physics operates in the former,

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yet all of the observations are of necessity, made in the latter. My

rules apply strictly in the local universe, and the main disagreements lie

in the translation from one system to the other.

I will present a description of the two universes, and work out the

conversions necessary to represent time, distance and velocity in the

galactic universe, when the measurements are made in the local

universe. In doing so, I hope to explain why the Einsteinian

corrections to measured physical constants are unnecessary when

they are ascribed to the local universe in which they were measured.

In particular, there is a lot being done (at great expense) to explore

the internals of the fundamental particles the world is made of,

mainly protons, neutrons and electrons. The premier experimental

apparatus in this field, and possibly in any field these days, is the

Large Hadron Collider at CERN in Geneva, Switzerland. This very

impressive machine accelerates bunches of protons (which are a kind

of hadron) to 99.9999999 per cent of the apparent speed of light, and

smacks them into other bunches going the opposite direction,

producing unbelievable temperatures, and every kind of nuclear

particle known to man. I don’t presume to understand what they are

doing in detail or how they evaluate the results. I do believe that the

protons in the accelerator are going many times the apparent speed of

light, when looked at as taking place in the local universe of the

experimenters. How this could be the case will take some explaining,

and I will try to furnish the explanation.

Finally, it has been difficult for me to define an experiment which

might produce acceptable results according to my theory, and

untenable results according to conventional physics. The Einsteinian

approach has worked pretty well. However, I may have found an

experiment or two which would be effective in supporting my

picture of the Universe as contrasted with conventional physics. I

will include a description of the proposed experiments.


5

CHAPTER 2 THE TWO UNIVERSES

In a previous Book2 A New Light on the Expanding Universe,

I presented the case that light is transmitted instantaneously from

the source to the receptor, without waves or particles transiting the

intervening space,

I was able to reconcile this concept with the generally accepted laws

of physics. However, there was one problem which was not

resolved. The energy which seems to be inherent in matter, in my

view, is

2E mc , EQUATION 1

regardless of the velocity of the mass with respect to the reference

system in question. This is based on the presumption that all of the

matter in the universe is moving in a fourth dimensional direction,

the direction in which the expanding universe is expanding, and that

the velocity we see in our three dimensional world is just a

component of the total velocity, c.

Conventional physics says the equation should be

22

2

mvE mc . EQUATION 2

In the previous book, I argued for the first case because it is simpler,

although it makes no provision for physical bodies moving faster

than c, presumably because there is no way for them to be

2 Hardison, Les, A New Light on the Expanding Universe, 2010, Self

Published ISBN978-0-615=37746-9

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accelerated past c by gaining energy from other physical bodies, as

all have exactly the same absolute energy and therefore the same

absolute velocity.

After careful consideration, I believe that E=mc2 represents the

total energy of electrons and protons when they are considered to

be moving as observed in the local universe in which all of our

measurements are made. When these measurements are imputed to

the galactic universe, the illusion of the added component appears.

This chapter considers the proposition that perhaps both equations

are correct, but that they apply to different ways of looking at the

universe. Equation 2, when one looks at the world from the godlike

viewpoint, which I have called galactic space-time or the galactic

universe, and that Equation 1 is the correct representation of the

energy of moving bodies when the Universe is considered to be a

local universe, which can actually be seen by an observer at his own

local “present time”.

I will do my best to describe the two alternative ways of viewing

space and time. Throughout the discussion it is important to keep in

mind that the universe viewed by physicists is largely consistent with

what I have called the galactic universe, on which the Special Theory of

Relativity and most of the subsequent developments in physics is

based. The concept of the local time is my description of an

alternative way of looking at the things, and one which I believe is

simpler, and helps explain a number of the conundrums in modern

physics.


7

THE GALACTIC UNIVERSE

The galactic universe is most simply explained by reference to an

analogy, in which the real, 3D space is represented by the two

dimensional surface of a balloon. The balloon is expanding, as our

3D space is expanding, and it must have another dimension to

expand into. This third dimension in the analogy I have called T,

defined as

,T ct EQUATION 3

where:

T= a fourth spatial dimension

c= the apparent speed of light (about

300,000 Km/sec)

t =time.

Time is measured from some arbitrary time, which could be the time

of the Big Bang, or any subsequent time.

The galactic universe is defined as the space contained in the entire

volume of the universe where time is everywhere the same at any

given moment. If it is, right now, January 1, 2013 at precisely 12:00

noon Central Standard Time in the US, it is also exactly the same

time on the far side of the moon, or on a far distant planet in a

different galaxy. We choose to use different time zones for

convenience, but the essential concept of the present time is

presumed to apply uniformly throughout the galactic universe.

This is very difficult to visualize because the expansion of the three

dimensional volume requires a fourth dimension for it to expand

into, just as the two dimensional surface of a surface of the balloon

could not expand if it did not exist in a three dimensional world.

It is possible to picture a two dimensional analog of the universe,

where the expansion is taking place with the diameter of the balloon

increasing in a direction perpendicular to the surface. I have called

this the T direction, and the assumption that the velocity of

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expansion is c, the presumed speed of light, fits very well with the

estimated age of the universe and preset size of the universe.

In this analog, time is galactic time and is everywhere (on the surface

of the balloon) the same as it is at the point representing our location

in space and time as the observer at the origin of our own coordinate

system. This should not be difficult to grasp, as a balloon being

blown up obviously has all of the elements comprising the surface at

the same diameter, at the same time.

The surface of the balloon represents all of the points in the galactic

universe at the present galactic time.

FIGURE 1

INSTALLING A COORDINATE SYSTEM FOR THE GALACTIC

UNIVERSE

On the two dimensional surface resenting our three dimensional

universe, I have set up an arbitrary coordinate system, with the

observer, who is studying the universe at the origin. This origin could

be placed at any point on the balloon’s surface without altering the

geometry of the situation


9

In the local area close by the origin, the universe appears flat, and we

can make calculations and draw figures on a simple rectangular grid

without any particular problems. Because the diameter of the

Universe is very great, on the order of 27 billion light years, the

curvature is not likely to be a problem when we are dealing with

things within a few million light years of our reference system origin.

There should be no problem treating it as a nice orthogonal square

grid on the surface of the balloon, and 3D space as a similarly square,

well-behaved grid system. So, for the rest of this discussion, the two

dimensional analog surface and the 3D real world coordinate system

will be shown like this

.

FIGURE 2

THE 2D ANALOG OF THE 3D GALACTIC UNIVERSE

We can define time very simply in this snapshot of the universe. It

is, in every point in x – y portion of the universe, the same time as it

is at the origin. The time at the origin can be taken as a parameter

that is increasing at a constant rate, so time is independent of the

placement of the origin. Distance, presuming distance could be

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measured by the placement of measuring rods between any two

points, would be independent of the particular time the

measurement was made, for stationary objects, and would depend

on the time for moving objects, where the movement is measured

with respect to the observer at the origin.

One must bear in mind that our observations of real objects and

events does not permit us to use this galactic grid system, for the

simple reason that the Universe is expanding, and things which we

would define as distant objects cannot be observed as they exist at

the instant we make the observation. This is because, in this space

time arrangement, light appears to move at a constant, limited

velocity, c which is approximately 300,000 km/second. Because this

is enormously fast in comparison to our everyday observations, it

seems to be instantaneous. However on the scale of interstellar

space, it is slow enough that it may take years, or millions of years,

to reach us.

The conclusion must be reached that any observation of a distant

body or event involves, not the “present” galactic time, but a “past”

galactic time, at which time the body may have been different than it

is “now” and at a different location in three dimensional space. How

different depends on how far away the event or body is from us and

on how fast it is moving relative to our present location.

In the galactic universe, it appears that light and other forms of radiant

energy transfer move through space at a constant velocity c,

regardless of the choice of coordinates, or the relative motion of the

observer with respect to the “path” of the light. In this galactic universe,

E=.mc 2 for objects at rest with respect to our three dimensional

coordinate system, and seem to have an additional velocity and

kinetic energy (velocity energy) when moving with respect to the

coordinate system we are using.

Because the expansion of the universe is in a dimension of which we

have no sensation at all, it is difficult to conceive of it as anything

but a sort of abstract construct which complicates the straight-

forward three dimensional space we experience daily. Yet the


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evidence is pretty strong that the universe is, in fact, expanding. It

appears to have been doing so for a long time, on the order of 14

billion years, and to have grown in size from something very small

near the beginning of time, as we know it, to something on the order

of 14 billion light years in radius, or 28 billion light years in diameter.

There is more on the geometry of the galactic universe as I see it in the

appendix to this chapter.

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THE LOCAL UNIVERSE

Our own, local universe3, comprised of the totality of all that can see

or sense in any way at any given instant in time, differs considerably

from the galactic universe described in the previous chapter.

Generally speaking, modern physics models the world along lines I

have called the galactic universe model, where the entire 3D universe

as we know it exists at any given moment in time as a sphere where

every object, and all the space surrounding the objects, exists at the

same instant of time.

The shape of this space is not hard to imagine, if one leaves out the

fourth dimension into which the universe is expanding. It is simply

a sphere, with the observer at the center.

However, it is considerably more difficult to imagine this sphere with

a fourth direction, basically at right angles to the normal three

directions (forward and backward, left and right, and up and down,

or x, y and z) but it is analogous to the surface of a balloon, which

has a two dimensional surface curved in a third dimension, and

expanding continuously into that same third dimension. Every point

on the surface of the balloon has a common time. Every observer

located on the surface would have exactly the same time on his local

clock, but every observer at a different location than ours would see

a different picture of the universe. His local universe would be

different from ours.

3 Note: I have not italicized the words referencing local and galactic space

or time for the remainder of the book. These terms always reference the

special meanings I have defined for them.


13

The galactic universe is a very useful analog, but there is one striking

problem with it. That is, if the balloon surface represents the entire

universe, the parts that are far away from us cannot be seen from

any observation point on the surface. Because light appears to move

slowly (in comparison with the vast size of the balloon), by the time

light from a distant star gets to us, it will only give us information

about where the star was and what was going on there at some time

in the far distant past.

The same problem exists for observations of objects and events

which are much closer to us. As observers, we see nothing of the

surface of the balloon as it is now, but rather only things as they were

at some time in the past (the very, very near past for objects close

by, and the far distant past for objects far away.) Still, what we are

observing is not the universe the way it exists at the time we as local

observers define as right now, but rather the universe at it existed at

various times in the past by galactic standards.

On the other hand, the universe which we actually see, the

composite of objects reaching back in galactic time millions of years

for distant galaxies, comprises our local universe, which is entirely at

our present local time. So, what we see, at the present moment,

comprises our local universe at our local present time. We have no

access whatever to information from other points in the galactic

universe, or on the surface of the balloon at other locations.

Again, it is convenient to use a two dimensional analog to represent

the nearby relatively orthogonal portion of the expanding universe,

but instead of a two dimensional plane as our mapping surface, we

have an inverted conical surface with a 90 degree cone which

contains the x and y coordinate system with the origin, and the local

observer, located at the apex of the cone.

The one point at which the galactic universe and the local universe

share location and time is at the origin. The apex of the cone

representing the local universe is placed at the origin of the galactic

universe, so it appears to extend into the galactic past. All of the rays

extending out from the origin of the local present cone represent the

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pathways by which light or other forms of radiation could reach the

observer at the origin from any point in the local universe.

FIGURE 3

THE SHAPE OF THE LOCAL UNIVERSE

The shape of the local present is depicted in Figure 3.

In this picture, the entire universe that is visible from the origin lies

along the surface of the cone, and it is all presumed to exist in the

local present. As the galactic universe expands in the fourth

dimensional T direction, the local universe cone moves right along

with it, but the methods of keeping time and measuring distances

and velocity must be altered radically.

Whereas the nearby part of the galactic universe appears to be a flat

plane (actually a tiny segment of a vast sphere) when viewed as a two

dimensional analog of our three dimensional Universe, the local

universe appears as the surface of a cone. The x and y axes are bent

downward at a 45 degree angle, if our vertical, or T scale, is chosen

with units consistent with the units of the x and y axes. That is, all

of the units are given in length units, such as Km, or all of them are

given in time-like units, such as years and light years.


15

Figure 4 illustrates, in a cross sectional view of the local universe

cone, the relationship between galactic past, present and future, and

the past, present and future of the local universe. In the local

universe, everything lying along the 45 degree lines of sight

represents things which we can see at the moment, and which

comprises our local present. The local past is all of the area lying

inside the cone, which may have been seen in the past, but can never,

under any circumstances, be seen again from our position at the

origin. And outside the cone lies the future, which we may be able

to see at a later time.

FIGURE 4

THE LOCAL UNIVERSE PAST, PRESENT AND FUTURE

In Figures 3 and 4, the lines of sight are plotted as lines where

x = T, so they are at 45 degrees relative to the x Axis in the galactic

universe, and to the T Axis. If they are lines of sight, it is apparent

that things are receding into the past of an observer permanently

affixed to the origin at a velocity V, which represents the speed at

which the three dimensional universe is moving in the fourth

dimensional direction, T. So, there would be no quarrel with us

writing that T=Vt.

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However it is also apparent that, from the standpoint of the galactic

universe, T=ct. Therefore we can presume that in the local universe,

V = c, where c is the apparent speed of light. Thus the lines of sight are

along lines where x=ct and x=-ct. In Chapter 3, we shall make the

case that the relationship between these variables makes a

compelling case that the velocity of light, as seen by a real (i. e., local)

observer is infinite, and the velocity of the universe in the fourth

dimensional direction is c, the apparent speed of light. There is, however,

a missing piece to this story which needs to be filled in later.

We make all of our observations from our present location in the

local universe, where what we see at any given time is what we know

to exist. Yet, the historical practice in the physical sciences, dating

back to Newton and earlier, is to presume that reality is represented

by the galactic universe, where the time scale is independent of the

location. This has led to all sorts of corrections, and many

unexplained observations of physical phenomena. For example, the

presumption that light has a finite velocity which is the same for all

observers, regardless of their speed relative to each other.

The invariance of the speed of light is possible only under two

circumstances. One is where the velocity of light is infinite, which

would, of course be measured the same way by any two observers

whether moving relative to one another or not, and the other is that

described by the Theory of Special Relativity, which suggests that

time moves at a different pace for systems moving relative to one

another, and somehow modifies the properties of matter moving

with respect to the observer.

Science has accepted the latter case, wherein the time contraction

calculated for objects moving relative to us is presumed to be real,

and with it all of the consequential results. The dimensions of objects

shrink and their masses increases with velocity relative to any

arbitrary reference system. These are, of necessity, illusions of some

sort, because two observers moving relative to each other would

assign two totally different masses to the same object, and would

believe it had two different lengths.


17

So, there is some reason to consider the other possible solution to

the problem of the invariance of the speed of light; that is, that light

moves instantaneously from place to place. This would eliminate

many of the problems with relativistic physics, but would raise the

question, “what is c, the apparent speed of light, if it is not actually the

speed of light?” I will try to answer this in subsequent Chapters. But

for now, let us presume that the local universe is a coordinate system

superimposed on the galactic system of space and time coordinates

described previously, and that the local universe consists of

everything one can see at any given moment.

Whether one accepts the idea that the speed of light is infinite or

not, there is no choice but to accept that the local universe, which

one sees from his present location at the present time, is shaped like

the inverted cone in Figure 3, where everything he can see is lies

within the surface of the cone. This is true whether one accepts that

the light moves instantaneously from the various points along the

surface to his eyes at the apex of the cone instantaneously, or rather

gets there by moving through the intervening space as the apparent

speed of light, as though swimming through space like a fish swims

through water. Most of the following is true in either case.

The observer, at the apex of the cone is at the single point where the

local universe and the galactic universe are at exactly the same time.

As one moves away from the apex in any direction, the distance

increases, and one moves backward through galactic time, into the

galactic past. In the local universe, I have chosen to take the surface

of the cone as the local present, where one’s universe consists of what

one can see at the present moment. This involves the implicit

assumption that the light from distant objects is transferred

instantaneously, at least in term of the local time, which is the same

for all the point on the cone, so far as we, at the apex, are concerned.

We might presume that an object, such as another laboratory

containing another observer were located some distance away, but

close enough that we could see him from our position at the apex.

Were we to possess extraordinary eyesight, and a marvelous

telescope, we might be able to make out the clock on his work table.

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Because we would have assigned the time on our clock to the entire

cone, we might presume that the clock on his work table will read

the same as ours, but this is not true. He is, in terms of galactic time, in

the past, and his clock will, at some future time (from our point of

view) read the same as ours does now, when his balloon surface

reaches the same T value as our balloon surface is at now. But right

now, by our standards, he is in the galactic past, and his clock runs

on galactic time, as does ours. We would make out his time as being

earlier than ours by exactly the distance between us divided by the

speed at which the universe is expanding. That is, his clock will read

slow by (Δx/c)Δt.

This second observer, if he is not moving with respect to our

position, would see us at an even earlier time; and think our clock

was reading too early by the same amount we thought his clock was

reading too early a time.

During this discussion, it must be borne in mind that the local

universe, like the galactic universe, is simply a reference system for

depicting a particular instant in time, during which what we perceive

as the real world exists. The 4D universe seems to be quite

independent of time, and is unchangeable and immutable. The

galactic universe represents the point in time (in the fourth

dimensional direction (T=ct), at which we are right now. It is a cross

section of the 4D world at the present moment in time, and we can

picture what it looked like at past moments in time, and predict some

things about how it will look at future moments, but we can only see

the local universe.

The local universe is the part of the 4D universe we can actually see

at that time, because radiant energy transfer takes place at intervals

along relatively straight diagonal lines in 4D space. (Yes, space is

curved by the presence of matter and electric charge, but these

weren’t dealt with in Special Relativity, and we will simply consider

the surface of the balloon undistorted for most of this book.)

All of this discussion pertains to a 2 dimensional analog universe

with x and y as the coordinates, and z presumed to be equal to zero.


19

The third dimension in this analog universe is T, where T = ct. T is

a dimension measured in length units, such as micrometers or light

years, c is the speed of expansion of the universe in the T direction,

and t is time, measured in units of microseconds or years, or other

time units consistent with the measurement of the spatial

dimensions.

In the analog models, the galactic universe is the nearby, relatively

flat surface of a huge sphere. The observer’s local universe, on the

other hand, is a cone with its apex on the surface of the galactic

universe, and the time throughout the cone is the same. So, at the

observer’s location, galactic time and local time are the same.

However, at any other point, local time differs from galactic time by

the ratio of the distance away from the origin to the apparent speed of

light, c.

FIGURE 5

THE LOCAL UNIVERSE CONE BENEATH THE GALACTIC

UNIVERSE PLANE

In Figure 5, the cone representing the local universe coordinate

system is shown just touching the plane representing the galactic

universe with the apex of the cone at the origin of the galactic

coordinate system.

Les Hardison

20

For the most part, physicists have treated the two systems for

measurement of time, distance and velocity as though they were the

same. From my point of view, this has led to some very great errors

in perception of how things “really are”. This concept works quite

well in explaining many phenomena, and making useful predictions.

However, I believe the concept of the local universe offers a more

reasonable representation of reality, and certainly a simpler one.

In the local universe we must assume that, if we see something, it

actually exists in the local present time. This involves assuming that

the light, or other electromagnetic radiation used to detect an object,

reached our eye at essentially the same time it was emitted by the

source of the radiation. In other words, the speed of light is infinite

in the local universe.

It is not too different from the space Dr. Einstein was hinting at with

Special Relativity. He defined simultaneous events as those which an

observer could see happening at the same time. If I see two stars at

the same time, even though they may be light years apart, it implies

that the emission of light from each of them and the reception of

the light at my eyeball are simultaneous events. I know that I am

seeing them at the same local time I am experiencing, as though that

the light took no time to get from each of them to me, the observer.

I can understand that, from my observations I may be able to

calculate what things might be like in the galactic universe at this

point in galactic time, but there is no way to verify my predictions

until some later time.

So, I have two times I can use in making predictions. The local time

I assign to an object, which is the same time as my own galactic clock

reads, or the galactic time, which is still in my future. I have to keep

these two times straight, or I will get some misleading results.

An analogy that one may experience in ordinary life involves

traveling from one country to another, possibly by cruise ship. If one

carries a smart phone, it keeps track of time in two ways. Because it

contains a GPS receiver and computer, it always knows precisely

where you are at the moment, and adjusts the time on your clock


21

automatically to the time zone you are in. So, when you cross the

border from one time zone to the next, the clock jumps an hour

forward or backward, depending on which direction you are moving.

This is very much like my concept of local time, where the important

element is where your clock is located at the moment.

However, concurrently, you may also keep track of Universal Mean

Time, which used to be called Greenwich Mean Time. This is the

reading of the clock in the observatory in Greenwich. England.

UMT is exactly the same everywhere in the world. It changes

continuously, but, like galactic time, if you will, as it presumes the

time is the same no matter where you are on the surface of the earth.

The two clocks only agree when you are in the Greenwich, England

time zone.

In the following chapters, I will try to establish the rules for relating

time, location or distance, velocity and energy as measured in the

local universe of the observer, and how it would appear if a godlike

observer were able to make the measurements in the galactic

universe. I will try to point out where modern physics uses the

attributes of each, and how much simpler life would be if we stuck

to the local world as the place to do our calculations.

While I do not doubt that there is an element of reality in the galactic

universe model, it is a model of a reality which we can never

experience directly, while the local model is a true representation of

the world the way we see it.

Les Hardison

22

THE CHOICE BETWEEN THE TWO MODELS

So, when one wishes to represent the world as it really is, he has a

choice of using the galactic model or the local model I have

proposed, or some other model of his own choosing.

In the galactic model, the universe is analogous to a vast balloon,

expanding into a fourth dimension at a rate which appears to be

constant with time, where all of the points on the surface of the

balloon at any instant are presumed to be at the same time, and it is

presumed that observers at a distance from our own position would

have clocks which read essentially the same time as our own clock.

In the local model, it is presumed that the local time is the same for

everything we can see at the moment. Because those things we can

see are all at some distance from us, they would be in the past by

galactic standards, and the clocks of distant observers we could see

or communicate with would all read earlier times than our own. The

farther away they were, the earlier their clocks would read.

Although the two universes appear to be identical to the ordinary

observer, dealing with ordinary objects which are not moving very

fast (relative to the rate at which the universe is expanding) or not

very far away (relative to the amount of change in the size of the

universe in a time period a person can experience - a second, a year,

or even a lifetime), the difference becomes important when dealing

with fast moving objects, or those which are far away from us.

These are the things which Albert Einstein dealt with when working

on his Special Theory of relativity. At the time he did his work, there

had not been enough data collected by astronomers to lead them to

believe that the universe was, in fact, expanding, or to speculate on

what it was expanding into if it were. So, Einstein used the same

presumption that all his predecessor physicists had used, and that

was that time was everywhere the same within the universe.

Still, he was faced with the seemingly irrefutable observation that the

speed of light was finite and constant throughout the universe,


23

without regard to the velocity of the observer who was measuring it.

This was anomalous because all physical objects which move

through space, or through a medium such as air or water, are

observed to have different speeds when measured by different

observers who are moving relative to one another. Light or

electromagnetic radiation in general, seems to be an exception to this

rule.

This anomaly led to his development of the Special Theory of

Relativity, which provides a picture of the universe in which it is

possible for observed velocities which are close to the apparent speed

of light to appear to be moving at the same speed regardless of the

velocity of the observer.

However, the Special Theory of Relativity contains within it some

anomalies which sow seeds of doubt as to either the input data, the

interpretation of the model of the universe, or the derivation of the

equations. The relationships between the measurement of distances,

time, velocity and energy when viewed by a “stationary” observer,

and one moving at a significant velocity relative to the stationary

observer, all involve complex correction factors and seem to lead to

analogous conclusions when observers are presumed to be moving

relative to each other. For example, they will assign different masses

to any given object.

The local universe model is not an alternative to the galactic

universe, but is rather a part of it. However, it represents the part

which an observer can actually see, rather than simply imagine.

Thus, it is possible to assert that all of the measurements of

scientists of whatever type are made, essentially according to the local

model of the universe. However, it appears that they are often

attributed to the galactic reference system, as though the

measurements were made without taking into account the time

differences between the observer and the things being observed.

Einstein used the galactic system for the development of Special

Relativity, without defining it as such.

Les Hardison

24

This conclusion is based on his implicit use of the idea that time is

the same everywhere along his x Axis, which is a one dimensional

analog of our three dimensional space. I believe some of the

translations of data from the local universe observations to galactic

universe representations are faulty, and should be replaced by

equations which are based on my interpretation of the nature of the

local universe.


25

CHAPTER 3 RELATIVITY IN THE

GALACTIC UNIVERSE

Einstein correctly pointed out with his Special Theory of Relativity4

that time, when measured in a reference system moving with respect

to our own, must appear to run slower by an amount which becomes

significant when the relative velocity approaches the apparent speed of

light.

In order to make the speed of light invariant when measured by

observers moving relative to one another, he derived equations

relating to space and time that limits the velocity of all objects to the

apparent speed of light. Such objects appear to become smaller as they

move relative to the observer, and masses become greater.

The effects are not noticeable under ordinary, every-day conditions.

If they were, it would be easier to say that it is absurd that the

physical properties of matter change with velocity relative to any

arbitrary coordinate system.

A real observer looking for information about the present state of

the galactic universe must take what he sees at the moment, and

make presumptions about what will happen during the future, so he

may guess a position and state of the object in his present galactic

time. This is true of everything in the galactic universe. Nothing can

be known of it for certain, as it is not, at present, what we can see.

The fictitious observer at the origin of a coordinate system lying

wholly within the confines of galactic space would have to have

4 Einstein, Albert. Relativity, the Special and General Theory, Translated by

Robert W. Lawson, University of Sheffield, Crown Publishers. New York,

NY, Third Edition, 1918.

Les Hardison

26

some supernatural, god-like power to see what was happening

instantaneously in the space represented by the surface of the

balloon, or in the real world. Such an observer does not exist, but it

is be handy, from time to time, to imagine what he might see, if he

did exist.

USE OF GALACTIC SPACE-TME

In the following pages, I will try to walk you through Einstein’s

derivation of the equations of Special Relativity, and try to

demonstrate that they are presumed to apply to the galactic universe,

as I have defined it.

We can begin by looking at the expressions for length, time and

velocity in the galactic system. Einstein accounted for light from all

observers by starting with the assumption that light moved through

the space between the emitter of the light and the receptor much as

a fish swims through water, just a lot faster. Except that, no matter

whether you were moving relative to any arbitrary reference system

or standing still, the measurement would come out the same. Based

on this assumption, he deduced that time had to be different for

observers moving relative to the stationary coordinate system, and

he derived the equations of Special Relativity, which are still, after

over 100 years, taken to be essentially correct.


27

FIGURE 6

EINSTEIN’S DIAGRAM OF THE GALACTIC UNIVERSE

In this relatively simple diagram, he showed the path of light leaving

the origin in the diagram, and moving either to the left or the right

with a velocity c, which is what had been measured quite accurately

at the time Einstein did his work on Special relativity. Also, it had

been determined that, as close as measurements could be made, the

speed was constant, regardless of the motion of the observer relative

to anything else.

So, his simple plot shows the plot of the distance light shining out

from the origin moves to the left or right at the velocity c, if it is

going to the right, and – c if it is going to the left. These are not

unreasonable assumptions; although one would have to point out

that there is no way for an observer to determine what happens to a

beam of light which moves away from his present location.

Everything we see in the real world is the result of light moving from

somewhere else toward the observer, who is in the center of his own

observable universe.

He then postulated a second observer’s with his own coordinate

system, moving relative to the stationary observer, at a velocity v

relative to the stationary observer.

Les Hardison

28

He said that the second observers measurements of the path of the

light leaving the stationary origin would have to be exactly the same

path as that seen by the stationary observer, which means he would

have to agree that the velocity c was the same for him as it would be

for the stationary observer. This would not be true if they were both

observing a fish swimming through water, or a space ship moving

through space. Both would appear to be moving at velocities that

were different for the moving and stationary observers.

In order to make the arithmetic come out right, he used the Lorentz

transformation, which involved allowing the rate of passage of time

to be different for the moving and stationary observers. This not

only meant that, while the speed of light was measured the same by

all observers regardless of their motion relative to each other, all

other velocities had to come out the same also. Both the distance

and the time had to be “corrected” when the velocity of the object

or system was significant compared to the presumed speed of light.

These corrections are at the heart of the Special Theory of Relativity,

and have been treated as essentially holy writ since shortly after their

introduction.


29

SIZE AND DISTANCE

Essentially all of the equations derived as a part of the Special Theory

of Relativity are based on the assumption that light moves at a finite

speed, c, through empty space and that the velocity of light is

invariant. That is, two observers moving relative to one another will

both measure the same velocity for light. This was presumed to be a

special characteristic of light, or other forms of electromagnetic

radiation, although the prior experimental work was all done with

visible light.

The basic methodology involved using the Lorentz transformation,

relating special coordinates with a time coordinate and translating

them so that a single velocity, in this case c, would be measured the

same by each of two observers moving relative to each other at any

arbitrarily chosen fixed velocity.

The step by step application of the Lorentz transformation is, for

the reader’s convenience, appended to this chapter, so only the

resulting equations, which comprise the core of the Special Theory

are repeated and discussed here.

Les Hardison

30

MEASUREMENT OF DISTANCE AND LENGTH

The relationship he derived for distance measurement is

2

2

'

1

x vtx

v

c

EQUATION 4

where:

x’ = distance to the fixed object at x

observed by the moving observer

x = distance to the object from the origin

of the stationary coordinate system

t = time, measured in terms of a clock that

is stationary with respect to the

coordinate system

v = velocity of the object referred to the

stationary coordinate system.

This should apply equally well when we are talking about observing

objects which are moving relative to our coordinate system (and are,

presumably, stationary with respect to a coordinate system moving

with the object.)

In short, objects seem to be farther from us when they are moving

away from us at a velocity which is significant with respect to the

apparent speed of light, where x-vt is the distance we would ordinarily

agree upon if the velocity were small in terms of the apparent speed of

light.

Also, the implication here is that the distance to objects which are

moving away from us will appear to be smaller than someone

moving along with them would think them to be, and the lengths’

shorter, because for x =0,


31

2

2

'

1

v tx

v

c

, EQUATION 5

where v t represents the uncorrected distance of the moving

object.

Were an object originally at the origin considered to be moving,

relative to a stationary system, x in the above equation would be

equal to 0, and the velocity would be in the positive direction, rather

than subtractive. So, the coordinate of the object moving at velocity

v relative to the fixed coordinate system would be

2

2

'

1

vtx

v

c

. EQUATION 6

The time experienced by anyone moving along with the moving

object would have been taken by Isaac Newton to be t, just as a

godlike observer living in the galactic universe would presume it to

be, uniform throughout the galactic universe.

The notion that objects are shorter when moving away from the

observer is somewhat mystical, in that it should be apparent to

anyone that all of the objects surrounding him are, by his standards,

quite normal in size, and do not seem to be changing from day to

day, even though out velocity relative to some of the heavenly bodies

is quite high, and our velocity relative to the sun is changing rapidly

in direction, and also, to a lesser extent, in orbital velocity as the earth

approaches and recedes from the sun.

Therefore, the meaning of the shrinkage of length must apply only

to the observations of others, moving rapidly compared with c, the

apparent velocity of light, relative to our own position in space. The

method of measurement of the length of an object moving away

from us with a velocity significant with respect to c is tricky, in that

any sort of measuring stick used to measure the length would, of

Les Hardison

32

course, also show the same degree of shrinkage as the object being

measured.

This suggests to me that there is more to the story than is revealed

by the equations of Special Relativity. This is a point I will make

repeatedly.


33

TIME, AND ITS MEASUREMENT

The most significant departure from conventional physics contained

in Special Relativity involves the concept that time does not appear

to pass at the same rate for systems or objects moving at velocities

significant with respect to c, the apparent velocity of light. This was a

complete game changer for physics, which had previously regarded

time as a given, inflexible subjective experience which always passed

at a measured rate, whether the measurement was made by

astronomical observations or a mechanical clock.

In order to account for the invariance of the apparent velocity of

light, Einstein had to presume that the clocks of observers moving

relative to one another (in our three dimensional space) ran at

different speeds.

Einstein calculated that time would pass more slowly for the moving

observer, and the rate of passage of time would be such that

2

2

2

'

1

vxt

ctv

c

. EQUATION 7.

In this equation, x is the coordinate of a stationary point relative to

the stationary coordinate system. So, it is a constant in the equation,

as is the velocity. So, in comparing time intervals, as opposed to

absolute times,

2

2

'

1

tt

v

c

. EQUATION 8

Les Hardison

34

Generally speaking, for objects which are not very far away, the

numeric value of vx is much, much less than c, and the revised time

can be written as

2

2

'

1

tt

v

c

, EQUATION 9

or

2

2

' 1 1

1

t

t Fv

c

, EQUATION 10

for vx very small when compared with c2.

This gives the impression that the rate of change of time is slower in

the moving system than in the stationary one.

This is, of course, untrue. Otherwise, our clocks, which seem to run

at a very ordinary and reproducible pace, would change speed

whenever some arbitrarily chosen secondary reference system

changed speed. I will try to demonstrate, in a later chapter, that the

correction factor F is not a real characteristic of the physical

universe, but the correction of an error by making observations

made in the local universe and incorrectly attributing them to the

galactic universe.

I maintain that all clocks (accurate ones, at least) run at the same

speed, and do not change rates at all. However, when you observe a

clock attached to a body that is moving with respect to your position,

you will see it taking longer between ticks than yours because each

successive tick is farther away from you than the previous one, and

therefore farther in the galactic past. The frequency of the ticks will

vary just as the frequency of sound varies when the source is moving

relative to you. You are acutely aware of the apparent change in


35

pitch, but you know that the frequency of the fire siren does not

change as it goes past.

Here again, subjective experience is such that time usually appears

much the same for one observer as another, because little within our

direct experience attains a velocity high enough relative to our own

to produce measureable differences. However, astronomers deal

routinely with distant stars and galaxies which are moving at

velocities high enough to suppose that they would experience

significant difference in time, were we able to communicate with

observers on them.

And, closer to home, but just as inaccessible to most of us, are the

electrons orbiting the nuclei of atoms, which move at substantial

velocities relative to the apparent speed of light, and are subject to

relativistic correction factors.

The velocity of an object stationary with respect to the stationary

coordinate system would appear to be moving with respect to the

moving coordinate system at a velocity equal to that attributed to the

moving coordinate system by the stationary observer. That is to say

that either system could be chosen to represent a stationary observer

and the other the moving one, and the results should come out the

same, except for the sign of the velocity being changed.

So, in Special Relativity, the relative velocity of two systems is

accurately perceived by observers in each, as the rate of change of

distance with respect to time in their own system. However, Einstein

has used his basic supposition, that light moves at the fastest possible

velocity, v=c, to draw a further conclusion. That is that time, and

space, and physical objects within space, actually get smaller when

they are moving relative to you, the “stationary observer”.

Still, there is some disquieting aspect to the shrinkage of time. Again,

time seems pretty normal and regular to us in our everyday lives.

While subjectively, it appears to pass quickly sometimes and slowly

at other times, the clocks, the seasons, and the decay of radioactive

materials seem to agree pretty well, as though we were like the

Les Hardison

36

stationary observer in Einstein’s derivation, and the time shrinkage

applies only to somebody else.

This is as far as Special Relativity went in relating the properties of

space and time to the velocities assigned to them relative to a system

considered to be stationary. However, in General Relativity, he dealt

with accelerations, and found gravitational effects to be identical

with acceleration fields. Because as space and time shrink as objects

move faster, it was apparent that the same kind of shrinkage of space

and time applied to the spaces near massive objects. So, gravity is

also responsible for shrinkage of space and time, but in a complex,

non-linear way.

It should be borne in mind that this equation for the “shrinkage of

time” for moving systems and objects was derived for the case where

the moving system was moving away from the observer at the origin

of the stationary system. The situation where the object is moving

toward the observer produces identical results if the velocity is

considered to be negative, but the distance between the observer and

the object a positive quantity, r, which is simply the radial distance

from the observer to the object, no matter which way it is going.

FIGURE 7

PLOT OF EINSTEIN’S EQUATION FOR A MOVING

COORDINATE SYSTEM


37

For now, I will simply point out that all of the equations developed

by Einstein for the relationship between distance and time for

moving objects imply that the measurements are referenced to the

galactic system of coordinates.

Figure 7 is a plot of some of these relationships.

Here, the equation for the time experienced by one who is moving

with respect to the stationary coordinate system depicted, is plotted

for the translational velocity uncorrected for the shrinkage of time

2'

vxt t

c , EQUATION 11

which is obtained for velocities which are negligibly small compared

to the apparent speed of light, c. This suggests that as

v c , EQUATION 12

'x

t tc

. EQUATION 13.

This is essentially the equation I will use to describe the relationship

between local time and uncorrected galactic time in a subsequent

chapter comparing relativistic effects in the two reference systems.

At the other extreme, when the velocity of the moving system

becomes negligible as compared with the apparent speed of light.

0v , EQUATION 14.

't t , EQUATION 15

so the rate of passage of time in the galactic system is the same for

the moving and stationary observers, no matter how far apart they

are.

Les Hardison

38

VELOCITY MEASUREMENTS

The measurement of velocity is, of course, simply the measurement

of distance at two different times, divided by the difference in times.

If the time interval is large, this gives the average velocity of the

object being tracked over the time period. As the time interval is

shortened it gets nearer to the instantaneous velocity, and the

analysis of motion when the equations for position as a function of

time are known is handled elegantly by differential calculus, where

x dxv

t dt

, EQUATION 16

where the Δs represent finite differences, and the dx and dt represent

infinitely small differences.

Throughout the evolution of Special Relativity, Einstein took all of

the velocities, including the apparent velocity of light, to be

constants. This is not to imply that there is anything special about

constant velocities, because things are accelerating and decelerating

all the time for various reasons. He simply did not include these

things in this part of the theory for the most part. Accelerations play

a major role in the General Theory of Relativity5.

The application of the Lorentz transformation is based on a

presumption of an observer at the origin of a coordinate system

which is “fixed” in that it has no velocity. The choice of the reference

system is, of course, arbitrary; as every point in the expanding

5 Einstein, Albert (1917) Kosmologische Beltrachtungen zur allgemeinen

Relativistitaheorie. Sitzungberichte der Preubischen Akademie der

Wissenchhaften 142


39

universe seems to be much like every other point, save for presence

or absence of matter. In developing the equations, Einstein

presumed the existence of a second coordinate system, moving

relative to the “stationary” one.

After deriving the equations for the shrinkage in both measured

distances and time, the calculation of velocity with respect to the

stationary system is straightforward.

For two reference systems with their origins initially at the same

place in space and time, the equation for the velocity relative to the

stationary system is

x v tv

t t

, EQUATION 17

And for the moving system

' ' '' '.

' '

x v tv

t t

EQUATION 18

Because

2

2 22

22 2

2 2

1

' 1

1 1

vvx ttc vct t

cv v

c c

, EQUATION 19

OR

2

2

'1

t v

t c , EQUATION 20

for the case where the object is at the origin of the stationary system,

Les Hardison

40

2

2

' ' 1

1

t t

t t v

c

. EQUATION 21

So, an observer who regarded his position as fixed would regard the

passage of time on a moving system as slower than his own. The

ratio of the two rates of tame passage would depended on his

measurement of the velocity of the other system. Were the roles of

the observer and observed exchanged, precisely same equation

would hold true.

This appears to say that the velocity of an object measured with

respect to one system would be identical to that measured by

another, moving system. This is not correct.

Time, whether referenced to a moving system or a stationary one,

must go forward, and never backward, v must always be less than c.

This pertains to velocities of any sort whatever, whether light rays,

or space ships or neutrinos (more on those later).

Seemingly, the velocity v could be the velocity measured by

determining two distances to the moving object and the two times

at which each measurement was made. If we see a body move a

measured distance in one second by our clock, this suggests that the

velocity measured on the moving object would be measured as zero

Einstein does not take into account the curvature of space over very

great distances, nor will, I in the subsequent comparison of the

Relativity in the galactic and local systems. The effect of the

curvature of space, represented in our analogy by the curvature of

the surface of an expanding balloon, is negligible when the distances

between two objects which are apart from each other by an amount

that is negligible in comparison when compared to the

circumference of the balloon. Thousands of light years does not

constitute a very significant distance on this scale.


41

RELATIVISTIC MASS

After determining the basic equations for distance, time and velocity,

Einstein had a problem to dispose of that might have upset the

whole apple cart of relativity.

Very simply put, the problem is this. If one imagines a mass, m, and

applies a constant force F to it, Newtonian mechanics says that the

mass will accelerate according to

dvF ma m

dt . EQUATION 22

The velocity will increase as long as the force is applied. Suppose we

choose to apply a force F to accelerate the mass m, the acceleration

rate will then be

dvF ma m

dt , EQUATION 23

or

.Ft

vm

. EQUATION 24

So, every second the velocity would increase by a constant amount,

F/m, no matter how gentle the force was applied. Eventually v

would reach c. It would, according to Equation 24, do so in mc/F

seconds. Obviously, the velocity would exceed c, and would keep on

increasing toward infinite velocity as the force continued to be

applied for a very long time. One of the premises of Special Relativity

was that this could not happen, as nothing can go faster than c in the

coordinates used in the galactic universe.

Now, up until this point, Special Relativity had dealt strictly with the

relationship between space and time. There had been no mention of

forces, accelerations and the like. But the problem was too pressing

Les Hardison

42

to let go, so Einstein proposed a unique solution to the problem,

which has been good enough to convince almost everyone since.

He said that what happens is that the mass of an object increases

with velocity, according to

2

2

' 1

1

m

m v

c

. EQUATION 25

This ingenious solution allows us to keep some reasonable and

useful Newtonian concepts, while embracing the contractions in

space and time that Special Relativity implies.

While this is an ingenious solution to the problem described, it once

again defies certain elements of logic. For example, my clock, which

I insist keeps good time no matter what the motion of your reference

system, weighs one kilogram (it has a built in radio and iPod music

port). My perception of its mass is precisely the same if you choose

to make me the center of your stationary coordinate system, or if

you choose to use the center of the star, Arcturus as the origin of

your coordinate system.

Never the less, this is what is commonly accepted as the true state of

affairs. That is, as you accelerate something to high velocity, its time

system is slowed down, its length in the direction of motion is

decreased, and its mass increases as the velocity becomes appreciable

as compared with the speed of light.

ENERGY CONSIDERATIONS

Once the concepts of mass and acceleration were imported into

Special Relativity, it was necessary to account for where the energy

went that did not go into increasing the velocity of the mass, but

rather increased the mass.


43

Einstein’s answer to this was another startling concept, and that is

that energy could be converted into mass, and conversely, that mass

could be converted into energy. This, while completely outside the

space, time, velocity relationships developed in Special Relativity,

was the most important practical result of Special Relativity, and one

that led indirectly to the evolution of atomic energy and countless

other technological marvels.

It was, of course, the most famous equation since F=ma.

2E mc . EQUATION 26

This is, of course, the equation for the rest energy mass. Einstein

explained that this is a simplification of the more general equation,

2

2

21

mcE

v

c

, EQUATION 27

for the case where the velocity is zero.

He goes on to explain that the approximation by expanding the

denominator using the well-known series

2 4 6

2

1 1 1 3 1 3 51 ..

2 2 4 2 4 61a a a

a

,EQUATION 28

Reduces to

2 42

2

3..

2 8

mv vE mc m

c , EQUATION 29

And for

2

21,

v

c EQUATION 30

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44

22

2

mvE mc , EQUATION 31

Which has the Newtonian expression for kinetic energy as the

second term.

Here again, these equations have been accepted as gospel since their

introduction in 1905, and continue to form the foundation of

modern physics.

I cannot leave this chapter without saying that this entire collection

of equations are not physical laws, but rather derive from the single

main premise of Relativity, which is that light travels through empty

space at the apparent velocity c, which is invariant. All of these

equations, which comprise Special Relativity, absolutely require that

this be true, and beyond question.

I am questioning this basic “fact”, and with it all of the resulting

derivations.


45

CHAPTER 4 RELATIVITY IN THE

LOCAL UNIVERSE

The derivation of the relativity equations in the local universe is

simpler than that used by Einstein, because it is not necessary to try

to make the speed of light come out the same when measured by

two observers moving relative to one another.

In the local universe, with the velocity of light taken as infinite, or

the time interval between the emission of light and reception at a

distant point in space taken as zero, it is apparent that all observers

would agree that the speed is the same so long as they were moving

at finite speeds, relative to each other, or to anything else. So, there

is no great mystery to be reconciled, and perhaps Special Relativity

would never have been necessary to explain the velocity of light

experiments.

Quite possibly, Einstein would not have proposed that matter and

energy are different forms of the same thing, and that nuclear fusion

or fission theories would not have evolved. Fusion and fission

would, of course, continue to exist, but just not a theory to explain

them

But he did create an explanation that fit the facts as he knew them,

and it has been a good and useful theory, all be it with some parts

which are difficult to grasp. The physicists have been expert at

providing chinks in the structure of physics wherever they did not

seem to fit well together on their own.

Einstein pointed out that, if the speed of light is taken as infinite, the

relativistic correction factor which appears in every one of the

equations of Special Relativity,

2

21

vF

c , EQUATION 32

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46

Becomes 1, and the equations for distance, time, and velocity and

energy reduce to the Newtonian values. This is certainly true if you

are presuming that c is the speed of light. So, one way to arrive at

values to apply to the local space-time universe is to simply take the

velocity of light as infinite in the equations of Special Relativity.

I will, in subsequent chapters, make the argument that the proper

value of c in Equation 32 is, in fact, infinity, so the relativistic

shrinking factor F is always equal to 1 regardless of the velocity of

the coordinate system, or the object being observed. Elsewhere in

the equations of Special Relativity, v is the velocity and c is the rate

of expansion of the universe, which is numerically about 300,000

Km/sec.

That means that, following the path of a light beam from a source in

the past to the future, which appears to be traveling at velocity c in

the galactic universe, rate of passage of local time is decreased to

zero. The light passes from the source to the receptor in zero time,

regardless of how far apart in space, and in galactic time, they may

be.

However, this is not the whole answer, because there are still

corrections to be made in the position, and the apparent time

experienced for moving objects, due to the fact that the universe is

expanding and we experience the change in position in the T

direction with the passage of time. Newton was entirely right in his

understanding that the key to going beyond Newtonian mechanics

lay in allowing observers moving at different velocities to experience

time differently. Or, to at least accept that their time-keeping would

appear to us to be different, as ours is to them.

We can never see anyone else’s clock in our present moment by

galactic standards. We are always looking at images of their clocks in

our galactic past, when they read differently than ours do now. We

must use of the local universe as the background for formulation of

the laws of physics for bodies moving rapidly, or bodies at a long

distance from us, because everything we see is in our present

moment in our local time. Each observer has his own universe,


47

where the local for any distant object is different for different

observers. However, the local time at his location is the same as that

of all other observers at that same instant in galactic time.

This understanding leads us to a different role in physics for the

value c, which is not the velocity of light in the local world we live in

at all. It is, instead, the velocity of our universe in the fourth spatial

dimensional direction, or in the direction of the progress of time, if

you prefer.

Because we are not stationary with respect to the four dimensional

universe, ever since the beginning of time with the Big Bang at the

center of the universe, some 13 or 14 billion light years away from

us, in this same, extra dimensional direction we still have to take the

velocity of movement of our “stationary” observers in this direction

into account.

The value of c doesn’t change in the local space-time universe, and

is the same approximately 300,000 Km/sec. measured so precisely

by the physicists over the past 100+ years. They were just attributing

their measurements to the wrong thing. So, the local relativistic

system still uses c, and it is measured to be exactly the same for

objects moving relative to our own position in space and time, but

not because space and time contract around moving objects, or

masses become heavier, or energy equivalent to matter.

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DISTANCE MEASUREMENT IN THE LOCAL

UNIVERSE

The measurement of distance is a simple concept, experienced by all

of us, and it can be done in a number of familiar ways. However,

when we talk of making measurements of distant objects, which we

cannot reach with a yard stick or tape measure, we get into a little

deeper water.

The ultimate measurement of distance, particularly long distance,

involves radiation. Distance can be measured in many ways, such as

the use of a RADAR-like detector, or visual sighting using brightness

of an object, or the apparent size of something of known size. More

simply, the measurement of distance can be assumed to be by having

laid out a system of mile markers stretching out away from the

observer’s location, so that it is apparent where in space an object is

placed by looking at the mile markers which are in front of and

behind the object.

In any case, the measurement is made, not of the position of the

object at the present moment in galactic time, but rather of the

position at some time in the past by galactic standards. The fact that

we can see it at the instant defines it as part of our local present time.

So, it is apparent that the distances assigned to objects that are

stationary with respect to our local observation point will be the

same as those assigned by the galactic measuring system. However,

if the object is moving with respect to our present position (which is

the same in terms of both local and galactic reference systems) it will

change position in the interval between when we see it in the galactic

past, and when it arrives at its position in the galactic present.

The rules appropriate to the local universe are that the distance to a

point in space or an object from our present position is only the

distance in our three dimensional universe. We cannot measure, nor

do we count, the distance in the T direction, which has to do with

where, on the galactic time scale, the point is at the time of the

measurement.


49

Here, and in the remainder of this book, the subscript “L” is used to

denote a value which is measured in, or calculated with reference to,

the local coordinate system, as depicted in Figure 8.

FIGURE 8

DISTANCE AND TIME IN THE LOCAL UNIVERSE

In the local universe, the rule is that what you see is what you get.

That is, the universe as you see it at a particular moment, is your local

universe, and you cannot see or make measurements outside of it.

All of the points along the xL Axis in our analog diagram constitute

the local universe, and, correspondingly, everything you can see in

any direction constitutes your real three dimensional world.

That is, the only spatial dimension shown in the Figure 8 is xL, which

would be the distance from the observer at the origin, rL in the three

dimensional universe, with y and z coordinates equal to zero.

This is the difference along the local xL Axis, which represents the

three dimensional distance

2 2 2 2

:L L L L Lr x y z T . EQUATION 33

However, in the diagram showing only the xL and TL dimensions,

with T unchanging with distance along the xL Axis, this reduces to

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50

L Lr x , EQUATION 34

where the distance, xL, is measured horizontally.

Distance is always taken as the horizontal distance, parallel to the x

Axis, and the vertical distance T is not considered. Were distances in

the local universe measured parallel to the xL Axis rather than the x

Axis, they would always come out longer by a factor of 2 , and this

is a matter that will be left for consideration later.

FIGURE 9

DISTANCE TO A STATIONARY OBJECT

If the object is moving with respect to the observer, it will follow a

path in the T direction that is not parallel to that of the observer, so

that at the instant in time depicted, the local observer sees the object

AL (now renamed to distinguish it from the later occurrence of the

object as A) at a distance xL, (now renamed to distinguish it from the

distance x in the galactic coordinate reference system).


51

Figure 10 shows the path of an object through space time, when

there is a component of the velocity of the object in the x direction

relative to the stationary observer.

It is apparent that the distances measured to the object at points AL

and BL are not the same as they would be in the galactic system. The

important thing here is not that there are differences from the

galactic system of measurement, but rather that the distances are

simply what they appear to be, and each measurement is not

corrected for the fact that the object is moving.

FIGURE 10

LOCAL DISTANCE FOR A MOVING OBJECT

If one considers the measurement of distance from the standpoint

of a moving observer, one has only to note that the moving observer

would see himself as static (which he is, relative to his own local

universe coordinate system). Now in his position of static observer,

he would see his local universe comprised of the things he can see at

the present moment, exactly the same as the original stationary

observer would have done at various times in his past.

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TIME IN THE LOCAL UNIVERSE

Time, in my way of thinking, is in a sense absolute, and everywhere

the same. That is to say, the time is defined at every point in the

universe by the distance the universe has moved in the T direction,

and the constant rate, T=ct. Thus, if all observers, wherever located,

possessed a precisely accurate clock, all of them would read the same

at any instant in galactic time, because we would all have moved out

from the point in space and time of the Big Bang by the same

amount.

The rate of expansion of the universe is constant, simply because

there is nothing to exert a force in the T direction to cause the matter

moving in this direction to speed up or slow down. So, time has been

progressing at pretty much the same rate for millions of years, and

we can probably count on it continuing to progress at the same rate

in the foreseeable future.

Unfortunately, we can never see anyone else’s clock at the present

instant of galactic time, but instead, can only see their clocks as they

were at some time in the galactic past.

In the local coordinate system, the time is taken as being the same

along the xL Axis, just as in the galactic system, but the position of

the x Axis is not perpendicular to the T Axis. In the local system, it

is bent downward on the galactic x – T diagram at a 45 degree angle.

The angle is set by the rate of movement of the universe in the T

direction at the velocity c. Now, because everything we can see at a

given instant is located along this x Axis, and comprises our real,

local universe, it is necessary that light traveling along the x Axis

from a distant source, or from a nearby source, depart from the

source and arrive at the receptor (our eyeball) at the same instant in

local time. In other words, the speed of light has to be infinite in

reference to this coordinate system.


53

FIGURE 11

AN OBJECT MOVING TOWARD THE OBSERVER

While Figure 11 is drawn for a generalized object presumed to have

a defined velocity relative to the stationary observer at the origin, it

should be apparent that the T Axis and the hypothetical observer at

the origin could be chosen such that at the time of the original

observation, the observer and the object are at the same point in

space. This variation is shown in Figure 12.

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54

FIGURE 12

A MOVING OBJECT PASSING THROUGH THE ORIGIN

This simplifies the picture somewhat, with regard to the relationship

between the local and galactic time systems, but does not limit the

generality of the results.

Local time at the origin is always the same as the galactic time. Thus

our clock would read the same as that of an observer working in the

galactic system, should it be possible for a hypothetical observer to

work in that system.

The local observer, who sees time as constant along the 45 degree

cone with its apex at the origin, would place the objects he sees

L LT T x , EQUATION 35

or

LL

xt t

c .. EQUATION 36


55

When the galactic time is taken to be zero, the local time is the same

at the origin, but at other points along the x Axis it becomes

LL

xt t

c , EQUATION 37

which defines the right hand half of the local x Axis. The half to the

left of the T Axis is also defined by this same equation, for negative

values.

FIGURE 13

RELATIVE VELOCITY OF TWO OBJECTS

The time the local observer reads on his local clock when making

the observation is simply what he reads, without correction for the

motion or lack of motion of the object. Again, what you see is what

you get, without the necessity for correction. When the object is at

point A, the time on the observer’s local clock can be set to zero,

and when he observes it one second later, it is at point BL, and one

second has passed by his clock. As with distance measurements,

what you see is what you get.

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56

Two further situations should be of interest relative to the time the

local observer experiences. First, how does he perceive the time of

observation of two or more moving objects, and secondly, how

different is the time perceived by a second observer, moving relative

to the first.

The simple answer in the case of two moving objects is that he sees

each of them in his own local time, and he records their distance

from him as the observed distance without correction. He perceives,

or would if he had sufficient good vision, that each galactic clock, if

carried by each of the objects, would read an earlier time than his

own, and would be aware that the difference in the times would be

earlier than his own local time by exactly the x/c value for each of

them. There are no correction factors other than that associated with

their distance from him.

In the second case, that of a second observer who is moving with

respect to the “stationary” observer, and whose path, at some point

crosses that of the stationary observer, we would be interested in

how the stationary observer’s clock looked to him. Both the

stationary observer and the moving observer will, of necessity, see

their relative velocities as the same value, vR, because either might

have been presumed stationary, and the other the moving coordinate

system.


57

FIGURE 14

LOCAL TIME FOR A MOVING OBSERVER

In the case where the moving object is actually a second observer,

time is measured exactly the same way for the moving observer as it

is for ourselves. That is, he would perceive his own coordinate

system as moving in his own local T direction, and his galactic x Axis

perpendicular to it through his origin. He would define his local

universe, as he sees it, lying along his x Axis, according to

MM

xt

c , EQUATION 38

where I have used the subscript M to denote the measurements

made with respect to the moving system, where things existing at

clearly defined points in galactic space time, are viewed differently

than by the fixed observer.

Where the stationary observer sees himself as moving in the T

direction at the velocity c, with no motion in the x direction, the

moving observer sees him as moving in his T direction at velocity c,

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but with the added component of velocity in the x direction. That is,

he sees the distance ctL for the local observer as being

2 2 2 2

M L Lct c t v t , EQUATION 39

or,

2

21L

m

t v

t c . EQUATION 40

Thus the stationary observer would observe that time is passing

more slowly at the moving observer’s position, and the converse

would also be true. The moving observer would see things as though

he were stationary, and the stationary observer’s clock would be

running more slowly than his.

Both of these observations are, of course, mistaken, as all galactic

clocks, everywhere, are running at exactly the same time, and the

galactic time at any location in space time reads exactly the same as

the galactic time at that place.

The local observer knows this, and does not try to infer things about

the galactic time observed by the intergalactic space ship crew which

is influenced by the speed at which he is traveling.

Only when the moving observer and the stationary observer finally

cross paths and are at the same point in space and galactic time will

it appear that local time is exactly the same for both of them. Both

would continue to collect data which would seem to indicate that the

other’s time was passing more slowly than his.

We have no need to use this kind of calculation, in that we can

determine the time clock reading for any object in space simply

based on its linear distance from ourselves, and the illusion of the

time discrepancy is of no consequence.


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VELOCITY IN THE LOCAL UNIVERSE

The measurement of velocity in the local universe is a much simpler

matter than is the case when the velocities are presumed to be

representative of the galactic universe. In the local universe, we can

actually see objects and events, and identify the local time of the

observation. In the galactic coordinate system, we cannot see them,

and must calculate, from our observations of past positions, where

they would be “now” if we could actually see them. Of course, for

objects which are nearby, in terms of light seconds, or moving

relatively slowly, for example less than 100,000 miles per hour, there

isn’t much difference between the two systems of representing the

physical universe.

In the local universe, one simply measures the distance of an object

(using the brightness of a star, or the sight of an automobile passing

over a mile marker on the highway), notes the time reading on his

clock, and then repeats the measurement at some later time, again

noting the reading on his clock. As pointed out in the preceding

section, both the distance observed at any time, and the time itself,

are simply the values observed, and no corrections of any sort are

applied.

STATIONARY OBJECTS

His measurement of the distance to a stationary object will be exactly

the same as that attributed to the object in the galactic frame of

reference, because the distance does not change with time, even

though the two observers are unable to see the object at the same

time. Time doesn’t matter in this case.

In Figure 15, a reference system is sketched in which the local and

galactic coordinate systems have the same origin and there is no

motion of one coordinate system relative to the other.

On this coordinate grid, the path of an object is shown which is not

moving in three dimensional space relative to the local observer.

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60

That is, the direction to the object – the x direction – is not changing

with time, and the distance along the x Axis to the object is not

changing with time.

FIGURE 15

LOCAL REFERENCE TO A STATIONARY OBJECT

In order to determine that an object is, in fact, stationary with respect

to the position of the stationary observer, it is necessary for him to

make a series of measurements of distance and the times elapsed

between them. If he does this and finds that the distance has not

changed in any of the readings, it is reasonable to say that the velocity

is constant at zero.

Objects which are stationary with respect to a local observer would

also appear to be stationary when they are referenced to the galactic

system. The distances to the object measured horizontally from the

T Axis to the object would appear to be constant at x in the local

system, as the universe moves from AL to BL, and ∆x=0. This

distance and ΔT, and the distance in the T direction, would also be

constant as the galactic universe moved from A to B which is the

same time interval, ΔT .


61

The local observer would determine the velocity of the object to be

Δx/Δt = 0, and would also calculate the velocity for the galactic

system to be zero. The observers would not agree on the value of

time at the object, but they would agree that the same amount of

time elapsed between their respective readings, and that the distance

was unchanged.

MOVING OBJECTS

The picture becomes more complex if the object under observation

is moving with respect to the local coordinate system, or according

to the galactic coordinate system (for which the origin, linear scale

and direction of motion are all identical to that of the local observer).

However, if the object is moving with respect to the local observer,

he will see the object as being in his present time, but in the galactic

past. The galactic coordinate system presumes the observer to be in

the galactic present. That is, in the future with respect to the local

observer. So, it is necessary to calculate the position of the object (or

event) as it will probably be when we reach that future time.

OBJECTS MOVING TOWARD THE OBSERVER

In Figure 16, the stationary observer, with the same origin location

as the galactic origin, sees a moving object represented by the shaded

arrow. The moving object is approaching the origin as time passes

(T=ct increases), and will reach the origin at some future time.

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FIGURE 16

A MOVING OBJECT OBSERVED BY A STATIONARY OBSERVER

For convenience, the time interval shown in Figure 16 between the

two measurements is one second, so the ∆T dimension is

numerically equal to c, the rate of expansion of the universe, or the

apparent speed of light.

As the object moves from point A to point B referenced to the

galactic coordinate system, the distance traversed is the horizontal

difference between the x values at the points A and B. Because the

time interval chosen for the measurements is one second, the ∆T

dimension is c. Thus, the velocity of the object as measured in

galactic coordinates is

GG

G

xv

t

, EQUATION 41

where, for ∆t=1 second,

G Gv x , EQUATION 42


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which is the velocity in the galactic reference system by definition.

Hereafter, the subscript G will be omitted for the values referenced

to the galactic system.

The local observer sees the time differently, as he defines constant

time along the 45 degree lines as being the same as his local time at

the origin, whereas the galactic system defines time as being constant

along the horizontal x Axis. The coordinates for the two systems

were chosen in this figure so that the time interval depicted is the

same. That is there is one second of elapsed time between points A

and B along the path of the moving object, and also between points

AL and BL, which reference the positions of the object as seen by the

local observer.

Because the galactic origin and the local origin coincide, and move

together in the T direction, there is no disagreement about either the

time or the location in space between the two systems at the origin.

However, the local observer sees the object at an earlier time and at

a closer distance than the galactic observer.

It should not make any difference where the reference origin is

located for any given set of measurements. It is easier to establish

the locations in space time of the object as it moves along its path if

the origin is chosen so that the object passes through the origin at

the end of the one second observation period. This slightly modified

situation is shown in Figure 17.

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64

FIGURE 17

THE MOVING OBJECT SHIFTED TO ARRIVE AT THE ORIGIN

There is one exception, which is that the location of the coordinate

origin is immaterial, so long as the object is either moving at constant

speed toward the origin throughout the measurement period, or

moving away from the origin throughout the period. This distinction

requires a lengthy explanation, and will be dealt with later.

It should be clear that the local observer sees the object at the

beginning of the time period, not at Point A, where it is with

reference to the galactic system, but at an earlier time, and a greater

distance from the origin, at point AL. However, at the end of the

time period, the location of the object coincides with both the

galactic and local origins.

Here it is more apparent that the path lengths seen by the local

observer and the galactic observer differ by the addition of the

amount of the distance moved by the moving object from the time

the object is seen by the local observer at Point A’ and the time the

object reaches point A in the galactic system of measurement. The

distance traversed is A’–A, which is Δx. However, during this same


65

time period, the local observer sees the distance traveled by the

object as ΔxL, which is a considerably greater distance,

L L

vx x x

c . EQUATION 43

This can be rewritten as

. 1L

x v

x c

,

EQUATION 44

and because the time periods are the same for both systems,

L L

v x

v x

, EQUATION 45

so

1L

v v

v c . EQUATION 46

From this, the expression for the galactic velocity corresponding to

any value of the local velocity can be determined algebraically to be

1,

1 LL

v

vv

c

EQUATION 47

where:

Lt time interval in the local universe

(always a positive value)

t time interval in the galactic universe.

(always a shorter positive value).

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There is some caution which must be exercised here, in that the

velocity is determined by measuring a distance moved, and dividing

it by the time between the measured starting and ending positions.

The distances moved are actually distances away from the origin, and

may be considered as the scalar distance in the three dimensional

universe.

It should be apparent that either the time elapsed may be taken as

the same in the local and galactic systems, and the distances traveled

by the moving object will be different, or the distance traveled may

be taken as the same in the two systems, and the time required for

the travel to take place will be different.

It is a bit simpler if the latter case is used for comparison of the

velocity measurements, and the object is presumed to have traveled

a fixed distance, Δx in the galactic system, and the same identical

distance, ΔxL in the local system.

OBJECTS MOVING AWAY

The foregoing derivation was based on observations of an object

moving toward the observer. One would expect that the same

derivation would yield similar results for an object moving away

from the observer. The choice of the observer’s location is arbitrary,

and might just as easily have been chosen “on the other side” of the

moving object, so it would now be moving toward, rather than away

from the observer. However, this situation is not so straight forward,

and leads to some incorrect conclusions.

This situation is depicted in Figure 18 for an object moving away

from the fixed observer. In this case, the distance traveled in

reference to the two systems is taken as the same, so the time

intervals involved are different. However, this choice is of no

consequence, as the results would be exactly the same if the time

intervals had been taken as equal for the two systems, and the

distance traveled accepted as different.

The galactic observer sees the velocity as represented by the change

in distance in the time period between the two positions of the


67

horizontal x Axis, which moves in the T direction a distance of cΔt

as the object moves through the distance Δx in time period Δt.

The distance moved by the object may be taken as the same for both

measuring systems,

L L Lc t v t c t , EQUATION 48

FIGURE 18

VELOCITY OF OBJECT MOVING AWAY FROM OBSERVER

in which the time interval measured in the two systems is different,

as shown in Figure 18.

This indicates that the ratio of velocities in the galactic and local

reference systems is inversely proportional to the time required for

a given distance of movement of the object, and

1Lt v

t c , EQUATION 49

or

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1

1 Ll

v

vv

c

. EQUATION 50

This is quite anomalous, as the velocity immediately before the

object passed the observer would have been calculated as

1

1 Ll

v

vv

c

. EQUATION 51

These ratios can only be the same if the local velocity is zero.

Obviously, the velocity of an object does not change abruptly as it

passes the observer, and the two calculated ratios cannot be equal to

each other unless both are zero. There is something wrong with this

analysis.

This is an important point, because Equation 51 is always right, and

Equation 52 is not, but this is a subtle point, and a very important

one. It is important enough to devote a whole chapter to the

explanation.


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RELATIVE VELOCITIES

There is, finally, the question of how the velocities of two moving

objects appear to relate to each other in the local universe described.

Figure 19 illustrates this situation.

In Figure 19, a second moving object has been introduced.

FIGURE 19

TWO MOVING OBJECTS REFERENCED TO THE LOCAL

UNIVERSE

It should be apparent by inspection that the velocities perceived for

these two objects, vLO1 and vLO2, both follow the previously derived

relationship.

That is,

1

11

1

1 LL

v

vv

c

, EQUATION 52

Les Hardison

70

and

2

22

1

1 LL

v

vv

c

. EQUATION 53

So,

2 1 1 22 1 2 1 ,L L L L

L L

v v v vv v v v

c c EQUATION 54

from which it appears that the differential velocity observed by the

local observer is

2 1 2 1L Lv v v v , EQUATION 55

which is identical to the calculated differential in the galactic system.

The suggestion here is that, in the local system, the velocities are

simply the velocities measured, with no need for correction factors.

When the measured velocities are recalculated with reference to the

galactic coordinate system, they are more complex, but differences

in velocities should be identical to those measured with reference to

the local system.


71

WHY LIGHT APPEARS TO MOVE AT 300,000 KM/SEC

Now, it is apparent that the velocity of light reported by the local

observer would be infinite, whereas in the galactic geometry, it would

appear to be c, the apparent speed of light.

It is of critical importance to recognize that any velocity observed to

be very large (approaching infinite velocity, or instantaneous

transport through space) would appear to be equal to c, the apparent

speed of light, if it were to be assumed to have been measured in the

galactic universe.

It is true that all velocities based on observations in the local universe

(which is the only place where observations can be made) will always

be lower when recast into the galactic universe, for objects moving

either toward or away from the observer. This is because, as was

demonstrated, the velocity, v, in the galactic universe corresponding

to vL measured in the galactic universe is

1

1 LL

v

vv

c

. EQUATION 56

The question is, what is the velocity of light in the galactic universe

which corresponds to the observed infinite velocity of light in the

local universe? This can most easily be seen by rewriting Equation

56 as

1

1L L

v

cv v

c c

, Equation 57

or

Les Hardison

72

1

L

L

v

v cvc

c

. EQUATION 58

It is easy to see that as vL/c becomes very large, the significance of

the 1 in the denominator decreases, so the limiting value of v/c

approaches 1 as vL/c approaches infinity. In short, an infinite

velocity in the local reference system corresponds to the velocity c

in the galactic reference system.

This accounts for the presumption that light moves through three

dimensional space at the apparent speed of light c, and also explains why

nothing---no solid object in motion, or any phenomenon like the

force of gravity---ever appears to move faster than c, so long as one

is relating all observations to the galactic reference system.

This is one of the reasons why I am so sure the OPRA scientists

working with the CERN Large Hadron Collider, who presumably

measured the velocity of neutrinos passing through the earth as

slightly greater than c, were in error. I will deal with this in a separate

chapter, and suggest a reason for the error.

But, you may say, the scientists have measured the velocity of light

many times, and are in good agreement that the velocity is very close

to 300,000 Km/second. What were they measuring if it was not the

speed of light in a vacuum?

I have proposed that they were measuring the speed of the universe

in the fourth dimensional direction, and that their experiment looked

like this.


73

FIGURE 20

THE MEASUREMENT OF THE SPEED OF LIGHT

Here, the scientists presumed that they were working entirely in the

galactic reference system, and had no concept of the motion of the

universe in a fourth dimension. So, instead of imagining themselves

moving from Point A0 to Point A1 to Point A2 as the universe

expanded in the T direction, they presumed that they were

“stationary” and that time was simply passing.

To measure the speed of light, they sent a series of short beams of

light out toward point B1, where there was a mirror at a known

distance, and recorded the time it took the light to return to the

starting point after being reflected from the mirror. These events ---

the emission of the light, reception at the mirror and reflection back

toward the source, and receipt of the light pulse at very nearly the

same place it originated --- were all presumed to take place in the

galactic plane, and that, as time passed, the light moved through the

intervening space like a fish swims through water, only much faster.

However, had they taken into account that the universe was

expanding, they would have recognized that their view of the

situation was limited, because they could not actually see the light

moving through the empty space toward the mirror, and their only

actual measurements were of the distance to and from the mirror

Les Hardison

74

and the amount of time which passed between the emission of the

light and its reception at the point of origin.

Instead, they presumed that the light was making its way relatively

slowly to the mirror during the first half of the elapsed time period,

and making its way back during the second half. Its velocity was, of

course, calculated as

2

2

c tv c

t

. EQUATION 59

I believe that the correct way of viewing the experiment involves

recognizing that the location of the experimenter and the mirror are

both “stationary” in reference to the three dimensional everyday

universe, but are moving at the velocity c in a fourth dimensional T

direction. The experimenter is able to see things which are in his line

of sight, which extends outward in the three spatial dimensions, but

also extends backward in galactic time, and that the things he can see

at any instant comprise his local universe at that instant.

Thus, things he sees simultaneously exist at the same local time, so

far as the local observer is concerned.

So, the local observer is able to see the mirror at any time, but he is

always looking at a position of the mirror that is in his past. He

cannot look forward into the future, and see the mirror as it will be

at some future time. He has to wait for the time to elapse for it to

come into his view.

So, he sees the experiment as shown in Figure 21.

Here, the observer at A1 cannot see the mirror at Point B1, because

it still lies in his future. He could, were he at the location of the

mirror, at Point B1, see the light source at A0, and he would presume

he was seeing it at the exact same local time as he experienced. He

should not be able to see the mirror at Point B1 until he had, in fact,

reached point A2, where he would presume the time at B1 and A2 to

be at the same identical local time.


75

FIGURE 21

THE SPEED OF LIGHT EXPERIMENT FROM THE STANDPOINT

OF THE LOCAL OBSERVER.

Thus he would perceive that the light had crossed the gap between

A1 and B1 in no time at all, and that he would see no additional time

difference between point A2 and B1. So, it appears to the local

observer that it moved through the distance from A0 to B1 in no time

at all. In other words, the speed was infinite. It is relatively obvious

that this is how local time is defined.

So, the question is, what did the local observer actually measure?

Clearly there was an elapsed time difference for according to his

clock, the light left the source at t = t0, and was next observed at t =

t2. The distance moved by the source and the receptor during this

time was 2VΔt, where V is the rate of expansion of the universe. So,

it is apparent that the local observer measured the velocity V of the

expansion of the universe in the T direction. His measurement is

simply that

2 2V t c t EQUATION 60

or

V = C. EQUATION 61

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76

That is, the velocity of the universe moving in the fourth

dimensional direction is c, the apparent speed of light.

A minor question arises from this presentation of the experiment in

terms of measurements by a local observer. Does the mirror need to

be stationary?

Were the mirror in motion with respect to the source of the light and

the receptor (which are in fixed positions relative to each other), as

shown in Figure 22, the result would be exactly the same, provided

the position of the mirror at the point half way between the time the

light was emitted and when it was received was known accurately.

FIGURE 22

LIGHT SPEED ECPERIMENT WITH A MOVING MIRROR

The motion of the mirror only has to do with determining its

position in space at the time the light signal is received.

The same must be true for the situation where the receptor is moving

with respect to the location of the light source and the mirror. If the

T Axis were rotated a few degrees clockwise, such that the path of

the mirror through time were vertical, the same geometry would

exist with respect to the relative positions of the source, the mirror

at the time of reflection and the receptor. So, one can conclude that


77

it is not important that the elements involved in the experiment

should all be stationary with respect to one another.

Les Hardison

78

MASS IN THE LOCAL UNIVERSE

In the local universe reference system, there is no need to account

for the invariance of the speed of light. It is infinite, and would

simply be measured as infinite by any observer who confined his

measurement to the system in which he made them; that is, the local

universe reference system.

Because this is true, there is no concern that the velocity of an object

subjected to a uniform force for a very long period of time would

exceed the speed of light. Nothing can exceed the speed of light

because it is infinite.

The fact of the matter is that there is nothing in the universe with

any substantial mass that is presently moving faster than c, because

c is the velocity imparted to all matter at the time of the Big Bang,

and it is that velocity which defines the rate of expansion of the

universe.

When the universe got its start with the big bang, all mass got an

equal share of energy, all of it being accelerated to the same velocity

c, the apparent speed of light which I think is what it has had more or

less ever since. Nothing can go faster simply because there isn’t

anything already going faster to give it a push.

So, there is no basis for supposing that mass actually changes with

changes in velocity. Our ordinary concept of kinetic energy as

2

2

vE m , EQUATION 62

is completely compatible with an invariant mass.

This whole line of reasoning makes me rest easier at night, knowing

that my mass (weight while I am near the earth) is not subject to

someone’s arbitrary choice of a reference system. I am, already,


79

moving at the apparent speed of light in a direction that I have no way

of detecting, and while the precise direction may be altered by, say,

a collision with a moving automobile, the total velocity will not be

changed.

The exact direction of my path through space time determines how

much of my velocity, c, the speed of expansion of the universe, can

be detected by other earthbound observers. This has nothing

whatever to do with the amount of material composing my body.

All my belongings are, likewise, immune to arbitrary weight

adjustment by observers choosing arbitrary reference coordinates.

There is no reason, when measurements are made in the local

reference system of the observer, and interpreted correctly as

applying to the local system, to determine that mass and energy are

different forms of the same thing, or that one is convertible into the

other.

I can’t prove that they are not, but there doesn’t seem to be any

reason why they should be. Fortunately, the mistaken impression

(from my point of view) that mass is convertible to energy has

produced a great deal of technological advancement. Which proves

to me that you don’t necessarily have to be right to succeed, you just

have to have a consistent set of rules that work well.

Les Hardison

80

ENERGY IN THE LOCAL UNIVERSE

Just as mass is, in terms of all the measurements one can make in the

local universe (and there is no place else to make measurements),

constant, regardless of the velocity of the mass or of the observer

making the measurements, energy is likewise very simple and nearly

as unconvertible.

The energy of a body moving in the direction of the expanding

universe is simply

2E mc . EQUATION 63

I have conjectured that the kinetic energy due to the velocity in the

T direction of expansion of the Universe in the fourth dimensional

direction is only half that,

2

,2

cE m EQUATION 64

with the other half attributable to the spin of the electrons and

protons making up the majority of all matter. I have no sound basis

for this.

It could be that the distances in the local universe ought to be

measured from the T Axis along lines parallel with the local x Axis,

in which case, all measurements of distance in the local universe

would be larger by 2 than those in the galactic universe. Were

this the case, the velocity of light in the galactic universe would be

2 c, and, in the galactic universe, E=mc2 .

However, for the time being, I will stick by my guns, and maintain

that all matter has the velocity c rather than 2 c in the T direction,

and the velocity we are able to recognize for objects moving relative

to our own stationary position is simply the component of the


81

velocity vector c which is out of parallel alignment with our own

vector in the T direction.

An observer at the apex of his own cone, representing his local

universe, perceives himself to have no motion. Indeed, he has no

motion relative to his own private coordinate system in the three

dimensions he can perceive.

When he sees a body in motion, he can determine the velocity

component in the three dimensions he can perceive by direct

measurement. He is led to believe that the moving object is moving

in the T direction at the velocity of expansion of the universe, and

he natural assumes that that velocity is the same for everyone.

It is, of course, slightly different for everyone, but so far as he can

tell, the energy of the moving system is that due to his own velocity

in the T direction, c, plus the velocity component he can measure,

vL. Hence the appearance that the energy of the mass is

2 2

2 2

Lmc vE m . EQUATION 65

The second term, the one he measures, is really part of the first term,

which he does not measure, for massive bodies.

Einstein took this same energy to be

2

2

2

,

1

mcE

v

c

EQUATION 66

Which he expanded by the series

2 42

2

3...,

2 8

mv vE mc m

c

EQUATION 67

Les Hardison

82

and goes on to say this is approximately

22 ,

2

mvE mc EQUATION 68

when v/c is relatively small.

However, it is, of course, only the case where v/c is appreciable that

calls for the application of relativistic mass. So, Einstein concludes

that the Newtonian concept, plus his idea of relativistic mass, holds

for ordinary, everyday velocities, but is not a good approximation to

the energy of bodies moving at speeds which are appreciable to c.

In the local system of measurements, where

2 2

2 2

Lmc mvE , EQUATION 69

exactly, Newtonian mechanics seems to hold just fine, if you

recognize that only a part of E is visible in the ordinary three

dimensional world we live in, and where we make our observations.

Were one to translate the Energy equation, which I believe to be

exactly as shown in Equation 69, to the galactic system and do so

correctly, it would be by substituting the value of velocity v in the

galactic system for the corresponding measured value, vL in the local

system.

Thus the correct expression for the total energy of matter in the

galactic system is

2 22 2

22

2 1

Lmv mvE mc mc

v

c

. EQUATION 70


83

The expression for Energy referenced to the galactic system given in

Equation 70 is not the same as that derived by Einstein, as illustrated

in the following figures.

.

FIGURE 23

COMPARISON OF EINSTIENIAN ENERGY BASED ON LOCAL

VELOCITY

It is apparent that the energy levels calculated by either approach is

very close to mc2 at values of galactic velocity less than about 70%

of the value of c. and that both result in the energy becoming

infinitely great as the value of v/c approaches 1.0. However, the

energies calculated on the basis of the observed local velocity are

much greater than those based on Special Relativity the range of

velocities between 0.6c and 1.0 c.

Furthermore, E is the kinetic energy associated with all matter, and

there seems to me to be no other form of energy at all. This may

sound like too broad a statement, but I believe it to be true.

Radiant energy I believe to be associated with the velocity of

electrons orbiting atomic nuclei, and not waves moving through

space. Thermal energy is associated with the mostly random

velocities of atoms and molecules making up a matter.

0

100

200

300

400

500

0.0

00

.10

0.2

00

.30

0.4

00

.50

0.6

00

.70

0.8

00

.90

1.0

0Re

lati

ve E

ne

rby,

E

Velocity v/c

Energy as a function of Galactic Velocity

EinsteinEnergy

Les Hardison

84

Potential energy, relating to the distance masses are from one

another, seems to be a device used to account for the increasing

velocity or objects as they “fall” toward one another, instead of

recognition that the direction the object is moving in the four

dimensional space must, at all points along the path of the object be

perpendicular to the three normal spatial dimensions. The curvature

of space is simply the variation of the slope of the T Axis to our

concept of the right angle direction at our location. It seems likely

that the curvature of space is, in reality, a reflection of the changes

in the direction of time in the presence of gravitational masses, or

electrical charges.

Finally, I do not believe energy can be converted into matter, or

matter into energy. I think the processes which appear to be doing

this have alternative mechanisms involved. I will also get into this

later.


85

SUMMARY

In this chapter, I have developed a series of equations corresponding

to the equations of Special Relativity, as presented by Einstein in

1905. His equations have stood up pretty well, although I think they

have also raised a great many questions which physicists have had

only partial success in answering.

All of the derivations have been based, like those of Albert Einstein,

on the presumption that motion involves something moving toward

or away from the observer at the origin of the arbitrary coordinate

system. He took, for his derivation, the motion of a beam of light

leaving the origin of his coordinate system and being observed as it

moved away from the observer.

It should be apparent that one cannot, under any circumstances,

observe a beam of light moving away from himself. One only sees

things by directly emitted or reflected light when the light moves

from the emitting or reflecting object toward the observer, and is

finally registered when it actually coincides with his location in four

dimensional space.

However, if one defines his present local universe as all he can see

at the moment, the light reaches him as though it were moving at

infinite speed. In this universe he would determine that the universe

is moving through the fourth dimensional direction at the apparent

speed of light, c. If he prefers to use the model of the universe which I

have called the galactic system, he must calculate the values to use in

that universe from those he observed in his local universe.

I am suggesting that the equations of Special Relativity were derived

by Einstein to do just that, but that he did not take into account the

possibility of radiant energy transfer taking place instantly, as it

appears to do in the local universe, and therefore derived his

equations based on an incorrect set of premises.

In the local universe, there is no need to explain the invariance of

the apparent speed of light. It appears to move at infinite velocity in the

local universe, and is, of course, the same for any two observers,

Les Hardison

86

regardless of the relative velocity of the two sets of measuring

apparatus with respect to each other or to anything else.

Velocity (at least constant velocity) is likewise simply measured in

the local system. It is the decrease in distance to our observation

point divided by the change in clock time at our location. For objects

moving away from the observer, it must be calculated, rather than

observed directly, because the observer cannot see the path of the

object into his future. He can see the past positions, and thereby

calculate where it should be at his galactic time, but he cannot see it

at this time.

In order to get a correct assessment of the velocity of an object, he

must use the calculated distance to the object in his immediate

future, rather than rely on the historical measurements made in his

past.

Again, it is not necessary to correct the velocity in order to prevent

things from moving faster than c, nor to presume that space and

time are shrinking as the result of objects moving through space and

time relative to our own position.

We have to recognize that others moving relative to our own

position will measure velocities differently than we do, but not

because the velocities are actually different. It is only because they

will see the time at which the objects reach specific points in space

as different from those of any observer moving relative to their own

position.

Velocities measured for two moving objects can be added and

subtracted in the local system, based on observations in the local

system, without any necessity for limiting velocity to c, or any other

value, and without applying the relativistic shrinking factors derived

by Einstein.

The relative velocities of two systems will appear to be exactly the

same in magnitude from each of the two systems, although the


87

direction may appear to be to the left for one observer and to the

right for the other.

The laws of Newtonian physics hold for physical interactions

described with reference to the local coordinate system without

correction. The mass of objects is unaltered by velocity relative to

the observer, and the momentum of an object and its energy, both

quantities which can be described only in terms of their velocity

relative to the observer, are calculated simply from the observed

velocities, and there are no relativistic correction factors.

The proper use of the galactic system of coordinates, which may

appear to represent the “real” physical world better, requires

modification of the observed local data, but the modifications are

not those derived by Einstein. The picture of the galactic universe

using these correction factors does not require the relativistic

shrinking factors for measurements of distance, time, mass and

momentum.

Using local measurements properly to calculate galactic velocities

and positions, no matter how fast a body is moving in the local

system of measurement, it cannot appear to be moving faster than

c, the apparent speed of light, when translated to the galactic reference

system.

This is why it is impossible, in terms of the geometry of the space

time system used by modern physicists, for anything to “exceed the

speed of light”. Light or anything else moving at infinite speed in

the local reference system would appear to be moving at the apparent

speed of light in the galactic system.

Les Hardison

88


89

CHAPTER 5 VELOCITIES OF OBJCETS

MOVING AWAY

In the previous chapter, an anomalous result seemed to indicate that

the observed velocity of an object viewed by a local observer would

be translated to the galactic frame of reference by

1

1 LL

v

vv

c

, EQUATION 71

when the object under observation was moving toward the observer,

and

1

1 LL

v

vv

c

, EQUATION 72

when the object was moving away from the observer. In other

words, the velocity of an object which was by definition constant in

galactic terms, would have to decrease significantly in the eyes of a

local observer as it passes him by, and he would have to revise his

estimate by changing the sign of the velocity in equation 71.

This anomalous condition was due entirely to a misconception about

the way local observers translate visual information about the world

to the theoretical construct I have called the galactic universe. If one

agrees that an observer can only see an object if light moves from

the object to his eye, and that light always moves from the past to

the present or the future, and never the other way around, then it is

apparent that the local observer can only see objects in the galactic

past.

Les Hardison

90

But, the observe is moving through a static universe in the T

direction, and seeing things at any moment of his local time as the

way things are right now. He is unaware of his motion in the T

direction. Rather, from his point of view the universe is moving

downward in the negative T direction. In effect, he sees the future

coming toward him, and the world passing him by. If we picture the

universe this way, our coordinate system is static, and all of the

objects in the universe have paths within this moving, four

dimensional space time, which we can see whenever and wherever

the path of the object crosses one of our lines of sight. The path is

coming toward us from the future, whether the object is moving

toward us or away from us

Picture a marble thrown into the air, not as a sphere which moves

through space under the influence of gravity, but rather as a four

dimensional tube-like object, the three dimensional cross section of

which is a sphere. The curving path actually consists of the

continuous four-dimensional marble, looping through three

dimensional space, but having continuity and persistence, if you will,

for as long as it remains a marble. So, think of the trajectory of an

object moving through space not as the history of where it has been,

but rather as the continuous existence of the object fixed in four

dimensional space, the cross section of which we see when our

three-dimensional universe intersects the four dimensional object in

the local present.

If the object gives of light, or other electromagnetic radiation, we

can see or sense its presence in our local present at any particular

moment. Thus it will appear that over any relatively short period of

time, the path of a moving object shifts downward relative to our

apparently fixed position.

Figure 24 illustrates this slight shift in viewpoint, where the observer

sees an object to his right moving toward his position. Initially, at

point 1, he sees it to his right along the xL Axis at some time in the

galactic past. After a short time has passed, the path has moved

downward, but to him it appears that it has moved to his left and

now coincides with his position. He calculates the velocity of the


91

object as the ratio of the distance moved in the x direction divided

by the time elapsed as measured by his clock.

FIGURE 24

THE STATIONARY OBSERVER IN A MOVING UNIVERSE

In essence, he uses the shaded triangle in Figure 24 to determine the

position of the starting point of the object at the initial time in the

galactic coordinate system. The end point, in both systems, is at the

origin, where the observer is located.

This would work exactly the same if the object were approaching his

position from the left, where the diagram would be essentially a

mirror image of Figure 24.

However, when the object reaches the observer and passes by him,

it becomes an object moving away, and Equation 71 doesn’t seem to

work quite right any more. We would calculate the galactic velocity

higher than the local velocity using Equation 71. If, instead, we say

that he must calculate the local velocity, and then reverse the sign we

Les Hardison

92

can get a galactic velocity consistent with the approaching galactic

velocity. Although this point of view is a little reasonable, it still

leaves the problem of the object moving away appearing to move

more slowly than it did when approaching, and we know this is

contrary to our actual experience.

FIGURE 25

OBJECT MOVING AWAY FROM THE FIXED LOCAL OBSERVER

These anomalies lead me to believe that we should look at the picture

I have been presenting of the relationship between the two

coordinate systems and the construction of the four-dimensional

universe a little differently. In particular, we, the local observers, do

not see ourselves sitting on the point of a cone, where peculiar things

appear to happen to the velocity of objects which approach and then

pass us by. Rather, our world looks like we are in the center of a

sphere, and can see things pretty much as they are in any direction.

This leads me to believe that the representation of our local universe

ought to be the one with a straight, horizontal x Axis in the one-

dimensional diagram we have been using, as shown in Figure 26.


93

FIGURE 26

ANALOG UNIVERSE WITH THE LOCAL AXIS HORIZONTAL

The straight line xL Axis is the one dimensional representation of out

three dimensional universe. In two dimensions it would be a segment

of an enormous circle, or on the surface of a sphere representing the

three-dimensional universe. With all three dimensions present, it

would be a sphere, with ourselves at the center, and space stretching

out in all directions, and the fourth, spatial dimension capable of

depiction only as a series of spheres which change as time passes.

In this picture, the coordinate system is oriented properly to the

spatial dimension, the xL Axis, and the time-like T dimension, so

objects we perceive as moving at a uniform speed and direction of

motion change position in a uniform way.

In this diagram, the present local time, represented by the horizontal

xL Axis, divides all of space-time into the past, below the line, and

the future, above the line. The present is, of course, moving in the T

direction at the velocity c, but we are unaware of this motion.

Everything we see is moving in this direction at the same speed.

Les Hardison

94

Figure 27 illustrates how the reorientation of the x and xL Axes

removes the problems connected with the observation of objects

going away from the observer.

FIGURE 27

OBJECT MOVING AWAY ALONG A HORIZONTAL XL AXIS

In this picture, a uniform velocity from left to right in our local

universe results in a similar path from left to right in the galactic

universe. The mythical galactic observer will see the velocity of the

moving object as lower than does the local observer by the factor

given in Equation 71, and this velocity will not change as the object

passes him. Nor will there be any confusion as to whether the object

is moving into the past or the future relative to the local observer.

He will see the object continually in his local present, as it

approaches, passes, and then recedes from him, just as we might see

the baseball fly past us and recede into the distance.

Were the object moving from right to left, the picture in Figure 27

would be exactly the mirror image. The velocity relationships would

be precisely the same.


95

In this picture, light is transmitted in the horizontal xL Axis, where it

appears to move instantaneously, or at infinite speed in either

direction, but only coming toward the observer. In the

corresponding galactic universe, it appears to move more slowly,

along the 45 degree lines and appears to have the velocity c. This

follows from Equation 71, where the limit of v is c as vL approaches

infinity.

We have previously envisioned the horizontal x Axis as the dividing

line between the past, below the line, and the future, above the line,

as shown in Figure 28.

FIGURE 28

PREVIOUS REPRESENTATION OF COORDINATE SYSTEMS

This is in keeping with the viewpoint that the galactic universe

represents reality, and that the surface of the sphere properly divided

the four-dimensional universe into that volume inside it (the past),

and the remainder of four-dimensional space-time outside it (the

future). The proposed revision essentially reverses the roles of the

two coordinate systems, as shown in Figure 29.

The coordinate systems are, of course, completely arbitrary,

manmade constructs, which have no influence on the way the

universe is constructed, and are simply to help us make sense of it.

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FIGURE 29

THE COORDINATE SYSTEMS REVERSED

In figure 29, we have a local coordinate system which satisfies all of

the observations of objects which have linear motion with respect to

the observer, and which correspond with the way we actually see

things. The inconsistency in the velocity attributed to a mythical

galactic observer is an artifact of the construction of the galactic

system, which is, itself, artificial. The local observer can, with

complete consistency, map the path of an object through space-time

based on his observations and accurately establish the corresponding

path as it would be observed in the galactic system, were it possible

to make observations in the galactic system.

The lines forming the cone represent the paths of light to or from

the galactic observer. The paths of light are not changed by altering

our reference coordinate system, and the 45 degree angle lines

continue to represent infinite velocities with respect to the local

system, and the apparent speed of light, c, in the galactic system. So,

the properties of light, unaltered by the change in the coordinate


97

system, continue to limit real object velocities to c in the galactic

system, but place no limit on them in the local system.

A stationary object at a distance from the observer which appears to

be at a distance d from the local observer will also be at a distance d

from the galactic origin at some time in the past (the lower right hand

dot) and will be at the same distance d at some time in the future.

If the object is moving at velocity vL in the local system, it will appear

to be moving at a lower velocity given by Equation 71 in the galactic

system.

The present position of the object measured by the local observer

appears to be exactly the average of the past and future positions of

the object as they would be projected to be in the galactic past and

the galactic future at that particular time.

So, the system seems to behave consistently.

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SPECULATIONS ON THE POSSIBILITY OF HAVING

TWO TS

There exists another possibility, and that is that there are two extra

spatial dimensions, and two separate directions of motion of the

universe through space, as shown in Figure 30.

FIGURE 30

TWO T DIRECTIONS

Here there are three dimensions shown. T1, T2 and x. T, as we have

been using it, is simply the sum of T1 and T2, and the rate of motion

of the universe in the T direction would be the vector sum or the

rates in the T1 and T2 directions. If the velocities in each of these

two directions were c, then the velocity of the universe in the T

direction would be 2c .

This speculation has a couple of interesting possibilities associated

with it.


99

First, it would help account for why the energy of matter is given by

2E mc , rather than by

2

2

cE m .

Also, it would give some rational basis for the fact that light is

transmitted only along the 45 degree lines in our conventional view

of the four-dimensional universe. I had speculated that the

mechanism of light transmission involves the direct contact of two

atoms separated by both space and time, by virtue of the lines of

sight being wrapped up like strands of yarn around a very tiny ball.

Two special directions at right angles to each other and at 45 degrees

to the direction of motion of the universe would make this more

plausible.

This is, of course, mere speculation, but it seemed to me to be an

interesting possibility.

CONCLUSION

This rather tedious explanation of why the appearance that objects

moving away from a local observer appear to be moving more slowly

than they really are with reference to the local coordinate system

does not alter any of the conclusions reached elsewhere in this book,

and it is more convenient to continue to represent the three-

dimensional universe as the very small, approximately planar,

segment of the vast sphere which represents the entire three-

dimensional universe at some arbitrary point in four-dimensional

space.

Les Hardison

100

CHAPTER 6 TIME IN THE TWO

UNIVERSES

In this chapter, I would like to convince you that the difference

between the two systems of measurement is that the local observer

sees time differently than the theoretical observer who keeps track

of things using galactic coordinates. This is the only real difference

between the two systems. People make measurements in their own

local universe, and the common practice is to plot the results on

graphs which have scales calibrated using the galactic reference

system coordinates.

I hope to make the case that the observations made in the local

universe, and used for calculations within the local universe

reference system are consistent and meaningful, and that all sorts of

complexities arise when the time associated with events is measured

in this local system but used as though it had been measured in the

galactic system.

WHERE THE TWO TIMES AGREE

In the galactic system, time is uniform everywhere in the entire

universe, and is presumed to be progressing at a constant rate. The

universal expansion is defined by T = ct, where c is the apparent speed

of light and t represents the time starting at zero at the time of the Big

Bang. There is no reason I can see why the rate of expansion of the

universe should be changing with time, as all of the forces we are

familiar with --- gravity, electrostatic attraction and repulsion and

magnetic attraction and repulsion --- appear to act in the normal

three spatial dimensions. The Strong and Weak Forces, which have

to do with the binding of the components in the nucleus of the atom

are beyond my limited means to make measurements, but I believe

that they, too, could be presumed to act only within three

dimensional space.


101

The T dimension is the direction in which the universe is moving as

it expands, and it is at right angles to all of three of the spatial

dimensions, so there is nothing to cause an increase or decrease in

the velocity of expansion in the T direction. Only forces acting in

the T direction can cause accelerations or decelerations in the T

direction. The only such force apparent in my model of the

expanding universe is the attraction of gravity due to the matter on

the opposite side of the universe, which is billions of light years away.

This should have essentially no effect on the matter expanding in the

T direction on “our side” of the universe.

In the local system, the things an observer can see in any direction

are what the galactic observer would say were in his past.

For two observers located at the same point in space and time, but

with their own separate coordinate systems --- that of the local

observer, and the second of the hypothetical galactic observer ---

both of them agree on the time at their common location at the

origin, where the galactic observer is in the center of a nearly flat

plane with the same value of T everywhere. The local observer is at

the same point, and experiences the same time. However, he deems

all that he can see at the present instant as having the same time as

his own. It is only at this point in space that the observers can agree

on the time.

FIGURE 31

STATIONARY OBJECT AT THE ORIGIN

This is illustrated in Figure 31, which simply shows the galactic x

Axis, labeled x Axis, and the local x Axis, labeled xL Axis.

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102

At the instant of time pictured in Figure 31, the two observers would

both presumably have their own clocks, and the two clocks would

read exactly the same time.

However the galactic observer would look out his window in the

positive x direction, and (were he actually to see any part of his

present world out there) he would presume that anyone or anything

out there would have his clock set to exactly the same time as his

own. This is, essentially, my definition of the galactic universe. It

consists of all of the points in three dimensional space where the

time, represented by a clock at that point, would agree with our own

clock. The best I can tell, this is the picture of the universe used in

the development of the Special Theory of Relativity, and used as a

reference coordinate system by physicists and astronomers.

Now, even those points in space or objects closest to him would not

be visible to him at his galactic time, because, in his own perception,

light or other forms of electromagnetic radiation would take a finite

amount of time to reach him, so whatever he actually saw would not

be objects which coexisted at his own present time. True, that nearby

objects might only be microseconds or picoseconds in his past, but

they would still not qualify as being exactly in his present time.

So, I believe the galactic observer who sees the entire universe as

existing at the same time he is experiencing is a purely imaginary

creation, and the world, as it really exists at this moment in galactic

time is completely unknowable. Were he a god-like creature, who

could determine the time and position of events and objects as they

exist in his galactic universe, he would have to do so without the use of

electromagnetic radiation.

That is, he would have to be able to see things as though light

traveled at infinite speed in his galactic universe. But it doesn’t seem

to. It seems to move more slowly, at the velocity c. So, he must agree

that either he cannot see beyond the end of his nose in the galactic

universe, and will have to rely on what a co-located local observer

tells him he calculates for the location and velocity of objects, or he

might try to convince us that the light he is seeing actually moves


103

through space infinitely fast. I don’t think it appears to move

through his galactic space infinitely fast, but it does move through

the local observer’s space infinitely fast. That is basically how we

defined his local universe.

What the real observer sees, when he looks out his window to the

right, is all of the objects arrayed along the xL Axis as they were in

the galactic past --- the very recent past (like a microsecond ago for

nearby things) to a million light years ago (for a distant galaxy). But

what he sees is, in short, what I have defined as the local universe,

and that the local universe is just as “real” as is the galactic universe.

Both systems of measure are mathematical constructs, created by

humans attempting to generalize the laws of nature. They represent

the way things seem to be to us, as observers of the universe. The

two systems are so close together than ordinary life can be conducted

as though they were identical. It is only when in very special cases

where things move very, very fast or are very, very far away from us,

that it seems to make any difference at all which one we use. But, in

those cases, it seems very important to keep them clearly sorted out,

and not confuse one model with another.

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WHERE THE TIMES DISAGREE

But, for the moment, let us presume that a god-like galactic observer

exists and can deduce from the observations of his local companion,

determine the galactic positions and velocities of all the local

observer sees. Thus he can “see” the galactic universe at the present

moment, at least in his mind’s eye. We can compare what he “sees”

with what the real, local observer sees, and examine the differences.

The local observer, looking out the same window, recognizes that

his world, including all that he can perceive, is the closest he will ever

get to seeing the universe as it is at present. He recognizes that any

measurements he makes of distance, length, velocity, mass, energy,

or any other physical property of anything will be based on his view

of the universe. He can construct mathematical models of the

galactic universe, or of any number of other space time constructs,

but he will have to base them on his observations in his local

universe.

In his local universe, he realizes that if he sees an object at a distance,

the clock associated with that object will read an earlier time than his

own. He can calculate exactly what it will read if he knows the

distance to it, according to

( ) (0) ,L L

xt x t

c EQUATION 73

where the left hand term gives the reading on the clock located at x

units of distance from his observation point, and c is the velocity of

expansion of the universe. The value of the local time at his location,

x = 0, is always greater than at any point where x has a larger absolute

value, because x actually represents the distance from the observe to

the object, and is always a positive real number...


105

It is obvious that x is not an algebraic quantity, where the sign

matters, as the local universe appears symmetrical, and distances to

the left of the observer appear to be earlier locations than at the

origin, just as distances to the right do. So, x must be, and rather

obviously is, simply the distance to the point in question in the one

dimensional model of the three dimensional universe. That is

2 2 2x x y z , EQUATION 74

and would be more reasonably described as rL, the radial distance

from the observer to the object. However, for simplicity, it is useful

to continue to think of this as a distance along the x Axis, but always

a positive distance, when considering the local universe, consisting

only of objects which are in the galactic past.

Now the square root can be taken as either positive of negative, and

the geometry of the situation requires that the positive value applies

to those things in the galactic past, which the observer can actually

see at the moment. The negative root would apply equally well to the

future, or to the distance from the object to the observer. That is,

things located distant from the origin but at a future time would be

represented by Equation 74, but with the negative root rather than

the positive one.

The galactic observer, “seeing” the same object, says that the time is

( ) (0)t x t . EQUATION 75

They obviously disagree by the difference

( ) ( )L

xt x t x

c . EQUATION 76

That is to say, they see the time at the distance x to be x/c earlier in

the local system than in the galactic system. Or, in other words, the

galactic observer would see the point xL to be in the past by a time

period xL/c, while the local observer would say it was in his present

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time. Points xL and x represent the same point in space at two

different times.

This difference between the time assigned to object locations and

events will exist everywhere in the entire universe and at any time in

the past, present or future, except for the exact present location and

the exact present moment in time.

If x represents a point in space which is at a fixed distance from the

common origin of the two measuring systems, the distance to x will

be equal to xL, only at t =tL.

OBJECTS AND EVENTS

This equation applies equally well to objects and to events, and it is

reasonable to pause for a moment to define the difference between

these two. It appears, from my point of view, that the universe

consists of objects, which include everything from electrons to

galaxies, which have persistence and continuity in time. That is, they

seem to be four dimensional entities, which have dimensions in our

three dimensional space, but which are present in the three

dimensional universe as though they were three dimensional cross

sections of a four dimensional entity. If every electron, proton,

neutron, etc. were, in fact, a very, very long (in the T dimensional

direction) thin (in the x, y, z direction) string, where the embodiment

we are aware of is simply a three dimensional cross-section, this

would account for their continuity.

It would also account for their apparently unchanging properties

with time, while allowing for them to assume varying locations in

three dimensional space as time passes. Strings which are straight

represent objects, or points in space which are either stationary or

are moving at constant velocity relative to the observer.

This continuity would not allow for the favorite exercise of the

quantum mechanics devotees, which is the presumption that the

positions are probabilistic in nature, and that electrons can change

location in a discontinuous way. Bending of the strings represents

acceleration or deceleration relative to the observer, but for now we


107

are only concerned, as Einstein was in the development of Special

Relativity, with bodies which are moving at constant velocity.

Objects have a significant persistence, and exist for a finite, and

usually substantial period of time. Objects have continuity, which

means that if something is present at one instant in time, you can

count on it being present at some later time.

Events, on the other hand, occur at a particular time, and have no

existence outside that period. For example, the emission of

electromagnetic radiation from an excited atom is an event. The

atom is an object, but the change of its state is an event. So, objects

can have velocity, which involves changing their position, but events

cannot.

VELOCITIES

Things are a little more complicated if x represents the distance to

an object which is moving with respect to the position of the

observers. Here they disagree about the time at which any point

exists at a given location in space, and the disagreement is linear with

the distance of the point from the observers. The greater the distance

to the point, the greater the disagreement about the time at that

point.

It is necessary to think of the point in three dimensional space as

being represented by a line in four dimensional space, and the

disagreement between the two observers as to where the point is in

space at a given time, or in time at a given location, is the difference

between the positions along this line of the observations.

The difference between the two times is simply

x v t vt

c c c

. EQUATION 77

Here they disagree about the time at which any point exists at a given

location in space, and the disagreement is linear with the distance of

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the point from the observers. The greater the distance to the point,

the greater the disagreement about the time at that point.

It is necessary to think of the point in three dimensional space as

being represented by a line in four dimensional space, and the

disagreement between the two observers as to where the point is in

space in time is the difference between the positions along this line

which the observer assigns to it as he makes his observations.

So, it is apparent that, although the local observer and his imaginary

counterpart, the galactic observer, agree completely on the time at

their present location, they are unable to agree about the time of any

point at a distance. The local observer will say that the distant point

exists at his present time, and the galactic observer will say that it

exists at his present time, and they are talking about two different

times. The error can be viewed as a difference in opinion about the

location of a point at any given time, but it is more realistic to regard

it as a disagreement about the time, in the history of the point, that

is being considered by each of the observers.

However, we will have to talk about measurement of distance before

we can get into the influence of velocity on the measurements of

time.

For the most part, the differences in time between ourselves and all

of the things we observe around us are very, very small, whether

measured according to the galactic system or the local system. For

example, the time difference between ourselves and someone we see

on TV, broadcasting from Europe, perhaps 5000 miles away, is only

5000/186,000≈1/37 seconds,

Which is essentially the difference between the times assigned to the

event in the two systems.

The galactic observer describes the delay as the time it took the

electromagnetic radiation to move through the space between the

European broadcaster and our eyes, and the local observer would

say that the signal moved instantaneously from the broadcaster to


109

his eyes, but that his eyes had to have moved through the T

dimension 5000 miles at 186,000 miles per second in order to get to

where he could the signal had arrived.

So, there is no complexity in the relationship between time as seen

by the real observer using the local coordinate system for his

observations and the “galactic” observer, who, blessed with god-like

vision, can see how things are throughout the universe “right now”.

The two observers agree absolutely on what time it is right now, and

if they could perceive, other than by virtue of the time indicated by

their respective clocks, where they stand in terms of the expansion

of their point in the universe in the T direction, they would agree

about that also.

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AGREEMENT ABOUT THE SPEED OF CLOCKS

Both the galactic observer and the local observer experience the

passage of time as their position moves through space in the fourth

dimensional direction at a velocity which appears to be constant, or

very nearly so, with the passage of time. That is, both would find

their clocks running at exactly the same rate, and if they had more

than one clock (or means of producing regular, recurring motion,

like a pendulum by which they could measure the passage of time)

the clocks could all be depended upon to run in synchronism.

The complexity arises when the real observer carries out his carefully

done experiments with moving objects, and tries to translate his

findings to the galactic universe, which he cannot really experience.

When working with local objects, the galactic observer and the local

observer could scarcely tell the difference between their two bases.

That is why, for several centuries, Newtonian mechanics seemed to

hold a complete description of how physical objects interacted with

each other. The observations were made in the local universe, and

the laws of motion, gravity, etc., were treated as though they had

been determined by observations in the galactic universe. Even the

motions of the planets are slow enough and near enough to us that

the deviations from Newtonian laws are almost unnoticeable, except

with the closest of observations.

Time, in the two universes, is so nearly identical that it is very

difficult to tell the difference.

The same similarity in the observations of time and distance between

the galactic and the local reference systems applies to velocity as well.

As long as we are concerned with objects and events relatively close

at hand, where disagreements about time and distance measurements

are insignificant, velocities measured by local observers will appear

reasonable if they are presumed to be the same when used as though


111

they were measured in the galactic system. However, even for nearby

objects moving in reasonably short time periods, anomalies will crop

up if the velocities are very, very high.

For very long distances over significant periods of time, some

problems began to emerge.

FIGURE 32

DIFFERENCES IN VELOCITY BETWEEN THE TWO SYSTEMS

When physicists began to be concerned with things that moved very

fast, such that they had to look carefully at changes in location over

very short periods of time or otherwise look at things moving over

very great distances over longer periods of time, inconsistencies

began to appear.

Figure 32 illustrates how, as the observers move through time,

traveling in the fourth dimensional direction, they would fall into

disagreement about how fast a moving object is traveling, because

of their disagreements about the length of time which passed

between their two observations on the distance to the moving

object. Not about the time on their own respective clocks, because

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112

these would always be in perfect synchronism, but rather how each

regarded the time at various distances from their present position.

As the object illustrated in Figure 32 moves to the right, initially

approaching the observer at the origin, and then passing him, it

would occupy positions numbered 1, 2, 3, 4, and 5 along the x Axis,

so far as the galactic observer was concerned. In each case, he would

assign his galactic time to the position. However, the local observer

would recognize that he could not perceive the position of the object

moving into his future, and could only calculate its position is space

and time from observations when the object was in his past. Thus,

when the galactic observer placed the object at point 3C, the local

observer would have only reached point 3B, and would assign an

earlier time to its location.

The galactic observer would see point 3 out his window at time t,

counting from the time it left point 1. He would have moved in the

T dimensional direction a distance ct, and the object would have

moved through this same distance in the T direction, and would also,

according to his system of relating time and distance, have moved

through the distance vt in the x direction away from his location. So,

he would calculate the velocity of the object as

v t x , EQUATION 78

or

x xv

t t

. EQUATION 79

The local observer, on the other hand, would not be able to see the

object yet, but would calculate that, if it continued at the same

velocity, it would be at point 3C already. Thus the local observer

would presume the distance the objet traveled took less time than

the galactic observer thought it did.

ΔT. =ΔX/C. EQUATION 80


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At each point along the way from point 1 toward point 5, the galactic

observer and the local observer, sharing a laboratory, as it were,

would agree absolutely on the time according to their respective

clocks. However, as the galactic observer drew even (in the T

direction) with point 3, he would proclaim that point 3 had moved

the distance Δx in time Δt, and would therefore have velocity v.

At this point in time, the local observer, who had been tracking the

object on his radar screen, would say that it reached that point some

time back and was really moving faster than the galactic observer

thought it was. His determination of velocity as the object passed

him by would be exactly the same as it had been while it was

approaching him. That is

l

L

L

xv

t

, EQUATION 81

and goes on to compare his findings with that of his galactic

colleague, making the following calculations:

l LL

L

x xv

xtt

c

. EQUATION 82

Because xL and x are the same in this example, we could simply write

LLL

x xv

xtt

c

. EQUATION 83

One can replace x in this equation with vt, yielding

1L

vt vv

vt vt

c c

. EQUATION 84

It is convenient to look at the ration of vL to v, which is

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1

1

Lv

vv

c

, EQUATION 85

or

1

1 LL

v

vv

c

. EQUATION 86

This indicates that the velocity registered by the local observer will

always be greater than that which would be “seen” by the galactic

observer, could he in fact measure distances in the galactic universe.

This correction factor, which must be applied to the local observer’s

data to get the data to be used in the galactic system is very small if

the velocity of the object or event is relatively small compared to the

apparent speed of light, c.

This rather involved explanation can be summarized simply by

saying that the local observer and the galactic observer’s clocks

always agree on the time at their common location, but disagree on

the time of things everywhere else. The disagreement is proportional

to the distance of an object from the observer, so if it isn’t moving,

they will agree exactly on the time difference between two

observations of the object. On the other hand, if it is moving, and

they will always agree on whether it is moving or not, but not

necessarily on whether it is moving toward or away from their

position. The local observer will always assign a greater velocity to

it, because he will see a shorter time interval between successive

sightings than does the galactic observer, whichever way it is going.

In the case of objects moving toward the observer, he can see them

clearly and calculate their velocities directly. In the case of objects

moving away from him, they are moving into his future, where an

observer located on the object could see him at his present position,

but he won’t be able to see the object at that position until sometime


115

in his future. So, he has to calculate, rather than observe, the preset

position of the object moving away from him. Or, for a given

position of the object, calculate the time at which he can expect to

see it.

The galactic observer, on the other hand, can never actually observe

anything in his present time, because light from the object won’t

reach him until sometime in his future. This applies to objects both

stationary and moving. So, he is always going to have to ask his local

observer partner for the information about the local time and

location, and calculate the position of objects at his present time.

The local observer will be similarly limited and unable to help when

the object is moving away from his position. He might, however, be

able direct a beam of light toward the place where the object might

be at some time in the future, and then see the reflection at some

later time and use the distance and the time interval to calculate the

velocity of the object.

He could share this information with the galactic observer, and both

of them might calculate the position of the object at some time in

the galactic past. The local observer would know for certain where

the object was “right now” in terms of his local clock, but the galactic

observer would still think of this as a past position, which he might

use to calculate the present galactic position, provided nothing has

changed the velocity of the object in the meantime.

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MEASURING THE APPARENT SPEED OF LIGHT

At the time of the publication of Einstein’s Special Relativity, in

1905, no distinction was made between the two systems I have been

describing, and it did not seem that there was any real problem with

the use of the commonly accepted (galactic) system of coordinates

for making measurements in the real world. In my opinion, this

distinction is still not made most of the time, and it still does not

matter most of the time. However, when dealing with large velocities

and great distances, it does, and should always be taken into account.

At the beginning of the 20th century there was a very troubling

problem which had arisen because it was found that the velocity of

light did not seem to follow Newtonian mechanics. If one really

could see the world at the present moment, then the velocities he

saw would be simply, the change in distance over a given period of

time divided by the length of the time period.

If a second observer were moving relative to the first, his

observations would simply differ by their relative velocities. That is,

if you saw a train moving 60 miles an hour along a track in front of

you, an observer in an automobile moving in the same direction as

the train at 20 miles an hour would see it as moving relative to his

position at 60 – 20 or 40 miles per hour. It wouldn’t make any

difference if you were using the galactic system or the local system

of measurements, you would get the same answer as close as you

could measure.

However, if the train were moving at the apparent speed of light, and

you clocked it at 186,000 miles per second, you would expect that

the observer in the automobile would see it as moving 20 miles per

hour more slowly. It would take some petty fancy measuring

apparatus to determine this, but it is what you would expect.

Very carefully done experiments, using ingenious physical

arrangements to time the travel of light from one point to another

had established the apparent speed of light fairly accurately before the


117

end of the nineteenth century. The experimenters made their

measurements essentially by causing a light beam to leave a location

in their laboratory, reflect from a mirror a significant distance away,

and return to the laboratory. By using one of several ingenious ways

of determining the time between when the light beam left and when

it returned, they determined the apparent speed.

FIGURE 33

LIGHT MOVING THROUGH SPACE IN THE GALACTIC TIME

SYSTEM

In the experiment, the observer, initially at point A0 caused a beam

of light to reflect off a rotating mirror momentarily in the direction

of the stationary mirror at point B1, and back to the same rotating

mirror at point A2. The distance from A1 to B1 was not important,

but it had to be known quite precisely, and it had to be far enough

away that the time interval between A0 and A1 was great enough to

measure accurately.

Their universe was the galactic universe, by default. It was what they

inherited from Newton, and had no reason to change.

That is, they presumed that light moved through empty space much

like a fish swims through water, or a sound wave passes through air.

That is, traversing the space in between, little by little, and occupying

each point in space in a straight line between the origin and the end

point of the travel.

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Thus they set up their experiments in a way crudely represented by

Figure 33, with the light source in their laboratory, a mirror (or

complex series of mirrors) some distance away, and a system for

measuring the time between the light leaving the source, and arriving

at the receptor, having traversed twice the distance to the mirror in

the measured interval. It is important to note that the light source,

the reflecting mirror and the light receptor were all stationary with

respect to each other. So, they were moving with the expanding

universe in the T direction at the same velocity, but were not moving

relative to each other in the three ordinary spatial dimensions.

This system provided quite accurate measurements of the velocity,

around 186,000 miles per second, or 300,000 Kilometers per second.

They had no reason to ascribe the measurements they made to the

local universe, as opposed to the galactic universe as I have defined

it, and no reason to suspect that the measurement could represent

anything else other than the speed of light, making its way through

space like a material object travels through space.


119

THE APPARENT SPEED OF LIGHT TO A LOCAL

OBSERVER

I submit that these experiments were made by scientists in the

position of the local observer using both his measuring tools and his

clock in the local coordinate system, as I have described it, rather

than with reference to the galactic system, as they assumed.

This all seems very straight forward, except for two items. First of

all, the observer at point A0 cannot see light leaving his position. One

does not see beams of light, but only recognizes light falling on his

eyes from some source in his past, so he must presume that light

departed from his location and headed through space toward point

B1. At point A1, he cannot see point B1, as it is in his future, and he

has no ability to tell what is happening at a distant point at his exact

time. So, he takes it on faith that the light leaving his source does go

away from him into his future, behaving much like light coming from

a distance source, which he can see, behaves.

However, if he places a mirror at point B1 (prior to starting the

experiment, point B is on the same horizontal line with Point 1,

representing his galactic present time and a local future time), he can

avoid this difficulty by presuming that the mirror (having moved

through space in the T direction just as he, the observer did)

reflection occurs instantaneously, and that the light beam moved

through twice the distance to B1 in the time 2Δt.

So, from the point of view of the classical physicist, he has observed

that light moved away from his position, and moved through the

vacuum of space much as a fish swims through water, changed

direction instantaneously at the mirror, and arrives back at his

location at a later time, t0+2Δt, having covered the distance 2Δx, and

arrives at the velocity

2.

2

xc

t

.EQUATION 87

Being familiar with fish swimming through water, it makes sense that

this is what happens.

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120

However, this is not how the local observers would have interpreted

the experiment at all, yet they would have to admit that they got

exactly the same measured result. They were good physicists and

experimenters, and got substantially the same answer when they

repeated the experiments. However, knowing that they were in an

expanding universe, and that their position in space time was

changing continuously as the experiment progressed would give

them a different perspective.

FIGURE 34

THE LOCAL TIME SYSTEM OBSERVATION OF LIGHT SPEED

Figure 34 shows the experiment from their respective viewpoints.

As the diagram shows, the galactic observer would assume that the

light moving away from him toward the mirror would get there at

some time in the future, but he would not be able to see it until it

had time to make its way back from the mirror to his position at A2.

The light beam seemed to be traversing the distance to the mirror,

which is vΔt. Of course he could not see the light beam moving away

from him, nor could he see the present position of the mirror when

he is at Point A1, because a galactic observer can only see things in

the galactic past. However, after the time interval 2Δt has passed, he


121

arrives at point A2, just in time to see the reflected light return from

the mirror. He definitely sees the reflected light return to his location,

again traversing the distance c, and now two seconds have passed.

So, he concludes that the velocity of light is

2.

2

c tv c

t

EQUATION 88

The local observer would, if he assumed himself to be a local

observer in a universe expanding in the direction of increasing time

at a fixed velocity v, describe the local velocity of light as infinite,

and his task that of determining the rate of expansion of the universe

in the T direction.

So, he would see his experiment as that of sending the burst of light

into the future, presuming it to move through space at infinite speed,

reaching the mirror when the universe had expanded through the

distance VΔt. He would presume that it reflected from the mirror

back to the starting point, now at A2 in the same amount of time,

again traversing the distance VΔt, but again, with no lapse in local

time. As the light made the return trip, he would, by definition, say

that

0L

cv . EQUATION 89

Clearly, neither observer can see the light leaving his location and

moving toward the mirror. The local observer can, however, see the

light which is reflected back toward point A2, and deduce that it took

no time for it to make the trip back. It is reasonable for him to

assume that the speed of light was the same in both directions, as

this is what all of the experiments to date had seemed to indicate.

So, there are two interpretations which can be put upon the results

of the “speed of light” experiments.

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122

1) The conventional interpretation, which is that light

moves through empty space like a fish through water or

a sound wave through air, as the universe coincidentally

expands as time passes, so the velocity of light is c, and

the velocity of the universe moving in the fourth

dimensional direction is unknown, let’s call it vT, and of

no particular importance, or

2) The “New Theory of Light” interpretation, which is

that, at least in the local universe, transfers of radiant

energy between atoms take place instantaneously,

without anything passing through the intervening

space, provided the emitting and receptor atoms are

properly lined up. Thus, the light is transferred

instantaneously from the source to the mirror, and

again instantaneously from the mirror back to the

receptor in the laboratory, but at a later point in time,

without ever having traversed the intervening empty

space. Thus, what the experimenters measured was the

velocity of the expansion of the universe, c.


123

THE INFLUENCE OF TIME MEASUREMENT ON C

Let us look at the classical picture of the path of light moving

through the space from the source in our laboratory to a mirror at

some distance, and back to a photocell in the laboratory, and

presume that we had measured the velocity as c. We have agreed

that both the galactic observer and the local observer, sharing the

same laboratory would have no disagreement about the time, as their

clocks would run in synchronism. Nor would they disagree about

the spacing of the light source and the mirror.

The two observers would differ as to when the light beam arrived at

the mirror. The galactic observer would insist he had measured the

speed at which the light traversed the distance to the mirror as the

distance c divided by Δt, and the local observer would complain that

he got the times wrong, because he (the local observer) didn’t see

the light reach the mirror during that time at all, but rather saw it at

the mirror at the end of the time interval 2Δt, but believed that the

light had arrived the same instant in local time that it left the source.

What took the two seconds for the receptor and the light source to

get together was that it took the observer two seconds to reach the

location in the future where he could see it! It was already there

when the observer arrived at that point in space-time.

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THE SIGNIFICANCE OF C

But, both the local observer and his galactic counterpart measured,

or calculated from measurements, a finite value for c, not an infinite

value, so c must have some other significance. Because something

physically moved the distance 2c during the time interval 2 seconds,

I assert that it was the physical three dimensional universe which

traversed the distance in the fourth dimensional direction, T, much

as a fish swims through water, occupying each increment of space

along the way in sequence, while the radiant energy skipped passing

through both the space and the time between the two points.

By the “physical universe” I mean all the matter within the universe,

so that all of it has the velocity c, and the inherent energy content

E=mc2. /2. There is some question in my mind as to the condition

of the empty space between the massive objects, as I do not see it

fulfilling any particular function. At any point in space, there is either

matter there, which is moving in the T direction at the velocity c, or

there is not. It does not seem to be important whether one thinks of

the space between as having any motion. It certainly has no mass,

and I find the concept of dark energy completely without merit. But

that is a different story.

What is important is that we are all rushing through four dimensional

space at a terrific pace, and don’t have any sensation of doing so. We

are not all rushing through four dimensional space in lockstep,

though, as we each seem to define the direction of expansion of the

universe as slightly different for many other objects, which we see as

moving, relative to ourselves, in three dimensional space.

What we are seeing is a tiny component of the velocity, c, of the

object which is out of alignment with our own velocity c. This

velocity and c itself may be thought of as vectors which have both

magnitude and direction, or simply as the magnitude which has a

direction simply by being associated with a time vector, which always


125

points perpendicular to the x – y surface of our the two dimensional

analog of our three dimensional universe.

The difference between us and an object moving 60 miles an hour is

a very, very slight disagreement about which way the arrow of time

is pointing

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126

THE UNIFORMITY OF TIME THROUGHOUT

GALACTIC SPACE

The relationship of time to two observers who are moving parallel

to each other in the T direction (which means they have no velocity

relative to each other in three dimensional space) is fairly straight

forward. Everyone’s clock synchronizes with everyone else’s

whether or not they are moving with respect to our location in space.

However, when a body is moving relative to us, the time clock it

carries reads differently than ours, or at least would appear to if we

could read the time it indicates. This is because we see it in our local

present time, which consists of all of the points in space which are

visible to us. All of these points lie in our galactic past. If we could

see a distant clock, it would always read an earlier time than our own,

because we would be seeing it in our galactic past, and it would be

synchronized with the past galactic time. The difference in the two

times for any moving object increases as it gets farther away from

us, and decreases as it approaches us.

The question is, how can we tell with certainty what the reading on

someone else’s clock will be if they are at a substantial distance?

Provided we know how far away they are, the time will simply be the

galactic time, calculated as

L

L

xt t

c . EQUATION 90

Because everyone’s clock is synchronized to the same galactic time

regardless of location, it does not make any difference whether the

object is moving or stationary with respect to our own position, so

the time we see on his clock differs from ours only in proportion to

the distance from us. It is, however, important that we note that we

can only see objects in the galactic past. When an object is moving

away from us, it is moving out of our galactic past, where we can see


127

it and make measurements of its position, into our local future where

we will not be able to see it until a later time.

The reason the absolute value of xL is used is because it is the value

of the distance from our observation point, independent of the

direction. This is one of the few points which might be more simply

made with reference to the real, three dimensional world than the

simple one or two dimensional world in our model. The distance to

the remote object with three physical dimensions is

2 2 2

Lx r x y z , .EQUATION 91

when y=z=0.

If the object is moving toward us, its clock will synchronize with

ours when our paths cross at some time in the future. In the

meantime, it will appear to us that his mile markers are farther apart

in his TL’ direction, and we would say that time on his moving clock

must be passing more slowly than ours, but it would not be doing so

by the moving clock. If the object were a moving space ship, the

captain would think it was our clock that was running more slowly

than his.

So, as long as we limit ourselves to talking about things getting closer

to us or farther away, there is no real problem with presuming that

the galactic universe runs on our galactic time, and that in the local

universe, we are surrounded by a continuously varying time zone

system so everyone and everything remote from us has his own local

time that is different from ours. However, it is our local world, so

we can consider that everything in it is at our local time.

We are not troubled, in the local universe by the notion that nothing

can go faster than the apparent speed of light, or that light itself moves

at a finite but invariant speed regardless of the speed of the observer.

Light, in the local universe, moves infinitely fast. There is no

problem explaining why all of the measurements of the speed of light

come out with the same value. They are all measuring the velocity of

expansion of the universe, which is exactly the same for all

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128

observers. The conclusion anyone doing the speed of light

measurement with mirrors ought to reach is that he is really

measuring the speed of advancement of the universe into the fourth

dimension.

This explains why things which seemingly have no relationship to

light or other forms of radiant energy, like the force of gravity, or

the speed of a space ship or a far-away galaxy, all seem to obey the

limitation imposed by the apparent speed of light. The simple answer

to my question, “What gives light the authority to set a speed limit

for space ships?” is that it does not. However, our mistaken

impression that we can see what is happening in our galactic present

makes it look like all velocities are lower than they are to a local

observer.

The fastest any of them could conceivably move involves moving

from one place to another in essentially no time at all, or at infinite

velocity. This is possible in the physical universe in which we make

all of our measurements, but infinite velocities appear, when

translated to the galactic universe, to be equal to the apparent speed of

light. Everything shrinks when measurements in the local universe

are translated into the galactic coordinate system.

There is the case which Einstein didn’t talk about in Special

Relativity, and which I have not addressed up to this point, of objects

that are not moving toward us or away from us, but are rather

moving at right angles to a line from us to them. This has a very

important place in the physics of just about everything, and deserves

its own chapter.


129

ACCOMODTING THE INVARIANT SPEED OF LIGHT

Because experimenters determined that the apparent speed of light

seems to be invariant according to carefully done experiments, and

they, and the theoretical physicists such as Einstein, were unable to

account for any mechanism whereby it could move instantaneously,

they were hard pressed to explain their results.

So, they reasoned that the relationship between time and space must

be such that the things which were moving experienced time and

space differently than things standing still. If one is limited to

working in the galactic coordinate system, and attributes the

invariance of the speed of light to this system rather than to the local

system in which it was measured, it requires some rather extreme

assumptions about space and time.

These are, of course, the relativistic corrections, which appear to

make the local observations fit into the galactic frame of reference.

This can done primarily by modifying the expression for time

according to

2

2

' 1

1

t

t v

c

, EQUATION 92

or

2

2

' 1,

1

t

t v

c

EQUATION 93

where the primes refer to a second moving observer’s observations

of time, distance and velocity.

This seems to say that clocks run more slowly when they are viewed

from a frame of reference moving rapidly relative to our particular

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130

“stationary” frame of reference. This is not because we actually see

them running more slowly, but because we see them at different

points along their path through space and time.

They appear to slow down, but they don’t.

But, once having accepted that the clocks slow down (even though

it is only an apparent slowing down), all of the other conclusions of

Special Relativity become necessary. The measurement of distance is

different, and moving objects experience a shrinking of their linear

dimensions according to

2

2

' 1.

1

x

x v

c

EQUATION 94

Velocities of objects moving relative to our galactic coordinate

system are never able to reach c, the apparent speed of light, because the

whole scheme was derived to provide a system in which velocities

could never exceed the apparent speed of light.

And finally, because no velocity can exceed c, the apparent velocity

of light in the galactic system of measurement, it is necessary to

postulate that the mass of objects must increase as their velocity

increases according to

2

0

2

1,

1

m

m v

c

EQUATION 95

so as to avoid the problem of where the energy goes as bodies are

accelerated and v approaches c.

This leads to the a revised expression for the energy a moving mass,


131

20

2

1

1

E

E v

c

, EQUATION 96

where E0 is the “rest mass”, or what we think of as the ordinary mass

of an object, which leads to

2 22

0 0 0 02 2.

v vE E m m c m

c c EQUATION 97

And, finally, mass becomes interchangeable with energy according

to

2E mc , EQUATION 98

for objects at rest relative to our coordinate system.

These corrections are all required because of the misinterpretation

of the passage of time, which is, in turn, due to making observations

in the local universe, and treating them as though they were made in

the galactic universe. This point is important enough to have its own

section in the book.

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132

CHAPTER 7 COMPARISON OF THE

TWO SYSTEMS

My objective in this chapter is to examine how the galactic system

of coordinates used by Einstein and other physicists relates to the

local system. In doing so, I will point out how observations, which

must of necessity, be made in our local universe, can be properly

translated to the equivalent values which will probably exist in the

galactic universe at subsequent times. This would allow the galactic

system to be used precisely when dealing with uniform velocities,

and some forms of non-linear motion such as orbital velocities.

However, this translation does not account for the apparent

shrinkage of time and space with motion which is built into Special

Relativity, and is the most difficult concepts to understand based on

everyday experience.

I will offer a rationale for the inclusion of these shrinkage factors,

which results, I believe, from the failure of physicists to distinguish

between the local system of coordinates, in which the measurements

are made, and galactic systems of reference, to which they are being

attributed.

I will take this one step at a time, first defining the translation of

measurements of time, distance and velocity from the local system

in which the measurements are made to the galactic system, using

the presumption that the velocities being dealt with are constant.

Then I will move on to the more complex situation where two

observers make measurements, each in reference their own local

coordinate system, and compare the translations to the galactic

system for differences which would be unexpected.

This is, basically, the route followed by Einstein in the development

of the basic equations of Special Relativity, which still serve as the


133

cornerstones of modern physics. I will point out that Einstein

applied this comparison of the apparent velocity of light c, which was

determined to be the same when measured by pieces of apparatus

moving relative to each other, and was presumed to apply to other

velocity observations as well. The misinterpretation of the meaning

of c led to many of the complexities associated with Einsteinian

space time.

I will also point out how the equations derived from the

presumption of two systems moving relative to each other have

mistakenly been translated to the case of a single observer making

measurements of a single object moving relative to his position. This

has resulted in the general application of the space and time

shrinkage factors to all objects in motion.

Finally, I will consider the case where the a single observer, making

measurements of distance and velocity in his local coordinate system

mistakenly uses these measurements without correction as though

they were made in the galactic system. This is the error which results

in the calculation of the shrinkage factors to space, and time, and the

increase in mass with velocity of objects moving with respect to the

observer.

This is not an easy comparison to make, because both use coordinate

systems involving time, which is not only difficult to describe, but

which is also a bit difficult to define.

Furthermore, in the local system, I have replaced time with a fourth

physical dimension, which is even harder to visualize. We have

experienced the passage of time in various ways, but we do not

perceive the motion of our universe through a fourth dimension, just

as we do not sense the very rapid motion of our earth with respect

to the sun. I believe the velocity of the universe in the fourth

dimensional direction is steady and unchanging, except for minute

differences in direction, which we recognize as accelerations or

decelerations of objects in our three dimensional world.

Yet, if the universe is expanding as time progresses, then the fourth

dimension must be there for it to expand into, and our location in

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134

the three dimensional universe must be moving in this fourth

dimensional direction. These seem to me to be inescapable

conclusions once the expansion of the universe is accepted as real.

Both the galactic and the local systems are simply attempts to

describe the universe we experience, and fit the measurements

relating to how it works into the description. I maintain that we can

only observe how it works in the context of the local universe I have

described, and that the galactic universe, which may be the more

appropriate measure of things, is beyond our reach. It can only be

constructed graphically or mathematically, but cannot be

experienced. Not only can we not see into the future, but in a very

real sense, we cannot even see into the galactic present.

Once again, I will emphasize that ordinarily we are dealing with

objects which move at relatively low velocities. These are slow

compared to the speed of expansion of the universe, which I have

consistently referred to as the apparent speed of light. And, we are

usually dealing with short distances, which are small compared to the

distance light travels in a few seconds. So, in our everyday experience

it makes no practical difference which of the two reference systems

are used. The measures used by physicists – length, time, velocity,

mass and energy – all come out pretty nearly the same in both of

them.

Only when the velocities of objects relative to one another become

significant compared to the apparent speed of light, or when the

distances become large relative to the distance light travels in a

second or two, does there seem to be any problem with the use of

the Newtonian laws of motion. But, it is those cases which have to

be considered to make a comprehensive picture of the way the world

works, including a consistent theory for the properties of light, a

consistent model of atoms, and the behavior of the galaxies.

I am going to start by presuming that we make all of our

measurements in the local universe where we live, and that these are,

or should be, translated by rational means to the galactic universe

coordinate system used by Einstein and other physicists. The


135

translation ought to fit the actual measurements into the framework

of Special Relativity, and, with some exceptions, they do.

For the most part, despite all of the modifications of General

Relativity, the development of Quantum Mechanics, Quantum

Chromodynamics, and the Standard Model used by physicists to

describe the internal workings of atoms and molecules, the basic

concepts of Special Relativity are still pretty well taken as being

correct. I do not presume to understand all of the complexities of

modern physics, and for the moment, ask the reader who is well

versed in these things to give me license to simply deal with the

elementary concepts of Special Relativity as it was originally

presented.

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MEASUREMENT OF TIME

I am going to try to go through the comparison between the

measurement system I have described as the local coordinate system,

within which all of our physical measurements are made, and the

idealized picture of the universe, in which time is everywhere the

same, regardless of the distance of an object or event from the

observer.

My aim is to present a relatively concise picture of the relationship

between the two systems of measurement, and the means by which

an observer, working in his local universe can produce an adequate

picture of the galactic universe, at least so long as the objects he

observes do not change their velocities between the time he sees

them and measures their properties and what he considers to be the

“galactic present time” in reference to the galactic coordinate system.

The difference between the two systems boils down to a difference

in the measurements of time. When the translation from the local

system of measurements to the galactic frame of reference is made,

the result does not correspond with the equations of Special

Relativity. Something is clearly being left out, and my main objective

in this chapter is to establish the difference between my derivation

and Einstein’s, and to offer an explanation of how it comes about.

All the difference between the two derivations and much of the

complexity in Special Relativity seems to result from making

measurements using one system (the local system), and then

applying them improperly to the other (the galactic system), without

using the corrections defined in this section.

In particular I will point out how the failure to recognize the

difference between the two systems has led to much of the

complexity in the equations of Special Relativity, and the application

of the ubiquitous correction factor, F, to the measured times,


137

distances and velocities of objects moving with respect to the

observer.

2

21

vF

c , EQUATION 99

In the local system of coordinates, each observer regards the time at

his location as the time his clock reads. I will postulate that he has a

clock which reads the precise time in terms of fractions of a second

since the time of the Big Bang origin of the universe, and that it reads

the same as the galactic time at his location. This is true for all

observers, regardless of location in our ordinary three dimensional

space, so everyone, everywhere, sees the same time on his clock if

they are all in the same galactic present. The local observer will,

however, ascribe his own local time to everything he can see, or

detect by means of electromagnetic radiation. That is, his present

time will apply to all the universe he can see.

So, he would see, if he had a sufficiently powerful telescope, which

points in his local universe remote from his location would have

clocks which read an earlier time than his own. He would have no

trouble understanding that his present represented a collection of

points in the galactic past. So he would think of each distant point

as having two distinct times. According to which system of keeping

time he chose to use.

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THE LOCAL TIME ZONE ANALOGY

A more familiar case of the use of two different time systems

involves the earthbound traveler’s use of Universal Time (UT),

which used to be called Greenwich Mean Time (GMT). This is the

time at the Prime Meridian which runs north and south through

Greenwich, England, and has been used as a reference time

throughout the world. We all have our local time zones, in which our

clocks are set more or less in keeping with when the sun passes

overhead each day. I live in the Eastern US time zone, where the

clocks are normally set to a time five hours earlier than Universal

Time, or,

5:00EST UT .EQUATION 100

This is complicated a bit by the use of Daylight Savings Time, which

advances the local (EST) clock one hour during the summer months,

for reasons that are debatable. There are, arbitrarily, 24 irregularly

drawn time zones forming irregular segments of the spherical

surface of the earth, such that nearly all of the clocks can keep the

minute hands synchronized while only changing the hour hand.

So, at the equator, one could, by counting the time zone immediately

west of Greenwich as 1, for the first time zone, and numbering them

consecutively around the globe, write the equation for the local time

as

L Gt t N , EQUATION 101

where:

tL = Local time in hours

tG = Greenwich Mean Time in hours.

N is, of course an integer running from 1 to 24. Between the 12th

and 13th zones lies the International Dateline, where, when it is 12:00


139

Noon in Greenwich, it is midnight locally, and the date increases by

one calendar day.

One could easily imagine a time zone system consisting of many

more time zones than 24, in which the minute hand on the clocks

would not all be in synchronism, just as the hour hands are not in

the present system. As an extreme, one could consider that, instead

of 24 time zones, there were, instead, an infinite number, so that

each individual would have to have a clock which read the time

applicable to his unique position, and whose clock would have to be

reset each time he moved any finite distance to the east or west. The

setting of each individual clock would require knowing exactly how

far east or west of Greenwich the clock happened to be at the

moment. It could then be set to read

360L G o

Longitudet t , EQUATION 102

where 360o represents an angular velocity of 360o/day.

It is not hard to imagine that, faced with this complex situation,

individuals would prefer to simply set their clocks to UT, which is

the same at every point on the surface of the planet, and abandon

the local time concept altogether. This is, essentially what aircraft

pilots do.

So, we each have our own local time, which is changing at a

presumably uniform rate due to the rotation of the earth. We have

no sensation of the velocity of rotation, but we can, in easily perceive

the changes in the location of the hands on our clock, or of the sun’s

passage overhead, and conclude that these motions are related. The

common factor is, of course, what we call time. And it is, on earth,

related to the rotary motion of the earth, which cannot sense directly.

If, instead of using the observatory at Greenwich, England as the

location of the reference time zone, we instead used our own present

location, wherever that might be on the surface of the earth, we

would have a situation comparable to my concept of local time in

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140

the four dimensional model of the universe. We would, of course

think of our local time being the same through the world, although

we would understand that everyone else had a local clock that read

their local time, not ours.

The relationship between our CDT and Universal Time is quite

analogous to the relationship between local time and galactic time,

L G

xt t

c , EQUATION 103

indicating the relationship between the local time on the surface of

the two dimensional sphere of the analog universe, which changes

with distance from the observer, and galactic time, which is exactly

the same at every point on the surface of the sphere.

In this analogy, the speed of the earth’s rotation is the analog of the

expansion of the universe in the T direction. Were we to depart in

an aircraft to fly westward from the our initial location, say at

London, at about 800 miles per hour, we would find that the local

time along our path did not change at all, and we would appear to

be moving instantaneously from point to point. If we left London at

noon, we keep resetting our local clock continuously as we flew

westward, we would arrive at our destination, wherever it was,

at…..noon, by our local time clock.

In terms of Universal Time, we would be moving 800 miles per

hour, or at about the rotation speed of the earth at his latitude.

Or, one could say that we were, in fact, standing still, and the earth

was rotating beneath us at 800 miles per hour. In terms of local time,

our departure time and arrival time would be exactly the same, and

our velocity would be, not 800 miles per hour, but infinite.

Were we to use a cell phone to call ahead and advise friends at our

destination of our departure, the message would arrive at the

destination as we were leaving London, in substantially no time at

all. However, we would not be at the destination to check that the


141

message was received, and could only attest that the message was

there when we got there, so it might appear to us to have traveled

only 800 MPH instead of at essentially infinite speed.

If we then postulated that the telephone call progressed across the

ocean at 800 MPH, and that nothing could possibly go faster than

that, we would have arrived at a lot of misconceptions about the way

the world worked.

When there are two alternative ways of defining time, keeping the

differences between the two in mind is very important.

Les Hardison

142

TIME IN THE LOCAL AND GALACTIC SYSTEMS

The relationship between galactic time at any given location and the

local time assigned to that location is simply

L

xt t

c , EQUATION 104

and the differences in time between measurement of distance is

L

xt t

c

, EQUATION 105

or

L

v tt t

c

, EQUATION 106

for objects moving toward the observer, from which

1Lt v

t c

. EQUATION 107

Finally,

1

1 LL

t

vt

c

. EQUATION 108

This corresponds to the difference in time between two events

presumed to take place at the different measured distances. That is,

for example, at the beginning and end of the timing of a race, or the

motion of a space ship between the earth and the moon.

The relationship between the elapsed time for any two events in the

galactic and the local systems depends solely on the local velocity

observed, and is independent of the placement of the origin of the


143

coordinate system. Wherever it is, the origin is presumed to be

stationary.

The local time is what one can measure by looking at his own, local

clock. The galactic time at his location is presumed to be the same,

because the local observer is at the origin of his own local coordinate

system. And the time at all other points is presumed to be the same

as his local time. However the galactic time is the same everywhere.

Any other observer at a different location at the same galactic time

would be presumed to have the same local time.

It is noteworthy that there is no F factor which shows up repeatedly

in the equations of Special Relativity.

Les Hardison

144

MEASUREMENT OF DISTANCE

The measurement of distance in the local system is a purely

mechanical problem, but there are many mechanical solutions. For

example, the distance to an object can be measured against a pre-

established grid, with mile markers spaced evenly apart like the

yardage lines on a football field. Or, the object can be detected by

RADAR, or SONAR. More complex methods may come into play,

such as the brightness of a star of known type, or the apparent size

of an object of known size. The method of measurement is not

important, but it is important that all of the possible measurements

depend in some way or another on the transfer of electromagnetic

energy from the object to the observer. This is done in the local

universe, and it is presumed that the objects seen exist in the local

present.

The location of the object in four dimensional space is simply

determined from the distance measurement in three dimensional

space, and has been represented by the single x dimension in one or

two dimensional analogs used in the derivations so far.

There is no ambiguity about where the object is in space at any given

moment in either local time or galactic time. If one chooses to use

the local time system for measurements, the distance to the object is

simply the x coordinate of the object at that time. If the object is

stationary, the x coordinate will be exactly the same as in the galactic

system, because the distance in the galactic coordinate system will

not have changed during the passage of time between tL and t. The

measurement in the galactic system will be exactly the same,

Lx x , EQUATION 109

for stationary objects. However, if the object is moving, the position

will be measured differently for different velocities, according to


145

Lx x v t , EQUATION 110

where Δt is the galactic time difference between two events, like the

beginning and the end of a race. We would ordinarily presume that

Δt is a positive time difference, and time is progressing in the normal

fashion. The velocity, however, may be either positive or negative.

If it is positive, xL will be greater than x, and the object under

observation will be moving farther away from the observer, with the

distance increasing with time if the object is on the right hand or

positive side of the x Axis. If the velocity is negative, the distance

will be getting shorter, and the object is moving toward the observer,

if on the right hand side of the x Axis. When the time interval is zero,

Equation 110 reduces to Equation 109, as it does when the local

velocity is zero.

When observations of change in distance with time are made, the

changes are related by

2 1 2 1 2 1( ) ( )L Lx x x v t x v t x x . EQUATION 111

It is apparent that the measurement of length in both systems should

give the same results, regardless of velocity of the object whose

length is being measured. There is no shrinkage of the dimensions

with motion relative to the observer. Only if the object were actually

growing longer or shorter, would there be a difference when the

measurements made in the local system were applied to obtain values

to be used in the galactic system.

There is one possible ambiguity which arises if one presumes that

the measurement of distance in the local system should not be made

by taking the difference in the x values along a horizontal line,

representing a constant galactic time, but rather along the 45 degree

line representing a constant local time. The ratio of measurements of

the distances by these methods is obviously 2 , and would suggest

that distances measured at constant local time should be reported

higher by this ratio than the corresponding galactic distance. This

might well account for the energy of a mass “at rest” with respect to

Les Hardison

146

the observer being mc2 rather than mc2/2, as conventional dynamics

would have it. However, this would lead to some confusion, because

the local observer is only able to recognize the location of objects in

three dimensional space. So, for the remainder of the discussion, the

local distance xL will continue to refer to the distance between the

observer and the object measured as though both were at the same

galactic time.


147

VELOCITY IN THE TWO SYSTEMS

The measurement of velocity in the local system of coordinates is

quite straightforward, at least in the case of objects moving directly

toward the observer. It is simply the observed change in distance in

a measured time period. The time period is exactly that indicated by

the local observer’s clock. Remember that this clock always reads

exactly the same as the galactic observer’s clock at the observer’s

position at the origin of both coordinate systems.

It is a bit more complex in the case of objects moving away from the

observer, because he cannot observe future positions of the object

(neither “future” according to his own definition of the present time,

or in terms of the galactic present) because light simply does not move

from the future to the past. However, he can observe past positions

of the object at various times, and therefore calculate the speed of

the object prior to it reaching his present position. As all of this

discussion has been based on the assumption that we are dealing

only with objects which move at constant velocity, this doesn’t cause

any problem.

There is no way an observer can determine the velocity of an object

in the galactic present by direct observation, because he cannot see

anything removed from his location at the origin of the coordinate

system at the present moment in galactic time. What he really sees

are the items in his galactic past which are a part of the local present. But,

making the conversion from local velocity to galactic velocity is

perfectly straightforward, and has been dealt with in several previous

chapters.

The conversion is done according to

,

1

L

L

vv

v

c

EQUATION 112

regardless of whether the object is moving toward or away from the

local observer.

Les Hardison

148

The galactic velocity is always lower in value than the local value

determined by observation, and always appears to be less than the

value of c, the apparent speed of light, whereas the value of vL, the local

velocity, has no such mathematical limitation.

Thus, if the velocity is determined for an object in the local

coordinate system, the corresponding velocity can be calculated in

the galactic coordinate system.

FIGURE 35

PLOT OF GALACTIC VELOCITY VS OBSERVED LOCAL

VELOCITY

For velocities toward the observer, the velocity in the galactic

coordinate system are taken as positive in Equation 112. When the

velocity is away from the observer it is taken as negative, but is

subtracted rather than added, so the same equation applies to motion

in either direction.

Thus the galactic velocity will always be less than the observed local

velocities. This is illustrated in Figures 35 and 36, which show that

the velocity for the local system is always greater than for the galactic

system.

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

v/c

vL/c

v/c vs vL/c


149

If for example, the local velocity is c, the elapsed time will be twice

as long as the galactic system, while the galactic velocity will be half

as high (i. e., the galactic velocity will be only c/2. Conversly, if the

galactic velocity is c (as is usually assigned to the velocity of light) the

velocity in the local system is infinite.

FIGURE 36

GALACTIC VELOCITY FOR LARGER VALUES OF LOCAL

VELOCITY

Another way of comparing the velocities in the two systems is by

noting that the slope of the path relative to the T Axis is a direct

measure of the velocity. The value of the velocity is different for the

local systems, as indicated in Figure 34.

It is apparent that the vertical line, corresponding to motion which

coincides with the motion of the universe in the fourth dimensional

direction, involves no motion in our three dimensional universe, so

the local velocity is zero. Motion at 45 degrees to the x Axis

represents velocities which are infinite. Light moves from one point

in space time to another located along these 45 degree lines. The

velocity c measured in the local universe corresponds to c/2 in the

galactic universe.

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120

v/c

vL/c

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150

FIGURE 37

ARRAY OF LOCAL VELOCITIES

The same motions in referenced to the galactic universe, as depicted in

Figure 37, show the 45 degree slope, where

Δx = cΔt, interpreted as the velocity c. It apparent that to reach this

velocity, and object would have to be moving infinitely fast when

referenced to the local coordinate system.


151

FIGURE 38

ARRAY OF GALACTIC VELOCITIES

These charts illustrate the very great difference in the interpretation

of velocity in the two coordinate systems. It should be emphasized

that the velocity of matter at the time of the Big Bang and

subsequently has been c, most of which is directed in the fourth

dimensional direction. The velocities we observer in the three

normal dimensional directions are usually only a small fraction of

this. So, it is unlikely that any objects in the universe near our

location will have a velocity approaching c with respect to the local

coordinate system, which would appear to be only about c/2 in the

galactic system.

Les Hardison

152

TABLE 1

RELATIUNSHIP BETWEEN LOCAL AND GALACTIC

VELOCITIES

vL/c v/c=1/(1+vL/c)

0.0 0.0000000

0.1 0.0909090

0.2 0.1666670

0.3 0.2000000

0.3 0.2307690

0.4 0.2857140

0.5 0.3333330

0.8 0.4285710

1.0 0.5000000

2.0 0.6666670

3.0 0.7500000

4.0 0.8000000

5.0 0.8333330

7.5 0.8823530

10.0 0.9090910

20.0 0.9523810

30.0 0.9677420

40.0 0.9756100

50.0 0.9803920

75.0 0.9868420

100.0 0.9900990


153

By way of summary, the distance, time and velocity measurements

are all, of necessity, made within the local system of measurements,

and the conversion to the galactic reference system universally used

by engineers and physicists can be made using Table 1.

The concept of mass in the local system is completely different than

it is in the galactic system. In the latter, Einstein was led to the

conclusion that mass had to be a variable quantity for any physical

body. Were it not, he reasoned, a force tending to accelerate the body

long enough could cause it to reach velocities exceeding the apparent

velocity of light, c, and this was not, in his estimation, possible. So,

he derived the famous equation,

220 2

0 02

2

21

m c vE m c m

v

c

, EQUATION 113

in which m0 represents the “rest mass” of an object which is not

moving with respect to the observer, and

0

2

21

mm

v

c

, EQUATION 114

where m is the relativistic mass of the object. In other words, objects

become more massive as they are accelerated to high velocities

relative to the observer. This prevents the velocity of an object from

ever reaching the apparent speed of light, c.

In the local reference system, there is no limitation on how fast

things can move, although nothing can achieve the true speed of

light which is infinite. So, there is no need for the relativistic

conversion factor as it applies to mass.

There is no reason implicit in the geometry of the local system why

a mass could not exceed the velocity c, the velocity of expansion of

the universe in the fourth dimensional direction. However, there is

Les Hardison

154

a strong suggestion that the energy imparted to all matter by the big

bang, and accelerating it to the velocity c, would make it difficult for

any body with a substantial mass to be accelerated to a higher

velocity, simply because there is nothing of significant mass which is

already moving at a higher velocity than c.

In the local system, mass is simply mass, and it is not influenced in

any way by acceleration with relationship to any coordinate system.

There is, in the local coordinate system, no concern for what

happens to the mass of my lunch pail if someone chooses to use a

coordinate system moving a significant fraction of the apparent speed

of light.


155

ENERGY CONSIDERATION

The need for the relativistic increase in the mass of an object

accelerated to a high velocity with respect to any arbitrarily

established coordinate system was explained away in the previous

section. Along with the need for the increase in mass with velocity,

the need to modify the energy of a moving body so that the galactic

velocity could not exceed that of light also disappeared.

So, in the galactic system based on proper conversions of physical

measurements, there is no shrinkage factor applied to the energy of

an object at high velocity. The total energy is simply

2E mc , EQUATION 115

where the mass is invariant with velocity, and c is the apparent speed of

light, but actually the speed of the expansion of the universe.

The part of the energy that is observable in the local universe is the

part which represents a velocity in the three spatial dimensions we

can observe. Essentially all physical masses have the same intrinsic

velocity, c, with nothing to indicate that it is changing with time. The

velocities of all objects in four dimensional space are not perfectly

aligned with each other in the T direction (where time seems to be

pointed slightly different for one body than for another) and the

misalignment is what we recognize as observable velocity.

So, in the properly treated galactic system, there is no need to modify

the energy calculated on the basis of the local velocity to prevent the

violation of any physical laws.

Les Hardison

156

COMPARISON OF RELATIVISTIC AND LOCAL

VALUES

A relatively straightforward comparison of the local system of

measurement is given in the table below. In this table, the relativistic

contraction factors are shown where appropriate, and are used for

measurements of the position and velocity of a moving object even

when there is only a single reference coordinate system involved,

because this is how the contractions are used.

TABLE 2

COMPARISON OF LOCAL MEASUREMENTS WITH

CONVENTIONAL RELATIVISTIC VALUES


157

The values of local velocity, energy and mass may be calculated

either by using the time difference for a given distance traversed or

the distance traversed in a given period of time.

As has been demonstrated, the use of the relativistic contraction

factors for time, distance, velocity and energy, and for the increase

of mass with velocity, are artifacts of the misinterpretation of data

obtained by observation in the local universe. Were it properly

corrected to give the corresponding values in the galactic system,

rather than used without correction, a much simpler system could be

applied for the galactic calculations.

The proper correction factors are shown in Table 3 below. In this

table, the values actually measured in the local coordinate system,

but incorrectly assigned to the galactic system without correction,

are included with the subscript “A”, indicating that they are

“Apparent” values.

This table makes the point that there is no shrinkage in time for

moving objects. Instead, the time associated with the objects can be

alternatively the time read by our clock, as observers, or the time

read by a clock associated with the moving object, but read at an

earlier galactic time. Both readings are valid, and there is no conflict

between them, just as my clock may simultaneously indicate US

Eastern Standard time, and Universal Mean Time (Greenwich Mean

Time), without either reading being in error.

The length of moving objects does not shrink because they are

moving, but the local time associated with the two ends is not the

same when the object is moving with respect to the observer’s

position.

The velocity is not limited to the apparent speed of light in the local

universe, but the simple geometry of the expanding universe makes

it look like anything moving at infinite velocity in the observer’s view

is moving at the velocity c in the galactic universe.

Again, the velocity measurements may be taken as the distance

traveled in a given period of time common to both systems, or as

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158

the time required to traverse a given distance which is the same in

both systems. The energy and mass calculations are the same for

either method.

TABLE 3

GALACTIC VARIABLES CALCULATED FROM LOCAL

MEASUREMENTS

In Table 3, the velocity vA is understood to be unlimited, as it is

measured in with reference to the local coordinate system, whereas

v, the correct value in the galactic system, cannot exceed the apparent

speed of light, c.

The light is not slowed by its progress through empty space, because

it doesn’t really come through the empty space at all. It bypasses both

space and time in getting from the source to a receptor.


159

Because velocity is not limited to c in the local universe, the energy

an object can obtain is not limited, and could, theoretically, become

infinite in time. However, in order for it to do so, there would have

to be a massive object already moving at greater than the velocity c,

from which to transfer the energy. There is no evidence that massive

bodies with velocities above c exist in the universe although one

might suppose that, if one could travel a quarter of the way around

the universe, he would find that the bulk of matter there would be

moving at the velocity c referenced to our local coordinate system.

All things considered, I believe that the use of the galactic reference

system as the setting for physical events and objects is valid, but that

the translation from the local system of observation to the galactic

coordinates should be made so as to avoid the complexities of the

relativistic corrections and the misconceptions of how velocities,

masses and energy are interrelated in the galactic system.

Les Hardison

160

WHY THE SQUARE ROOT FACTORS?

These are the ubiquitous shrinkage factors which are applied in

Special Relativity to the measurement of time, distance, length,

velocity and mass. So far in this discussion, they have not appeared

to be needed. The question arises as to where they fit into the picture,

where do they come from, and what they actually mean.

It is easy enough to account for the appearance of these factors in

the development of Special Relativity. If one represents the motion

of an object or a point in space relative to the arbitrarily chosen

stationary reference system to describe the galactic universe, there are

two ways of looking at a velocity vector. One viewpoint is that of

the stationary observer, who applies his own time standards, and

reports distances as though he had determined them at the exact

instants in time read by his clock. This is, of course, impossible, as I

have pointed out several times, but it is necessary, if one is using

galactic space and time coordinates.

The other way of looking at the same velocity vector is from the

viewpoint of someone traveling along with the moving object,

whose own clock is used as the time reference, and who sees things

as located differently relative to his coordinate system.

Because the galactic system is, in a way, a fabricated system, really

outside our normal experience, it is a bit difficult to ascribe a

meaning to the observations which would be made by a moving

observer at any location along his path except at the exact same point

where we are at the moment. This is because any time we can actually

see him or obtain any information about him whatever is at a time

he would regard as in his past. His present is in our future.

But, supposing we both observed his path through space, each using

his own clock and distance measuring tools but each of us had the

god-like ability to see how the world actually is at the present

moment in galactic time.


161

FIGURE 39

COMPARISON OF REFERENCE SYSTEMS

We could compare our measurements and see how they differ. This

is most easily pictured with the help of Figure 39.

Here, the velocity of the moving observer is depicted according to

his reference system which is moving along with him. His clock is

synchronized with that of the stationary observer, as they will read

the same when their paths cross, and the origins of their two systems

are located in exactly the same place. Each clock will read the time

at the horizontal galactic x Axis it is crossing, which physically

coincides with the surface of the two dimensional balloon

representing our three dimensional universe.

Each will presume his own velocity in his T direction is c, the apparent

speed of light. So, the moving observer will take the hypotenuse of the

triangle as equal to ctL, using his local time, and assuming he has no

velocity other than this. However, he will agree that his velocity

could consist of any two components at right angles to each other

which add up to his velocity.

The vertical side of the triangle, paralleling the motion of the

stationary observer and the horizontal side, representing the velocity

assigned to his motion by the stationary observer, are two such

components. The moving observer agrees that his stationary

position in space may be represented by the two vectors the

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162

stationary observer assigns to him. These are, of course the same

vectors, but the viewpoints are different.

In particular, the stationary observer sees the vertical component as

c, the apparent velocity of light. The moving observer views this

same velocity as

2 2 2 2'ct c t v t , EQUATION 116

so

2 2 2 2 2 2'c t c t v t , EQUATION 117

or

2

2

'1 .

t v

t c

EQUATION 118

This can also be expressed in terms of the time differences between

two events, presumably observed by both the stationary and the

moving observer.

2

2

'1 .

t v

t c

EQUATION 119

This suggests that the moving observer’s clock must run slower than

that of the stationary observer. This is, however, a total misreading

of the situation based on the presumption that we live in and observe

events which take place in the galactic frame of reference. Nothing

could be further from the truth. In actuality, everyone’s clock runs

at exactly the same speed, but when we see a distant clock, we do

not see it in the galactic present time, but rather in the galactic past,

and the distance in the past is proportional to how far it is away from

us in space. So, the correction we make for the speed of their clock

is a reflection of our misunderstanding the circumstances under

which we are reading the clock. It is not a measure of change in the


163

performance of the clock, but rather a measure of our error in

perception.

Thus, if we observe a distant clock far away from us, but stationary

(not changing in distance from us with time) the clock would appear

to be running in synchronism with ours, as it truly is. But set at a

different time.

However, if the far away clock is moving relative to our position,

then it is either going farther back into the galactic past or moving

closer to our galactic present time as we make subsequent

observations of the time it reads. The rate of change of the readings

will differ from those of our local clock, although the two clocks are

running at identical speeds. The time contraction factor is an illusion,

brought on by the failure to differentiate between the local system in

which the measurements are made, and the galactic system, to which

we mistakenly attribute the measurements.

We need not expect to see our astronauts who eventually depart in

spacecraft which move through space at a significant fraction of the

apparent speed of light to return to earth much younger than their

counterparts who remained behind. They will age exactly like we do,

who only wait out their return.

Once the shrinkage factor is applied to time, in the galactic system,

the other measureable quantities, velocity, energy and mass all have

to be corrected also. So, the ubiquitous shrinking factor gets into

every aspect of physics. However, while it is easy enough to

understand that the shrinkage of time, it is difficult to grasp the

concept of physical lengths of objects also shrinking, and mass

increasing as the velocity of the object increases.

A CREDIBLE MISTAKE

The relativistic correction factor as it is ordinarily used is not limited

to the calculation of how the universe would look with respect to

someone else moving relative to our own “fixed” position. It is, in

fact, attributed to anything moving relative to our own point of

Les Hardison

164

reference. That is, if we want to make calculations of the force

required to deflect an electron from its path when it is moving at

appreciable speeds relative to the apparent speed of light, we customarily

apply the relativistic factor, F, to the mass of the particle. We are not

looking at the properties with respect to a second reference system

moving relative to us, but simply of an object moving relative to

ourselves, in our own system, with no second reference system

entering into the picture.

As followers of Einstein, we understand that the mass of the particle

must increase as its velocity approaches the apparent velocity of

light, and we need the correction factor to make the laws of physics

produce calculated results in tune with what we observe.

This seems to be true even if there is no second coordinate system

involved, and the derivation of the F factor derives directly from the

assumption of a second reference moving with respect to our own,

and observing the speed of light to be constant when measured by

observers using the two separate reference systems. The question is,

why do these corrections seem to apply in a situation entirely

different from that for which they were derived?

I think I have an explanation for how this comes about, but it

requires a bit of speculation. I believe that the ubiquitous F Factor is

there because of a chronic and nearly universal use of the measured

local distances as though they were really galactic distances. While

they are distinctly different quantities, the differences between them

are not important for objects which are essentially stationary or

moving at relatively low velocities (compared to c) relative to the

observer. All of our day to day observations fall into the category

where there is little difference between the systems. When we hit a

baseball with a bat, we do not need to take into account that, by

relativistic standards, it becomes slightly more massive as the velocity

increases.

The failure to change points of view when dealing with fast moving

objects or objects very far away from us is quite understandable.

There is no clear-cut dividing line between the situations where


165

relativistic corrections are important, and when they are not. Failure

to shift points of view, when it is appropriate to do so is a very

understandable mistake.

I will try, in the following paragraphs, to explain how the mistaken

use of the measured local distances and velocities, rather than the

correctly calculated galactic quantities, leads to an error in the

galactic frame of reference which requires the use of a correction

factor which is exactly equal to F. This accounts for the need to apply

the correction factor to objects moving with respect to a single

reference system.

Les Hardison

166

THE F CORRECTION EXPLAINED

We may begin by looking at a body moving with an appreciable

velocity toward an observer in the local universe, as depicted in

Figure 40. I would like to look at the time required for the object to

move a specific distance, both from the standpoint of the local

observer and the fictional galactic observer. When the object

depicted is at point A, the galactic observer sees it as being on the

lower horizontal line, representing the x Axis at galactic time t = 0,

the starting point of the observation. The local observer does not

see the object to be at point A at this time, but at a later galactic time,

A’, with the time interval defined by the distance the object will move

to reach point B, which is the same for both systems.

FIGURE 40

AN OBJECT IN MOTION WITH RESPECT TO THE OBSERVER

AT THE ORIGIN

For the distance moved, Δx, to be the same for both systems,

L Lx v t v t . Equation 120


167

Because both observers see the object move the same distance, their

velocities are, necessarily related by

L

L

tv

v t

. EQUATION 121

The relationships worked out previously for use in calculating the

galactic velocity from the observed local distance of movement of

the object and the measured local time period still apply, even

though the conditions of the example have been altered somewhat.

These relationships are

1

1 LL

v

vv

c

, EQUATION 122

and

1

1

Lv

vv

c

. EQUATION 123

However, in this example, we will substitute the ratio of times

required for the object to move a specified distance for the ratio of

velocities, so

L

L

t v

t v

, EQUATION 124

and

L

L

vt

t v

, EQUATION 125

so

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168

1

1L

t

vt

c

, EQUATION 126

and

1

1

L

L

t

vt

c

.

.EQUATION 127

In the latter equation, we assume that the observer has measured the

local velocity but mistaken it for the galactic velocity. So, we may

simply drop the subscripts and call the velocity “measured” by the

local observer the velocity, v.

Now, to evaluate the relationship between t, the correctly calculated

galactic time period and tL, the local time period measured, one can

simply take the product of the expressions in Equations 126 and 127,

to obtain

2 1

1L

v

t cvt

c

. Equation 128

The evaluation can be simplified by multiplying the numerator and

denominator of the fraction on the right side by the quantity

1v

c , EQUATION 129

to obtain


169

2 2

2

2

2

1 1

1 1 1L

v v

t c c

v vt v

c c c

, EQUATION 130

from which one obtains

2

2

1

1

A

L L

v

tt c

t tv

c

. EQUATION 131

One can interpret this ∆tA value as the apparent value of the galactic

time, and compare it with the true value as obtained from

1

1

Lt

vt

c

, EQUATION 132

to obtain

2

2

11

11

A A L

L

vt t t c

vt t t vcc

, EQUATION 133

or,

2

2

1

1

At

t v

c

. EQUATION 134

Or, one could simply compare Equation 134 with the value used for

the Einsteinian time correction given in Table 3, which is

Les Hardison

170

2

2

1

1L

v

t c

t v

c

, EQUATION 135

and note that this is exactly the expression derived when the

measured values of time and distance obtained with reference to the

local system are used without adjustment to represent the galactic

values, but where the velocity in the table was for an object, or

system, moving away from, rather than toward, the observer.

In short, the Einsteinian shrinkage factor applied to time differences

appears to be entirely due to making measurements in the local

system, which is the only one actually available, and using them,

without modification, as though they were obtained in the galactic

system.

As has been pointed out several times, the correction factor, F,

which must be applied to time measurements, requires similar

correction factors for the measurements of position, and velocity,

and leads to the presumption that, size and velocity of objects

decrease with increasing velocity and that time and mass grow larger

for objects moving with respect to the observer.

The galactic time period used for velocity measurements is always

longer than the corresponding local time period for a given distance

traversed, so the galactic velocity is always lower than the local

velocity. Misusing the local distance measurements, and using them

as galactic measurements, causes the velocities to come out lower

yet.

The one application which is not explained is that pertaining to the

increase in mass of moving objects, generally cited as


171

0

2

21

mm

v

c

. EQUATION 136

This does not relate directly to the measurement error described for

the distance, time and velocity measurements. It comes, instead,

from the postulate that “nothing can move faster than c, the apparent

speed of light.” The application of a force of any magnitude for a long

enough time would necessarily accelerate the mass to a higher speed,

unless, of course, the mass were to increase so as to prevent it from

reaching the velocity c.

I have maintained that nothing can appear to move faster than c when

measurements are properly translated to the galactic reference

system, but that, when measured in the local reference coordinate

system, light actually moves at infinite velocity. The velocity of

massive objects obviously cannot exceed the true speed of light. The

kinetic energy of masses is not limited and the mass measured in the

local universe need not increase as the galactic velocity increases.

While this is all a matter of perception, I believe it is factual that most

measurements of physical properties are made, of necessity, in the

local system, where what we can see at the moment comprises the

universe, and that the local measurements are often used directly,

without modification, instead of being converted to the

corresponding galactic values in a systematic way.

Les Hardison

172

CHAPTER 8 CRITIQUE OF SPECIAL

RELATIVITY

While I think Einstein did a remarkable job, taking on the problem

of the day for physicists and astronomers and producing the Special

Theory of Relativity, I believe he would have done things a bit

differently were he working on the same problem today. The critical

difference is that it is now relatively clear that the universe is

expanding, which suggests that it is moving into a fourth spatial

dimension related to time. In turn, the inclusion of a universe

moving through a fourth dimension in space allows us to speculate

that it is this velocity which was measured by the experimenters who

were trying to determine the speed of light.

In this section, I am going to make an unfettered criticism of the

Special Theory of Relativity, as though it were done by a present day

student trying to make a good impression on his teacher, rather than

the modern era’s most brilliant theoretician. I will assume that the

velocity the universe in the fourth dimensional direction is c, and

that the velocity of light is infinite.

CONSTRUCTION OF THE BASIC DIAGRAM

Let me take Einstein’s approach step by step, and examine each in

terms of the knowledge that the universe is expanding, the

assumption that it is expanding at the velocity c in a direction at right

angles to the three ordinary spatial dimensions.

Let’s start with his diagram, as previously shown in Figure 40. For

purposes of simplicity, the x direction is chosen to be the direction

of a beam of light, and since light can move in any direction from

our position to wherever it is going, there is nothing wrong with

defining our x Axis to be that direction.


173

FIGURE 41

REPEAT OF EINSTEIN ’S TIME-SPACE DIAGRAM6

I have no problem with using a diagram like this to represent the

relationships between any sort of measurements one could make,

and both distance and time are measureable quantities. We have to

make sure we define what we mean by the variables, and abide by

the conclusions we draw that are consistent with the definitions.

The value of t presumably has to do with the measurement of time

using a clock of some sort, which is near at hand, and represents the

time at our point of observation, x = 0. The value of x represents

the distance from our observation point to any object not at the

origin on the graph. Because time is used as the ordinate, there is an

implicit understanding that the other two of our three spatial

dimensions, y and z, are zero, so far as the diagram is concerned.

6 Albert Einstein, Relativity, the Special and General Theory, Translated by

Robert W. Lawson, Crown Publishers, New York, NY, 1918

Les Hardison

174

Einstein chose time for the ordinate – the vertical scale – in his

diagram, and used x as the abscissa. He didn’t assign units to either

explicitly, and presumed, as physicists often do, that the reader

would, if necessary, supply his own. Here the implicit assumption is

that any consistent set of units will work.

Finally, by placing the intersection of the x and t axes suggests that

the observations of time and distance are made from this

intersection --- the origin on the graph --- and that both the time and

distances have the value zero at this location. Thus it looks like the

measurements may be made with things like a tape measure and a

stop watch.

IMPLICATIONS OF THE DIAGRAM

However, he did choose a pair of scale factors for the time and

distance axes that appears to be more than a random selection, and

we need to look at this selection in detail.

There is a wealth of information in the construct of this simple chart.

First of all, we should consider that when one makes a picture like

this, it can be intended as simply a way of illustrating a correlation

between two variables. For example, the annual average price of corn

can be plotted against the annual average rainfall in the Midwest for

a number of years. In this case it is perfectly clear that there is no

intention to depict any physical relationship between prices and rain,

only the numerical relationship, if there is one.

On the other hand, one could draw sketch of a man walking, and

plot the distance he travels vs. time. Now there is a physical

relationship between the variables, not just a statistical one. If he

walks at a constant speed, his path, on a plot of distance vs. time,

will be a straight line. If he changes his speed occasionally, the slope

of the line will change.

In either case, there is a great deal of latitude in the choice of scales,

and one can select whatever scale factor is convenient to show the

intended relationship to best advantage. For example, if the time

scale for the man walking is chosen as 0 to 3 hours, and he walks


175

three miles per hour and then stops, it is convenient to choose the

time scale to cover a little more than the three hour period, say 0 to

4.5 hours, and the distance scale to cover 0 to 5 miles. This will show

his whole journey, and that he stopped at a point well within the

range covered by the graph.

Einstein, in drawing his graph, chose to use the distance from the

light source to the receiver as the abscissa, and the time as the

ordinate, suggesting that the data represent measured times at which

a beam of light originating at the origin would reach a series of

measured distances from the origin. This is what one might use to

plot the progress of a race horse or several race horses, moving

around a track, with the time measured at various fixed points along

the track and again at the finish line, which is at the same location as

the starting gate. This follows the test methods used to measure the

speed of light, which timed the interval between the emission of the

light and its return to a receptor a known distance away. It underlines

the belief by both the experimenters, and Einstein, the theoretician,

that light moved gradually through empty space, like a fish swims

through water.

Further, if time is presumed to be at right angles to the x Axis, and

the x Axis serves as an analog for the entire three dimensional

universe, it suggests that, in addition to being a completely abstract

relationship between time and distance measurements, Einstein had

some inkling that time is, as I have been proposing, a kind of fourth

physical dimension, and it is at right angles to the three we ordinarily

perceive.

SUBSTITUTING T FOR TIME

Further evidence in this direction is the fact that the line describing

the path of a beam of light in the x direction is at 45 degrees to each

of the two axes. This has to be more than coincidental. The only

circumstance under which the line will come out at 45 degrees is

when light moves an equal “distance” through time as through

space. That is, the unit in which time is measured has to be the same

as the units used to measure distance. This can only be if there is a

velocity associated with time, i.e.

Les Hardison

176

T Vt . EQUATION 137

Where:

T= distance in the fourth dimensional direction

V=the velocity of light

t=time.

Now the abscissa has linear distance as its units. Still, in order to

make the 45 degree angle possible, for a measured speed of light

numerically equal to c,

V c , EQUATION 138

Or

T ct . EQUATION 139

So, I think Einstein must also have had in his mind some inkling of

the relationship between his simple time function and the notion that

the universe is expanding in the same direction time is flowing, and

further that it might be going that direction at the velocity c, which

was measured as the speed of light in a vacuum.

We can redraw his diagram so that it incorporates these implied

characteristics as shown in Figure 42.

In my picture of the local universe, Einstein’s t for time is replaced

with my T for distance in the direction the universe is expanding.

Also, it is apparent that, in choosing the scales for time and distance,

he selected scale factors which include the apparent speed of light, c as

the ratio of one time unit on the graph to one distance unit. Thus his

line representing the motion of a light beam away from the origin,

x ct is a 45 degree line upward to the right on the positive side

of the graph, and

x ct , upward to the left on the other.


177

FIGURE 42

T DIMENSION SUBSTITUTED FOR TIME

This is exactly the same graph one would get if the t Axis were

replaced by an Axis on which T=ct, a distance, and the units for

distance on both the T and x axes were identical.

Somehow, it seems that these considerations were implicit in the

simple graph which was used to illustrate the basic Lorentz

transformation used by Einstein.

While Einstein apparently had no intention of implying that he was

depicting the physical universe, rather than just the relationship

between distance and time for a beam of light, he chose his basis

quite consistently with my picture of the local universe, which is

aimed at depicting the physical relationship. In other words,

Einstein, too, drew something of a physical picture of the universe

as he saw it and which resulted in his ground breaking theory.

THE MEANING OF T

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178

Now, we get into the meat of the matter, which is about what the

variables depict. Because the origin is chosen at t = 0,

x = 0, there is no suggestion that the origin is moving in the t

direction. This implies that the values of time, t, represent values of

time subsequent to the present time, or times in the future of the

observer at the origin. The origin is not moving into the future, so it

must be the difference between the time at the origin and a later

time. In short, it is the reading on a stopwatch of sorts held by the

observer at the origin.

Thus there is the implicit assumption that the x Axis is where the

present time is defined as zero, and anything on the x Axis is at the

same time as the observer at the origin. In short, t, and therefore T

= ct, are constant, and equal to zero anywhere along the x Axis. All

positive values of t or T represent objects or events at a later time

than at the origin, and the entire x Axis at this zero time.

The universe at the present moment (where the x Axis is located) is

not moving into the future. The universe is static and unchanging

with time, at least in this picture. I think this is consistent with

Einstein’s thinking at the time, and that of most other physicists. So,

Einstein did not think it necessary to make his ordinate a physical

space dimension, or to consider the problem of where the origin was

moving in time, because he considered it fixed.

Still, he must have had some inkling that the fourth dimensional

direction, which was related to time, also had to be related to

distance. From which it is a very short step to saying that the ordinate

should be ct = T, rather than just t.


179

WHICH WAY DOES LIGHT TRAVEL?

A second major difference between what Einstein did, and what I

think he would do were he dealing with the same problem today, is

that he elected to show the light beam in his diagram moving away

from the origin, rather than toward it. I think it is apparent, on

reflection, that you cannot see a light beam moving away from you.

When you shine a flashlight into the midnight sky, you do not see

the beam of the flashlight cutting through the darkness. What you

may see is the reflected light from particles of moisture or dust, or

what have you, but the light itself is invisible to you. You simply rely

on your past experience with light to believe that it is moving away

from the flashlight. You cannot verify this by direct observation.

Only when it shines on something in your field of vision can you be

sure, by direct observation, that the light went where you supposed

it would. And then you are not seeing your light, but rather the light

emitted by the reflecting surface, in response to the energy imparted

to it by the light you directed to it.

So, I would have drawn the figure upside down. That is, with the

light moving toward the origin from some point in the past. It does

not really matter when in the past, or how far away from you the

light originated was, when you saw it. You would believe it

happened, and could verify that you had seen a light from a particular

direction, at a particular time. Specifically at the right now, zero time

at the origin.

So, my picture looks like I think Einstein should have drawn his, and

probably would have, if he were doing so today rather than a

hundred plus years ago.

Les Hardison

180

FIGURE 43

UPSIDE DOWN LORENTZ DIAGRAM

In Figure 43, the light appears to originate at some distance from the

origin, at some time in the past. With only one directional dimension,

x, it could be either directly to the left or to the right. The distance

from the observer at the origin would determine how far in the past,

according to

x v

T c

. EQUATION 140

In Figure 43, there is still no implication that the x Axis represents

the three dimensional universe, or that the time is anything other

than zero for all points along the x Axis.

Also, in Figure 43, the observed light had come to you, as the

observer at the origin, in an essentially straight line from somewhere

along the line x ct .

Here x is a positive distance to your right, and t is a negative time.

So the farther in the past the object of event was – the time interval

Δt - the farther away to the right the source must have been. Of

course, the light could have been on the other side of you, so it would


181

have come to you along the line x ct , where the negative time

values produce negative distances, or distances on the left side of

you.

The diagram looks much the same as Einstein’s, but now the source

of the light is presumed to be some place other than the origin, and

the receptor is at the origin. This way, the observer at the origin can

see the light arrive at his location, and by one means or another,

measure the distance of the source from his position. The problem

is, how does he know the time at the point of origin of the light, so

that he can determine the velocity of the light? This was addressed

in the experiments by Michelson and others.

Les Hardison

182

SEEDS OF DOUBT

In the experiments performed to measure the apparent speed of light,

the experimenters set up an apparatus consisting of rotating mirrors

which would direct a beam of light momentarily toward a second

mirror at a known distance, and measure the time at which it

returned to the rotating mirror source. In order to show the essence

of this experiment on the original graph used by Einstein, one would

use his original diagram with the light initially moving away from the

source at the origin.

Let me propose the thought experiment, where the observer at the

origin of the diagram in Figure 44 is intent on measuring the speed

of light, using a mirror placed at a distance, x to reflect the light back

to his position, so he can measure the elapsed time between the

emission of the light and the receipt of the reflected light. In Figure

44, the mirror is shown at a single location, but, like all other objects

in the universe, it also exists at all of the points along its path through

space-time in the T direction.

FIGURE 44

EINSTEIN’S PLOT WITH MIRROR EXPERIMENT


183

The only location of importance in the picture is that at which it

intersects the beam of light presumably emitted from point A for

only an instant.

The experimenter sends the light beam off along the x ct path,

and at known distance Δx, it is reflected back toward his location.

The progress of the light beam from point A, at the source of the

light, in the experimenter’s laboratory at the origin, is just as Einstein

pictured it; upward to the right at a 45 degree angle. However, when

it strikes the mirror, it is not reflected backward through time to the

observer’s location at the origin, but rather continues upward to the

left, because light never goes backward into the past. It always moves

from the past toward the future.

When the light reaches point c, the time elapsed will be given by

2 xt

c

, EQUATION 141

and the velocity will be calculated as

2.

2

x xv c

xt

c

EQUATION 142

While this is the right answer, the researcher would never know it, if

he were fixed to the x Axis at 0t as shown in the graph. The only

way he could receive the light reflected from the mirror is if he and

his apparatus and the x Axis had also moved the distance 2Δx in the

T direction during the time it took the light to get there.

Thus, the graph used in the application of the Lorentz

transformation to the problem of the invariance of the speed of light

has a basic inconsistency in it.

Les Hardison

184

THE SPEED OF LIGHT

The thing that has to give here is the assumption that “light moves

through pace at a fixed, finite velocity c”. This has a flaw in it

somewhere. This doesn’t invalidate the results Einstein got using the

Lorentz transform to interpret his input data, but it does tend to

invalidate the input data.

If one makes the assumption that the universe is expanding at the

apparent speed of light, c, and the time represented by Einstein’s diagram

is the absolute time, or galactic time, as I have called it, then the

origin, and the observer, and the x Axis, are all moving upward in

the T direction. The x Axis, where the time is t = 0, must be moving

upward at the same velocity as the origin.

The line representing the motion of light away from the origin must

be replaced by x vt , where v must necessarily be greater than or

equal to c, otherwise the source of the light would be “catching up

with” the light beam as it moved away, and the light would be

moving from the future into the past.

Einstein suggested this himself, saying that if c, the apparent speed of

light, were infinite, the equations of Special Relativity would reduce

to the Newtonian equations for distance, velocity and energy. This

was, of course, because the ubiquitous F factor in all of the equations

of special relativity would become exactly 1, regardless of the

velocity of the object.

This could not be the case, he reasoned, because light would then

not be observed to move at the same velocity when observed by two

experimenters moving at a finite speed relative to each other. But,

this is exactly what happens, if one presumes that it is the universe

itself, moving in the fourth dimensional direction, which is traveling

at the velocity c.

So, there was a built-in problem with Special Relativity, which would

require the observer to be moving along with time, but at the same

time would not allow the x Axis, on which he was located to be


185

moving with time if the constancy of the speed of light was a true

representation of the situation.

In short, the error seems to have been in presuming that the only

way of accounting for the apparent invariability of the speed of light

was to presume the measurements of the speed was accurate, and

that the universe were constructed rather peculiarly so as to limit the

speed of everything to the value c. Light just happens to be the only

thing that seems to move this fast. This is the reason it appears that

the speed limit which applies to light also manages to limit the speed

of everything, including electrons, space ships and the effects of

gravitational attraction, to c, the apparent speed of light.

To make a more consistent picture of the situation, Einstein would

have had to modify his viewpoint, but not very radically. In

particular, he would need to adopt the notion that one makes all

scientific observations in terms of the local universe he perceives. It

is not in terms of a universe in which time is everywhere exactly the

same, and “right now” does not include anything in the universe that

one can actually see “right now”.

So, it is much more reasonable to view the points on the x Axis as

being those which can be seen from the origin at the particular

instant of time. Thus at 0t , one can see to the left and right all of

the points that are located in the galactic past, along the lines

x ct to the right, and x ct to the left, as shown in Figure 44.

Les Hardison

186

FIGURE 45

LINES OF SIGHT FROM ORIGIN

Here, it is apparent that the observer at point A can see objects or

events happening at his local present time, t1, at any distance to his left

or right, and that the time along this line is earlier in galactic time for

greater distances in either the positive or negative direction. That is

to say, if the observer at point A sees a point at a distance to his left

or right, and could read the time on a clock at the point, it would

read an earlier time than his own clock reads.

This is exactly what I have called the local time viewed by the observer,

at A, and the objects and events visible to him comprise his local

universe. The observer can see and attest to those things which are

visible to him at his position and time t1.

It is also apparent that, to the observer at A, his present time is the

same time as would be reported anywhere along the xL Axis, were

he interpreting his sightings according to the galactic system of

Einstein and others. However, he cannot see an object at A ' which

is still in his future. A light switched on at position A ' in space

would not be seen by the observer while he is at A. He would report

seeing it at some later time which is still in in his local future while

he is at A.

The light would appear to be switched on when the observer has

progressed to point B. He would attest to the fact that the light

arrived at his location at his local time t2. From the diagram, he would

infer that it left point A and arrived at point B at the same local time.

In short, it traveled the distance between A and B in zero elapsed

local time.

The observer who references his observations to the galactic universe

described by Einstein would report the speed of light as the distance

from B to A, divided by the time difference between x1 and x2 which

would produce the value for the apparent speed of light, c, but which is

actually the speed of expansion of the universe.


187

TRANSVERSE MOTION NOT CONSIDERED

It is important to note that any motion in this limited one

dimensional picture must either be toward the observer, away from

the observer or stationary with respect to the observer. This is not

the case in the real three dimensional universe, where objects can

move freely in other directions. In particular, transverse motion,

which is neither toward nor away from the observer at the origin,

has not, as yet, been dealt with. This is a serious omission from

Special Relativity.

If a body is moving away from the observer’s present position, it is,

in effect, moving into his future. He will not be able to see any of its

future positions until he, the observer, has moved into the future far

enough that the now-present position of the moving object is in his

past. Objects moving toward him lie entirely in his past as they

approach, and are fully observable.

Objects moving transverse to the origin at any given moment are

neither moving toward nor away from the observer, and therefore

are in his present at the moment, just as are stationary objects. This

has some special consequences.

My last and final comment on the development of Special Relativity

has to do with the omission of any discussion of motion transverse

to the origin of the observer’s coordinate system. Motion of an

object relative to the observer at the origin generally consists of both

a radial component (which is the component of velocity either

directly toward or directly away from the observer) and a transverse

component, which is at right angles to the radial direction.

By selecting the observer at the intersection of the x Axis and the t

Axis in the two dimensional diagram, and presuming that light

emanated from the origin and moved into space, only motion which

was directly away from the origin was considered. Motion toward

the origin is seemingly included in the analysis, because the positive

value of v, the velocity away from the origin is simply replaced by –

v for a system or object moving toward the origin.

Les Hardison

188

The motion of light through space is considerably more complex

than this, because light moving in either direction in the three

dimensional space has an essentially infinite velocity in the T

direction, so there is a difference in the way the apparent velocity of

light must be viewed if it is moving away from the observer, as

depicted by Einstein, rather than toward to observer.

Transverse motion is another completely different case which arises

when motion is not directly toward or directly away from the origin.

This kind of motion cannot be depicted in the two dimensional plot,

where one of the dimensions is time, or the time-like fourth spatial

dimension. If the only dimension pictured is the x dimension,

motion can only occur along the x Axis, and it must either be toward

or away from the origin, and the presumed observer at the origin.

However, this does not represent the real world in which objects can

move at right angles to a line between the observer at the origin and

the object.

This is the case where an object may be moving toward the origin,

but not on a collision course with it; like an asteroid approaching

earth, but, fortunately, missing it by a million miles. This would not

fit into Einstein’s simple picture used in the development of the

equations of Special Relativity, and there are important

consequences of the omission.

In order to take the possibility of transverse motion into account,

Einstein’s simple two dimensional diagrams would have to be

augmented to include at least a third dimension. All three dimensions

cannot easily be drawn without crowding out the T dimension,

which we really need for relativistic calculations. But, two spatial

dimensions, x and y, are simple enough, and one presumes that the

z dimension, which completes our world, is taken as equal to zero

throughout the discussion.


189

FIGURE 46

ILLUSTRATION OF TRANSLATION

The three dimensional plot with x and y representing the expanding

universe, like part of the surface of a balloon being blown up so the

surface is expanding in the direction at right angles to the surface,

labeled T in Figure 46.

In this figure, the two horizontal planes correspond to the horizontal

x Axis in the diagram representing the galactic reference system. A

couple of inverted Vs are included to remind us of the local universe

system coordinate axes.

Here one can see not just the two dimensional x–t or x–T diagram

in which it is presumed that 0y z , and that these dimensions

are unimportant. When both x and y are assigned real value, the x

Axis becomes the x–y plane. Within this plane, motion can be

toward the origin or away from it, as in the simpler x - t diagram.

This is ordinarily called radial motion, as it would take place along a

radius extending out from the origin.

However, when the x – y plane replaces the x Axis, it is now possible

to depict transverse motion which is at right angles to any such radial

Les Hardison

190

line. Motion of an object that is perpendicular to the particular radius

on which it lies relative to the origin does not, at the moment, bring

the object closer to or move it farther from the origin.

It is a fundamental principle of the science of dynamics that any

motion can be defined as a combination of one component of

velocity in the radial direction plus another component in the

transverse or tangential direction relative to any arbitrary point in

space. Everything that has been said about the relativistic time

contraction/expansion applies only to radial motion.

This is such a significant feature of Special Relativity as it should be

written that I have devoted a separate chapter to the transverse

motion, and in particular to a special case of transverse motion

which is described as orbital motion.


191

PURE TRANSLATION

Pure translational motion of an object relative to a reference point

or observer who is considered stationary only occurs in special

circumstances.

For an object moving in a straight line at a constant speed, the

motion almost always consists of a radial component which is either

directly toward or away from the observer, plus a translational

component which is at right angles to the radial component. Pure

translation only exists for the brief moment when the moving object

is at the closest it will ever be to the observer, at which time the radial

component is exactly zero. At all other times, the distance to the

observer will be as illustrated in Figure 47.

FIGURE 47

PURE TRANSLATION

Here an object depicted at point 1 at time t=t1 is shown moving to

point 2 at t=t2. The path of the point relative to the origin is such

that it passes the origin at t2, where it is the closest it will ever get to

the observer at moving along the T Axis.

Les Hardison

192

At any time, the distance from the observer to the object is given by

22

0 0( x yr x v t y v t . EQUATION 143

It takes a bit of thought to recognize that the equations of Special

Relativity were all derived using the radial distance from the observer

to the object or moving system as the only dimension. Thus, we

could substitute r, the radial distance, in any of the equations without

distorting the meaning of them, provided, however, that there were

no transverse component to the velocity.

The equations do not hold if there is a translation component to the

velocity, and the task here is to determine what the different is when

translation is taken into account.

The distance to the object is obviously the minimum when the

velocity component in the radial direction, vx, is zero, and the

velocity in the y direction has just offset the initial distance from the

y Axis. In short, when 0r x .

The relationship between the radial and translational velocity

components for an object moving in the positive y direction past a

stationary observer at a distance x0 from the path line of the moving

object is shown in Figure 46.

It is apparent that the vector velocity in the y direction can be

resolved into components in the radial direction, toward the origin,

and the transverse direction, perpendicular to the radial line to the

object.


193

FIGURE 48

RADIAL AND TANGENTIAL COMPONENTS OF VELOCITY

EXAMPLE

These components are

22 2

2

1sin

1

rv y

xv x y

y

, EQUATION 144

and

22 2

2

1cos

+1

tv x

yv x y

x

. EQUATION 145

For illustrative purposes the radial and transverse components of

velocity are calculated for an object moving along a path at 10y

at a velocity of 5 meters per second. The radial and transverse

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194

components of velocity relative to the origin are plotted in Figure

49.

FIGURE 49

RADIAL AND TANGENTIAL COMPONENTS OF VELOCITY

EXAMPLE

The transverse velocity is not much of a factor except when the

motion is nearly at right angles to the radial line between the object

and the origin. In Figure 49, it is apparent that the radial velocity

becomes close to the velocity of the object when it is far from this

point. On the other hand, the transverse velocity, which is not much

of a factor when far from the point of closest passage, reaches its

maximum, just equal to the total velocity, when the point of closest

passage is reached.

Now, at, or near this point, the object is not moving toward or away

from the origin at a significant velocity, and the time rate of passage

observed on a clock carried along with the passing object would be

just equal to the rate of time on our clock.

-4

-2

0

2

4

6

8

10

-10 -8 -6 -4 -2 0 2 4 6 8 10Ve

loci

ty, m

ete

rs/s

eco

nd

Tme, seconds

Radial velocity, vr

Transversevelocity, vt


195

That is, the rate at which the local observer sees the clock associated

with the object is running neither fast nor slow, but is keeping time

at exactly the same rate as his own. It does not read the same time,

but sees it as being slow by the amount of time proportional to the

distance of passage.

0'x

t tc

. EQUATION 146

However, at this point in time, where the path of the object through

space is purely translation, there are no relativistic corrections except

that for the error in clock reading due to its distance from the

observer.

This would not be of very much importance were it not for a special

case in which translation is essentially the only kind of motion

involved. This is the case of orbital motion, where one body is

orbiting another. We are continuously involved with orbital motion,

as describes the motion of the earth around the sun, and also the

electrons around atomic nuclei, of which everything is made.

The whole next chapter of this book is devoted to this special case.

SUMMARY

Einstein did a remarkable job of explaining how light could appear

to be moving through space at the same velocity when measured by

two observers moving relative to one another. In doing so he

introduced new concepts that changed the whole complexion of

physics, and continues to be the foundation on which most of

physics, astronomy and quantum mechanics are based. The new

concept was that time is not the same for all observers.

However, in the development of Special Relativity he accepted as a

basic premise that the speed of light in a vacuum was a finite and

invariant number, independent of the motion of the measuring

apparatus. He did not accept the alternative explanation --- that the

speed of light was infinite, and the measurements of the apparent speed

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196

of light were actually measurements of the rate of expansion of the

universe, or more concisely, that time is simply a measure of the

position of the universe in the fourth directional dimension.

His application of the Lorentz Transformation introduced several

inconsistencies which might have provided clues to the questionable

nature of his input data.

He might well have:

1. Tried to conform the Lorentz Transformation diagram to

the physical model of the universe he was proposing to

represent. This would have led to a suggestion that the

universe was expanding at the velocity c, and the

presumption of a fourth spatial dimension, which I have

called T, instead of his simple time dimension...

2. He did not recognize that the x – t model used in the

application of the Lorentz Transformation was not one that

admitted of direct measurements of anything not at the exact

position of the observer at the origin of the x – t coordinate

system. That is, at any given moment in time, an observer

cannot see the “present state” of anything even slightly

distant from the origin in his galactic coordinate system. It

is a world which may exist, but it cannot be seen or sensed

in any way. One sees only the universe as it was in the past.

He did not make this distinction between the present he

could actually see, and the theoretical galactic present,

presumed to exist at the present instant in galactic time.

3. By assigning the time 0t to all points along the x Axis,

he precluded the possibility of measuring the speed of light

by the method which was, in fact used to measure it. In

order to make measurements of the speed of light, the

observer at the origin would have to be moving through

time, as light was presumed to do. This should have been a

clue to the inconsistency of the input data he used.


197

4. He took for his development the case of light moving away

from the observer at the origin. This is a situation which has

to be taken on faith, because there is no way of seeing, at

the present time, what happens to light that moves away

from the observer. It goes, in effect, into his future. On the

other hand, light which originated in the past (in Einstein’s

scheme of things) can arrive at the present time and be

observed by the observer. Einstein pointed his light in the

wrong direction.

5. Had he properly assigned different times to objects and

events seen at a distance from the origin, he would have, in

effect, defined his model identically to my definition of the

observer’s local universe, as opposed to his galactic

universe. It is a very small step to define all that one can see

at the moment as “the present” in the local sense. It is, in

fact, the world we live in.

6. The problems inherent in the inconsistency of making all

physical observations in the local universe and applying as

though they were determined by god-like observations in

the galactic universe would be eliminated by relating all of

the measured values to the local universe. The velocity of

light would be infinite and the velocity of the universe

through time would be the apparent speed of light, c. I think it

was possible to have deuced this at the time of the original

development of Special Relativity.

7. The ubiquitous correction factor F, involving the relativistic

shrinkage of distances and increases in time periods and

masses are mainly the result of making all of our physical

measurements in the local universe, limited to things we can

see at the moment, and then using these measurements

without proper correction in the galactic universe, which is

where all of the physical theories are rooted.

8. With the speed of light accepted as infinite, there are no

corrections needed for the measurement of mass. The pesky

square root correction factors are replaced by simpler, linear

corrections, which account for the fact that we read moving

clocks at a different time, by the standards of someone

moving with the clock, than when we think we read it.

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198

9. The clocks carried by moving observers do not run at a

different speed than that of any arbitrarily defined stationary

observer’s clock. Nor do the lengths, masses, or energy

levels of the moving objects or systems change with relative

velocity. Our perception of them is skewed by the necessity

of using radiation to make observations.

10. Clocks can appear to run either fast of slow when they are

moving relative to our point of observation. They will

appear to run slow when they are associated with objects

moving away from our position, and fast when moving

toward our position. They are, in the galactic sense, running

at precisely the same speed, and when we cross paths with

anyone else carrying a clock, it will read the same time as

ours.

11. All of Special Relativity deals with motion either directly

toward or away from the observer. It completely ignores any

velocity transverse to the direction of the object from the

observer. The corrections of observed position and velocity

by the addition of xv/c2 and v/c are correct only for the

radial components of velocity, and there is no correction

required for the pure translation component.

12. The energy of essentially all mass in the universe is constant

at E=mc2. It does not change with velocity. The mass does

not increase with velocity.

13. The reason “nothing can exceed the speed of light” is simply

that the velocities based on measurements in the local

universe are distorted when translated to the galactic

universe in such a way that the galactic version is always less

than the local version. Infinite velocity in the local

coordinate system is seen as c when translated to the galactic

system. This is true for light and for any moving object or

phenomenon. An actual velocity c in the local system is seen

in the galactic system as c/2.

14. Speeds greater than the apparent speed of light are possible but

not for significant masses of matter.


199

So, I believe Special Relativity needs to be updated, and many of the

concepts currently accepted as gospel based on Einstein’s version

should be recast in terms of the galactic values correctly translated

from local observations. Or, the local observations ought to be used

as they are made, and not converted at all.

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200

CHAPTER 9 ORBITAL MOTION

Orbital motion is not, strictly, within the scope of Special Relativity,

because it involves acceleration of the orbiting body toward the

object around which it is orbiting, and the acceleration involves a

“Force”.

Forces are not dealt with well in Special Relativity, and I won’t go

into any detail about them here, except to say that neglecting the

difference between a transverse velocity for a moving system, and

the same velocity in a radial direction has serious consequences.

ORBITAL MOTION AROUND THE OBSERVER

All linear motions may be resolved into radial and transverse

components relative to any point. The pure radial motion has a zero

transverse component, but most motions will have both a radial and

a transverse component. The exception is circular orbital motion,

which is always transverse; relative to the central point of the orbit,

or elliptical orbital motion, which has a small, variable radial

component relative to the translational velocity. Obviously, this is

the case that applies to measurements of the velocity of planets

orbiting a star, or stars orbiting the center of mass of a galaxy.

However, the observer is not, ordinarily, at the focal point of the

orbit. More often, he is either at, or adjacent to the orbital path of

the satellite, or far outside of the orbital path. These are situations

which need to be taken into account to correctly apply the

corrections of local observations to obtain galactic values and

particularly, correct galactic values based on the proper

interpretation of the local observations.

We can start by repeating the development of Table 1, derived for

pure radial motion of the moving reference system, and seeing what

differences arise when the motion is considered to be a combination

of radial and transverse motion.


201

Figure 50 depicts this situation on the x – y plane, presuming that

the T direction is perpendicular to the x and y Axes. In this figure,

the coordinates of point A are (x, y, T), and the velocity is v, in the

direction of the longer shaded arrow.

FIGURE 50

DEPICTION OF A VELOCITY WITH RADIAL AND TANGENTIAL

COMPONENTS

In dealing with velocities in both radial and tangential directions, it

is convenient to use radial coordinates, with the distance from the

origin to point A taken as r, the radius, and the vector denoting the

velocity of the point taken as V, which also has radial and tangential

components. The distance to the point is given by

2 2r x y , EQUATION 147

and the angle from the x Axis to the point is given as θ, so the

coordinates of point A can be given as ( , )r .

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202

The shaded arrow representing the velocity of the point relative to

the origin is given by V , and the components in the radial and

transverse directions by RVr

and TVr

. The angle of the velocity vector

with respect to the radius vector from the origin to point A is θA.

So, the radial vector can be equated with the two components

RV V V r r r

. EQUATION 148

Now, these references to the velocity of the point A are all presumed

to lie in the galactic plane representing the present moment of

galactic time. As we have emphasized before, it is not possible to

make measurements of events or objects in the present galactic time,

so we must have a way of converting from local measurements to

their equivalent in the galactic system.

The local time for an observer at the center of the circular orbit is

depicted by the cone in Figure 51. The circular orbit lays in a plane

in the galactic past relative to the observer, at a distance in the T

direction equal to the radius of the orbit r divided by the speed of

expansion of the universe, c. Both the observer and the plane of the

orbit are moving at the same velocity in the T direction, so the path

of the orbit relative to the observer appears to be at a fixed distance,

as shown. The position of the object along the path changes with

the passage of time, but the path itself is stationary with respect to

the observer’s coordinate system.

There is no radial component of the velocity of the orbiting object,

0nly transverse motion.


203

FIGURE 51

DEPICTION OF AN OBJECT ORBITING THE OBSERVER

It has been demonstrated that the radial motion is subject to

correction for the time at which objects are seen, whereas the

transverse velocity does not call for any correction. So, in calculating

the galactic velocity of an object in orbit around the observer, we

may treat the local velocity as though it is only the radial velocity

component, which is zero.

The galactic velocity of the object is corrected according to

1

1 LL

v

vv

c

, EQUATION 149

which indicates that the galactic velocity of an object orbiting the

observer is equal to the local, or observed, velocity. This is a very

significant point, which will be illustrated in connection with the

observations being made currently in particle physics laboratories.

For generalized motions, which have both radial and transverse

components, Equation 149 is very nearly correct for transverse

velocities relatively small compared to the radial velocity. As the ratio

or transverse velocity to radial velocity becomes large, the correction

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204

becomes less and less significant, until it disappears altogether for

pure translation.

FIGURE 52

ORBITAL MOTION IN THE LOCAL UNIVERSE

However, for circular orbits, or very nearly circular orbits around the

observer, it is of critical importance to note that there is no

relativistic correction for time or velocity whatever when the

observations are made from the point about which the object is

orbiting. There is no correction, according to Equation 149, because

there is no change in the radius of the orbital radius with time. And

of course, there is no relativistic shrinkage factor F.

The path of the orbiting object is the line of intersection of the

horizontal plane of the orbit at any moment and the observer’s cone

representing his local universe. This plane and the observer move

together in the T direction at identical speeds, so the orbit can be

thought of as being stationary with respect to the observer while the


205

orbiting object moves around the observer in a circular path as they

both move in the T direction at the velocity c.

The orbit can also be thought of as the intersection of a vertical

cylinder, representing the orbit of the object as it moves through

both its circular orbit and in the T direction with the rest of the

universe at the velocity c. Thus, in the three dimensional analog

universe, the object follows a helical path around the straight line

path of the observer, which is the T Axis. Once again, the

intersection of the moving cone with the static cylinder is a circle

which is stationary with respect to the moving observer at the apex

of the cone.

Circular orbits are simply a special case of the more general elliptical

orbit, which would be formed by the intersection of an ellipse

moving through space. Such an ellipse would have a shape given by

2 22

2 2

x yr

a b , EQUATION 150

which represents a circle of radius r when 1a b . There is little

difference in the interpretation of the measurements of the motion

of an orbiting object when the orbit is elliptical rather than circular.

While there are several situations in which the observer sees orbital

motion around his location, such as observations of the moon from

earth, or hypothetically, the observation of electrons orbiting the

nucleus of an atom, it is far more often the case that the observer

will be outside the orbit, or at some location inside the orbital path

that is not at a focus of the elliptical orbital path.

One case which is of particular interest is that which places the

observer somewhere on the path, or immediately adjacent to the

path, of the orbiting object.

Another case of particular interest is in the physics of satellites such

as those used in the Global Positioning System, which are tracked

very precisely, and the time experienced by the satellites is of critical

Les Hardison

206

importance. This s a special case of the more general situation in

which the observer is located anywhere in the universe.


207

ORBITAL MOTION ADJACENT TO THE OBSERVER

There are many situations in which orbital motion around a body

must be observed from a different location than the focus of the

orbit. In particular, one such circumstance is where the observer is,

in fact, located adjacent to the orbital path, rather than at the center.

In this situation, the circular orbit appears to be a circle in the galactic

plane, but the current position of the orbiting body cannot be placed

accurately on the circle because of the time differences between the

observer and the object being observed.

The local observer has no such problem, and might, if he were in

contact with an observer interested in establishing the motion within

the galactic plane, make the necessary corrections for him to use his

local observations. The question which must be answered is, “How

are the local observations of an orbiting object corrected in order to

make them useful in the galactic coordinate system?”

This special case is applicable to the detectors used to determine

passage of the circulating neutrons in the Large Hadron Collider at

the CERN installation in Geneva, Switzerland. The following

chapter is devoted entirely to this special case of orbital motion.

Here, the path of the orbit appears to approach and pass over or

near the observer at one point in the orbit, and then move to the

farthest possible point on the orbit before starting the return trip.

The path of the orbit appears to be an ellipse drawn on one side of

the cone representing the local universe at one moment in local time.

However a “top view’ (looking down on the cone from the T

direction) would show the path to be circular, just as was the case

when the observer was located in the center.

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[LCH1]

FIGURE 53

A CIRCULAR ORBIT VIEWED FROM THE ORBITAL PATH

This is simply a matter of the orbit of an actual object in four

dimensional space being independent of the observer’s location.

The local observer should have no difficulty in determining the

position of the object in orbit at any given local time because he can

measure the angle and distance relative to his reference system at any

local time, and make successive measurements to determine the

magnitude and direction of the velocity. He can, of course, only do

this for past positions of the object (from a galactic standpoint), as

he cannot see into the future.

The critical item here is that the velocity of the object, which appears

to be constant to the local observer, will not have constant transverse

and radial motions with respect to the observer. It was shown in the

previous section that the radial velocities of bodies are correctly

translated using the same equation as applied to motion toward the

body in the one dimensional model used in Special Relativity. That

is,


209

1

1 LL

v

vv

c

, EQUATION 151

but motion in the transverse direction requires no correction factor

at all. From the point of view of the local observer, as the orbiting

body approaches his position, the velocity is totally radial.

FIGURE 54

ORBITAL MOTION OBSERVED FROM THE PERIMETER

However, when it reaches the opposite side of the orbit and starts

back toward him, it is totally transverse. The velocity is constant in

magnitude, but varies in direction, and he must apply correction

factors which change continuously with time, and with the position

of the orbiting body.

The corrections are easily determined with reference to Figure 54. It

was pointed out previously that the velocity can only be determined

unambiguously for bodies moving toward the observer, which lie in

his local present. Bodies moving away from the observer are, by

definition moving into his local future, and he cannot observe their

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210

positions until they are in his local past. So, we need only be

concerned about the orbital motion as the object under observation

is approaching the observer from the most distant point in its orbit.

It is apparent that the position is at 0 degrees to the location of the

observer and that the velocity is perpendicular to this radial line, and

totally transverse. As the object moves around its orbital path, the

angle gradually increases until it approaches 180 degrees as it nears

the observer. The velocity always remains perpendicular to the

orbital radius, and at the observer’s position, is at 90 degrees, and is

completely in the radial direction with respect to the observer. As

the angle changes from 0 to 180 degrees, the radial component of

the velocity varies with the cosine of the angle of the orbiting object,

and the transverse component varies with the sine of the angle, such

that

sinLT Lv v , EQUATION 152

and

cosLR Lv v . EQUATION 153

So, at the 0 point in the orbital path, the object appears to be moving

at velocity vL in the tangential direction, and reports that this velocity

requires no correction whatever. For the 180 degree point in the

orbital path (where the orbiting object is adjacent to the observer’s

position), the velocity is totally radial, and requires the application of

the shrinkage factor given in equation 151.

For points in between, the correct factor is

1cos

1 LL

v

vv

c

. EQUATION 154


211

So, we need to determine this value over half a circuit, or an angle of

θ = 0 to θ = π.

0

1 1cos

1 1L LL

vd

v vv

c c

. EQUATION 155

So, it appears that an observer watching an object more around a

circular orbit toward his position along the orbital path will use the

exactly the same correction factor to get the equivalent galactic

velocity as if it were a linear velocity he were observing.

Numerous other situations can be described, some of which

represent recurring situations. An example is one in which the

observer is moving in orbit around a fixed object, rather than being

stationary at a fixed point on the orbit. This would apply to the

situation of an astronomer studying the motion of the sun or the

other planets, were they sufficiently far away or moving sufficiently

fast to require relativistic corrections.

Or, the observer can be at any other position relative to the orbit,

including inside of the orbital path or outside it. They are all equally

amenable to the same kind of analysis applied here.

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212

A FINAL OBSERVATION

In converting the velocities observed from local measurements to

the equivalent values in the galactic plane, the relativistic corrections

derived for radial motion of an object (motion directly toward or

away from the observer) do not apply because there is no radial

velocity when the observer is in the center of the orbital path.

Instead, the galactic velocity is equal to the local velocity.

Similarly, if the observer is located anywhere along the orbital path,

the galactic velocity is, again, equal to the orbital velocity, with no

correction factor.

I believe this situation to be true no matter where the observer is

located relative to the orbital of the object, whether it is in his local

past, and can be observed, or is in his local future, which can only

be deduced.

The equation

1

1L

L

v vv

c

, EQUATION 156

Still applies but only when the radial component of the velocity of

the orbiting object is used, rather than the total velocity. Likewise,

the time assignable to a point along the orbit around a fixed observer

is inversely proportional to the velocity when equal distances of

traverse are used, and again, when the velocity is radial, or completely

transverse, the proper value for the local velocity is the radial

velocity, which is zero, so

1 LL L

vt t t

c

, EQUATION 157

so


213

11

1

LL L L L L

L

vx x v t v t vt

v c

c

. EQUATION 158

This means that an object in motion appears to move at a slower

speed in the galactic universe than indicated by observations in the

local universe, when the velocity is measured over the same time

period in both systems. This kind of comparison can only be made

legitimately when the object exists in the proper quadrant of the

space-time graph. An object which is timed from the moment it

crosses the location of the observer and begins moving away from

him, has moved into the future of the local observer, and the future

locations can only be determined at some future local time.

If the object is stationary, with vL = 0, the location of the object is

the same in both the observed local universe and in the constructed

galactic universe. However, if vL is other than zero, in the radial

direction, there will be a difference in the location when the time

values are numerically equal, or in the time if the distances from the

observer are numerically equal. This is not in indication that time is

compressed when an object is moving nor that velocities are

decreased to avoid approaching the apparent speed of light.

Galactic time is still exactly the same throughout the plane of the

galactic universe. Local time is still exactly the same throughout the

cone of the local universe. There is no shrinkage of time, or distance,

or length of an object, and no change in the mass of the object when

the local velocity is increased, without limit on the velocity, and the

galactic velocity is increased toward the apparent limiting velocity, c.

However, for orbital velocity, there seems to be an exception.

Galactic velocity can also be increased without limit, and there is no

apparent shrinkage of time periods, or change in the length or mass

of orbiting objects as seen by the fixed local observer. There is no

shrinkage of objects with motion approaching the speed of light, nor

is there a foreshortening of the distances.

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214

It is important to remember that the observations are all made in the

local universe, and are not subject to any corrections at all, but that

the galactic clock associated with a moving object does not read the

same time as the observer’s clock. Observations translated to the

galactic universe are not corrected, but rather translated from one

system of defining time to another. Both systems have

straightforward relationships between distance, time, velocity and

energy, which derive from observations made in the local universe,

albeit mostly at velocities so low that there is little difference between

the two.

When the motion of an object being observed has a component of

velocity at right angles to the radial line connecting the observer and

the object, this translator velocity does not count. That is, only the

radial component of velocity requires any translation from the local

observed velocity to a galactic velocity. The translational component

has the same value in both systems.

In the case of orbital motion, there is no radial velocity at all, so there

are no relativistic corrections needed to get the galactic orbital

velocity.

It appears to me that Newton’s laws of motion hold quite precisely

when the measurements of position, time and velocity are made with

reference to the local system I have described. And when the

translation is done to the galactic system, they apply there also, but

are more complex.

It should be possible to show that just as the velocity of an object

seen in the local system must be translated when used in the galactic

system, so the momentum associated with an object, and the energy

content must be translated from one system to the other.

In the local universe, the momentum of an object is seen as the mass

of the object times the observed velocity, with no correction of the

mass due to the velocity. So,

L Lp mv , EQUATION 159


215

Where, once again, we have assumed that the local velocity was

measured along a radial path. Then there is a transverse component,

there will be a transverse momentum, which will be the same in the

two systems, whereas the apparent mass, in the galactic system,

increases without limit as the radial component of the galactic

velocity approaches c, the apparent speed of light. Again, the mass

of the object is an intrinsic property of it, not different in the two

observational systems. It is the same in both systems when the object

under observation has no velocity, and is called the rest mass in the

galactic system.

In the galactic universe, the mass is presumed to increase with

velocity of the object relative to the observer,

2

22

2

1

1

m vmv v

cv

c

, EQUATION 160

where the mass of the object is presumed to increase by division with

the relativistic shrinking factor, and the velocity decreases by the

same factor. When the velocity is orbital, there is no relativistic

shrinking factor to be applied. And the galactic value for momentum

and mass are both equal to the observed local values.

Les Hardison

216

CHAPTER 10 THE LARGE HADRON

COLLIDER

The questions relating to the orbital velocity of objects was given

considerable space in the previous chapters, although the situations

in which it is of significance are relatively rare. Most observations of

astronomical objects with orbits which may be observed from earth

are relatively slow-moving compared to the apparent speed of light, c,

and the corrections are minor.

The most troublesome situation, in my estimation, relates to the

velocity of the particles accelerated to very high velocities in particle

accelerators. While the velocity of major masses is probably limited

to a fraction of the apparent speed of light, there is no theoretical limit

on the velocity a particle can reach when subjected to acceleration

by very strong electric or electromagnetic fields. In these

accelerators, the energy from very large masses of matter can be

applied to a limited number of sub-atomic particles, and there does

not seem to be any limit as to how fast these can be made to move

relative to the fields which accelerate them.

The largest and most well-known of the particle accelerators in

recent years has been the Large Hadron Collider (LHC) at CERN in

Geneva, Switzerland. At CERN thousands of physicists are running

many experiments with various objectives, but much of the core

research is involved in trying to duplicate the conditions they think

may have existed near the moment of the big bang at the beginning

of the universe we live in.

They are hoping to create the ultimate transport particle, the Higgs

Boson, which is credited with being the thing which makes protons,

neutrons, electrons and everything else have the property we call

mass.


217

The Higgs Boson is a kinsman of the photon, which is supposed to

transfer light from place to place, the gluon, which is supposed to

transfer the strong force between constituents of the atomic nucleus,

and the graviton, which is supposed to carry the gravitational force

between masses which attract each other.

Without understanding all of this in much greater depth than I have

just displayed, I think they are on the wrong track. I just can’t bring

myself to believe in photons, because I think light is transmitted

instantaneously by direct contact of atoms across distances in both

space and time, without actually traversing the space or time. No

photons are needed.

The photon is the basis of the whole of quantum mechanics, so I am

suspicious of the whole system involving supposed transfer particles,

of which the photon is the prototype. No one has ever gotten ahold

of a photon, nor will they ever. The same is true of gluons and

gravitons. I used the word “supposed” purposely, because I question

whether such particles are real, in the sense of having a physical

embodiment which can be sensed in some way. The alternative is

that they are simply concepts which have been created to explain the

behavior of “real” particles, which can be sensed and measured.

So, good luck with your Higgs Boson, all you CERN guys. I would

be happy to be proved wrong but it will take more than an

unexplained occurrence during one of the proton head-on collisions

in the LHC to convince me.

But, while I am sometimes skeptical of their interpretations, I have

great respect for the experimental physicists’ ability to measure

things and accurately report what they measured. By and large, they

are a much more diligent and carful a breed than I am.

But, the LHC was designed to accelerate protons and other heavy

hadrons up to very near the speed of light (but that, of course they

can’t get to the speed of light because that is impossible. Einstein

said so.) In the process, they are increasing the mass of the protons

enormously, from almost nothing to about the mass of a butterfly,

Les Hardison

218

according to the physicist who took my Scientific American Tour

Group through the CERN establishment late in October, 2010.

So, I want to take a close look at what measurements they are actually

making, and how they use the velocity and mass of the protons in

their calculations.


219

GENERAL DESCRIPTION OF THE LHC AT CERN

The Internet abounds with descriptions of the Large Hadron

Collider, which is a physics super-project that rivals the US space

program in cost and time span. Its aims are no less spectacular.

Where space exploration strives to go start the journey toward the

myriad stars which we can see in the night sky, by taking the first

baby steps toward our moon and out sun’s other planets, the LHC

project is attempting to explore the nucleus of the atom, and by

doing so, trace our history back in time, perhaps to the time of the

Big Bang, the presumed beginning of our universe.

I will spare you all of the descriptions of the LHC which you can

find elsewhere, and try to outline only the aspects of it which are of

particular interest to me. These have to do, not with the technology

of accelerating the protons or other heavy ions (hadrons) like the

lead ion, or controlling the path using superconducting magnets and

high frequency electrostatic fields, although these border on the

miraculous. Rather, I am interested in how they know where the

protons are at any given time, how fast they are moving, and what

their energy level is.

The main reason I am interested in these things is that, from my

perspective, the velocity of light is not limited to c, the apparent velocity

of light which has been measured time and again, but rather moves

instantaneously, short circuiting both space and time as energy is

transmitted from one atom to another, which may be far removed

in both space and time. At least, this is what one would presume one

sees when making observations in the real world, where radiant

energy transmission can only be detected by an observer when it

exists within his local universe, defined by his local time.

Although the CERN physicists do not locate the protons they are

studying by sight (according to my perspective, there is no way to

see a proton or electron), they are still limited to the use of electrical

sensing devices which are subject to the same sort of velocity

constraints when the measurements of time and distance are referred

Les Hardison

220

to the galactic universe, where time is the same at all points within

the universe. Nothing can move faster than the speed of light in this

galactic plane, simply because it would have to be moving faster than

an infinitely great speed in the local universe.

So, how do the CERN physicists know how fast the protons are

going? They accelerate the protons by means of electrostatic fields

between charged orifice plates. The bunches of protons pass

through the plates, which must be at near zero charge at the time,

but must be negatively charged as the protons are approaching, so

the electric field accelerates them toward the plate, and positively

charged after the bunch passes through, so they are further

accelerated by repulsion from the plate.

The particles are moving fast and are speeded up by a negligible

amount according to the physicists, as they are already going at

almost the apparent speed of light, so the mass must increase to account

for the energy gained. Or. Alternatively, from my viewpoint, they are

going at many times the speed of light and are speeded up by a great

deal, with no change in mass at all. We can’t both be right, and there

are a lot more of them than there are of me.

Now, the Large Hadron Collider is designed with the objective of

reaching a proton velocity of some 0.99999999 times the apparent

speed of light, and there are numerous ways of corroborating their

measurements that this actually occurs. So, I am on pretty thin ice

when I say that they are mistaken about how fast their protons are

moving, by a factor of some 100 or so.

How could anyone be that wrong about anything?

I don’t know enough about particle physics to give a good, coherent

description of the way the physicists at CERN accelerate the protons

and other large hadrons to high velocities, so here is theirs:

The design of the LHC is for each ring to contain

2808 particle bunches in 3564 slots that are

separated by 25 nanoseconds. It is understood


221

that the wire scanner front end returns two

types of 1-dimensional profile data: transverse

profile information for each bunch and for each

(possibly empty) slot, and integrated profile

data over all bunches. These modes are

mutually exclusive. The wire scanner

application will be able to show these basic

data, both textually and graphically. These data

can be stored in a way that can be retrieved

later by the wire scanner application, by an

individual or by another program.

The aim of the collider is to direct streams

moving in opposite directions at 99.999999% of

the speed of light into each other and so

recreate conditions a fraction of a second after

the big bang. The LHC experiments try and

work out what happened.

Les Hardison

222

THE RADIOFREQUENCY ACCELERATION SYSTEM

Here is a description of the design of the electrostatic acceleration

system from the Journal of Applied Physics.

The RF system is located at point 4. Two independent sets of cavities

operating at 400MHz (twice the frequency of the SPS injector) allow

independent control of the two beams. The superconducting cavities

are made from copper on which a thin film of a few microns of

niobium is sputtered on to the internal surface. In order to allow for

the lateral space, the beam separation must be increased from 194

mm in the arcs to 420 mm. In order to combat intrabeam scattering

(see below), each RF system must provide 16 MV during coast while

at injection 8MV is needed. For each beam there are 8 single cell

cavities, each providing 2MV, with a conservative gradient of 5.5

MVm−1. The cavities are grouped into two modules per beam, each

containing four cells (figure 55 in this presentation).

Each cavity is driven by an independent RF system, with

independent klystron, circulator and load. Although the RF

hardware required is much smaller than LEP due to the very small

synchrotron radiation power loss, the real challenges are in

controlling beam loading and RF noise7.

7 New Journal of Physics 9 (2007) 335 (http://www.njp.org/)


223

FIGURE 55

ACCELERATION SECTION OF THE LHC

The segment immediately ahead of the bunch of protons passing

through the acceleration tube is charged negatively, exerting an

attractive force on the protons, and the segment behind the bunch

is charged positively, repelling them. Both fields tend to accelerate

the bunch of protons in the direction they are moving through the

tube.

As the bunch passes, the charges must change from positive to

negative and negative to positive, and the frequency of the

alternations would, it seems, be timed so that the frequency increases

as the velocity of the electrons increases. This is not so. A constant

frequency of approximately 400 MHz is applied to the single

acceleration station.

Ideally, the charge on the acceleration plate would be negative as the

cloud of protons (called a bunch by the LHC personnel) approached

the orifice plate, and would drop to zero just before they reached it,

to avoid the protons becoming strongly attracted to the cylindrical

inner surface of the orifice. After the protons passed through, the

charge would become positive, repelling the proton and accelerating

them on their way.

Les Hardison

224

I had presumed that there were accelerating orifices located all

around the perimeter of the 27 Km circle of the LHC, but

apparently, this is not the case. There is only one, although it has

four stages in it, each furnishing one quarter of the acceleration.

Here is CERN’s description of the acceleration chambers, or

cavities.

Cavities: The main role of the LHC cavities is to

keep the 2808 proton bunches tightly bunched to

ensure high luminosity at the collision points and

hence, maximize the number of collisions. They

also deliver radiofrequency (RF) power to the

beam during acceleration to the top energy.

Superconducting cavities with small energy

losses and large stored energy are the best

solution. The LHC will use eight cavities per

beam, each delivering 2 MV (an accelerating field

of 5 MV/m) at 400 MHz The cavities will operate

at 4.5 K (-268.7ºC) (the LHC magnets will use

superfluid helium at 1.9 K or -271.3ºC). For the

LHC they will be grouped in fours in cryomodules,

with two cryomodules per beam, and installed in

a long straight section of the machine where the

transverse interbeam distance will be increased

from the normal 195 mm to 420 mm.8

8 CERN Website http://public.web.cern.ch/public/en/LHC/Facts-

en.html 12/5/2011.

http://public.web.cern.ch/public/en/LHC/Facts-en.html%2012/5/2011

http://public.web.cern.ch/public/en/LHC/Facts-en.html%2012/5/2011


225

The interesting point here is that the cavities operate at 400 MHz,

which means that they deliver a push to each passing bunch of

protons once every 2.5 nanoseconds. Yet, the rate of circulation of

the 2808 bunches of protons, moving at essentially the apparent speed

of light, (c~300,000,000 m/second) has a bunch passing through the

acceleration cavity only every 24 nanoseconds.

TABLE 4

CALCULATION OF FREQUENCY OF PASSAGE OF BUNCHES

Les Hardison

226

THE EXPERIMENTS AT CERN

One of the subjects which caused me great concern was the fact that

the massive Large Hadron Collider (LHC) at the CERN facility in

Geneva, Switzerland was built around the concepts developed in

Special and General Relativity, and seems to work well. I have been

critical of the foundation on which Special Relativity was built, and

suggested that physicists, as a general rule, fail to distinguish between

the local universe, in which their observations are made, and the

galactic universe where time is uniform throughout all of our normal

three dimensional space.

This inconsistency is insignificant when dealing with relatively slow

moving objects, like supersonic aircraft, but makes measurable

differences for fast-moving objects, and becomes really important

when the velocity approaches the apparent speed of light. At CERN, the

objectives involve accelerating protons and other heavy hadrons to

velocities which are said to come very close to the apparent speed of

light. Velocities as high as 0.99999999c have been reported.

I do not want to comment in detail on any of the particular

experiments, or the objectives being sought, but rather on the

general question of whether the data being collected is being

interpreted correctly. I don’t think it is.

I realize that the odds are against one mechanical engineer with a

BS degree versus 20,000 PhD physicists, almost all of whom are

smarter than I am, particularly when playing on their own home

field. But, I bought a lottery ticket once, with just about the same

odds of winning.

So, let’s start with the consideration of the speed to which the

protons are accelerated and the measurement of the velocities when

they are moving at nearly the velocity c, according to the observers.

An interesting place to start is by noting that the acceleration cavities

operate at 400,000,000 cycles per second, yet only 41,000,000

bunches of protons are passing through them per second, .according


227

to the CERN reports. How does the frequency of the polarity

reversals in the acceleration cavities relate to the speed of the protons

being accelerated?

This situation is akin to that of a father standing next to the old

fashioned playground merry-go-round, giving it an occasional push

as his children ride around. If the merry-go-round has six segments,

he can give one push for every revolution, skipping five of the six

segments as they go by, or he can push each and every one , but not

so hard.

FIGURE 56

MAN PUSHING A MERRY GO ROUND

If he chooses to push each segment, the frequency of his effort is six

times the RPM of the merry-go-round. If he chooses to push only

one, it is the frequency is equal to the RPM. Or, he can keep it

spinning by only giving it one push every other rotation, in which

case his frequency is half the RPM.

At CERN, we have an acceleration section which administers (or is

at least capable of administering) ten times as many pushes per

second as there are bunches of protons passing through the cavity,

presuming that they are traveling at very nearly the apparent speed of

light, c. Of course, a push administered when there is no bunch of

protons approaching is simply wasted.

Les Hardison

228

However, the possibility exists that, once the roughly circular 27 Km

tunnel is filled with the 3705 bunches of protons, they might actually

be going around twice as fast as they are supposed to be able to go.

That is, if they were moving at almost twice the apparent speed of light,

they would be accelerated just as frequently as if they were going at

almost the apparent speed of light. In fact, the acceleration cavities could

accommodate speeds of up to 10 times the apparent speed of light,

without putting out much extra effort.

Now, the problem of relating what seems to be going on at CERN

with what would be the case if either A) the observations were

actually being made in the local universe (as I have been suggesting

is always the case) but interpreted as though they were made in the

galactic universe, or B) They were made in the local universe and

correctly placed in the context of the galactic universe.


229

HOW ARE MASS AND VELOCITY MEASURED AT

CERN?

This question bothered me, as I hadn’t a clue as to how they could

measure velocities like this, when there is no way to sense the

presence of a single proton other than by its electric charge, and that

doesn’t have a very long distance range. So it would take some

phenomenal timing to get a velocity by measuring the change in

distance with time if something were moving at or in excess of the

apparent speed of light, over a range of a few centimeters in the local

universe. Likewise, the measurement of the mass of the protons

moving at very high speeds seems to be a difficult task.

Apparently, what the CERN Physicists know with much better

accuracy is the energy which has been absorbed by each proton as it

passes through the electric fields of the accelerator.

Here is a summary of the explanation given on the Internet.9

The relativistic energy-velocity relationship is:

220

2

21

m cE mc

v

c

, EQUATION 161

where m0 is the rest mass of the proton, and m is the mass under the

high velocity conditions in the LHC. From these equations, and the

energy imparted to the protons (and apparently measurable when the

protons impact ordinary matter), we can calculate the mass and

9 http://physics.stackexchange.com/questions/716/relativistic-speed-

energy-relation-is-this-correct

Les Hardison

230

velocity of the protons, although neither is measurable directly in the

LHC.

Here is the calculation as summarized in the CERN Outreach pages

on the Internet.10

Because the energy of the fast moving proton is taken to be mc2 as

per Special Relativity, the mass is directly calculable from the energy

10 http://lhc-machine-outreach.web.cern.ch/lhc-machine-outreach/lhc-

machine-outreach-faq.htm

How much do the protons weigh in the LHC at 7Tev?

The energy of a proton is 7 TeV. Via E = mc2 the mass is simply 7

TeV/c2 - and these are the units usually used.

7 TeV/c2 divided by the rest mass .938272029 GeV/c2 gives us

7460.52 times the rest mass

Working in SI units we can do the same thing more explicitly:

At 7 TeV:

Energy = 7 *1012 *1.60206 *10-19 Joules

c= 2.99793 108 m/s

m = Energy/c2 = 1.2477-23 Kg

At rest (rest mass proton = mp):

Energy = mp c2 = 0.938272029 *109*1.60206*10-19 Joules (or just say

mp = 0.938272029 GeV/c2 )

mp = Energy/c2 = 1.672009-27 Kg

m/mp = 7460.52 as before


231

each proton is observed to have. So, if you accept the premises of

Special Relativity, the mass of the proton increases enormously as it

is accelerated.

TABLE 5

CALCULATION OF APPARENT MASS AND GALACTIC

VELOCITY

Symbol Value Units Formula Result

Ep Energy of a proton TeV 7.00E+00

Ep Energy of a proton Joules 1.12E-06

c Velocity of light m/s 3.00E+08

mP mass kg E/c2 1.25E-23

mp0 Rest mass of a

proton kg 1.67E-27

mP/mP0 Ratio of m/m0 - 7.46E+03

Gamma - 1/Sqrt(1-

v2/c2) 7.46E+03

F2 - 1-v2/c2 1.80E-08

- v2/c2 0.99999998

vp Calculated proton

velocity - v/c 0.99999999

The velocity of the proton may be calculated from the relationship

between mass of the proton at rest and the mass at high velocity.

For any given increase in velocity, there is a corresponding increase

in mass. I have repeated this calculation in slightly different terms

for clarity.

Les Hardison

232

So, there appears to be no question that the mass and velocity

relationships are based on an explicit belief in the equations derived

by Einstein in Special Relativity, which have not been altered nor

reinterpreted in the intervening 100 plus years since their

development. The mass-energy relation is based explicitly on the

presumption that no matter can move through space faster than the

apparent speed of light. On this basis the mass is presumed to increase

to account for most of the energy added to the protons, and their

speed is then calculated from the calculated mass.

I would, of course, put an entirely different interpretation on the

measurements, based on the presumption that the value c is the rate

of expansion of the universe into the fourth spatial dimension, and

that light, in the local universe which we observe, moves infinitely

fast, and does not, therefore, establish a universal speed limit for

material objects, or anything else.

In the local universe, the mass does not increase with velocity at all.

The velocity of protons is not limited to the apparent speed of light, c,

but may go many times as fast. The only things that do not seem to

be different when measured in the local universe are the rest mas of

the protons, and the energy. This is simply because one of the basic

formulae of Special Relativity is not true.

2

0

2

21

m cE

v

c

. EQUATION 162

I have pointed out previously that this equation, involving the

relativistic F factor, is the only one not based on the Lorentz

transformation, relating to the appearance of time, distance and

velocity when seen by a second moving observer. Rather, equation

162 is based on the presumption that v cannot, under any

circumstances exceed c, and the whole point of my approach is the

presumption that it can.


233

When v<<c, the relationship given in galactic terms by Einstein is

very nearly the same as is the exact relationship given in terms of the

local velocity.

2 22 0 0

02

2

21

Lm v m cE m c

v

c

. EQUATION 163

However, at velocities approaching the apparent speed of light, it is a

poor approximation to what I believe is the correct, and exact,

formulation shown in Equation 164.

22

2

smvE mc , EQUATION 164

where sv is the local velocity in excess of the apparent speed of light, c.

At galactic velocities equal to or greater than the apparent speed of light,

the right hand term in Equation 163 becomes meaningless. Without

calculated increase in mass for the protons as they accelerate there is

no basis for the calculation of the velocity which corresponds to the

energy 7 TeV2 energy level.

So, how should the velocity be calculated? The energy content of the

body is not absolute, but is an energy content relative to whatever is

taken as the “stationary” coordinate system. And the mass is, of

course, independent of the choice of reference.

So, the proper interpretation of the 7 TeV energy level imparted to

the protons circulating in the LHC is that all of this is involved with

the increase in kinetic energy, the m0vL2/2 part of Equation 163, and

none of it goes to increasing the mass.

Thus, the ratio of the energies, 7460.52, is attributable solely to the

increase in local velocity, vL.

Les Hardison

234

22 0

20

2 2

0 0

2 12

7460.52

L

L

m vm c

vE

E m c c

. EQUATION 165

Because the proton does not increase in mass,

122.152v c . EQUATION 166

Obviously, the velocity greater than c cannot represent a velocity in

the galactic universe, where an infinite local velocity would appear to

just equal to c. Therefore, it is appropriate to assume that the vL/c

value is a local velocity. .

So, I would say that the mass of the proton remains unchanged as it

accelerates, and the velocity is increased by the addition of energy

without upper limit. Thus the 7 TeV energy level corresponds to the

kinetic, or velocity energy of the protons entirely. The value of the

local velocity increases from 0 at rest to 122.152c when the energy

input to accelerate the proton is 7 TeV.

The calculation of the value of vL is given in Table 6, where all of the

energy imparted to the protons is presumed to contribute to their

velocity.

TABLE 6

RECALCULATION BASED ON LOCAL INTERPRETATION OF

DATA

Symbol Value Units Formula Result


235

Ep Energy of a

proton Tev 0.00E+00

Ep Energy of a

proton Joules 1.12E-06

c

Apparent

velocity of

light

m/s 2.00+E08

mp0 Rest mass of

proton kg 1.67E-27

mP/mP0 Ratio of

mp/m0p - 1.00E+00

Ekp Kinetic

energy Joules m0PvL

2/2=mPv2 7.46E+03

vL2/c2

Ratio of

vL2/c2

- mp/mp0 1.58E+04

vL/c Ratio of vL/c - sqrt(mp/mp0) 1.22E+02

v/c Ratio of v/c - (vL/c)/(1+vL2/c2) 0.99889

It is apparent that, to achieve the 7 TeV energy level, it is only

necessary for the local velocity to reach a value of approximately 122

times the apparent speed of light. This is, of course, quite phenomenal,

in that ordinary matter cannot be accelerated beyond a fraction of

the apparent speed of light, and likely cannot reach the apparent speed of

light by local measurement, because there is nothing massive in the

universe which is moving at this speed from which it can gather

energy.

It is also apparent that, as only a small amount of the energy used in

accelerating the protons to 122 times the apparent speed of light appears

Les Hardison

236

as an increase in the velocity of the protons by galactic standards, the

only way to account for it is by the appearance that the protons have

become more massive, as was the initial presumption of Special

Relativity. So, although the local observer sees no apparent change

in the mass, it is necessary to indicate a large increase in mass when

converting the data to the galactic plane.

However, it seems that the observations, having been made in the

local universe and with regard to the local timekeeping system, it

would be simpler to avoid the problem by recognizing that, in the

local universe, light really does move from place to place

instantaneously, and does not set a speed limit on anything. Mass is

not a flexible property of matter which varies depending on the

reference system chosen for it, but remains constant as the velocity

changes, and is independent of the motion of the reference system.

With regard to the possibility of sub-atomic particles accelerating to

velocities in excess of the apparent speed of light, it seems possible to

transfer the energy from huge numbers of atoms to the relatively few

circulating protons within the LHC by using the large amounts of

energy to create electrostatic and electromagnetic fields which

transfer energy to a relatively small number of particles, and result in

super c velocities.

The local velocity of 122.152c translates to a true galactic velocity of

0.99188c, rather than the 0.99999999 being used by the CERN

operators.

This is only very slightly slower than their value by the ratio

0.999999991.008

0.99189 , EQUATION 167

or 0.8% less than the value reported. However, there is still a

remarkable difference between the two values, as the CERN value

would require a local velocity of about 10,000,000c, whereas the

calculated value represents a local velocity of 122.152 c. How did we

get such glaringly different results?


237

Les Hardison

238

THE CERN RESULTS IN LOCAL TERMS

The disparities between the results I derived and those representing

the results reported by the CERN scientists are not difficult to

explain, if one accepts the three premises of this book. That is, the

value c represents the rate of expansion of the universe into a four

dimensional space-time, that the true value of the speed of light in a

vacuum is infinite, and that we are limited to making observations of

any kind to the local universe, where we can actually see objects and

events at the present instant in time.

Let us suppose for the moment that we can actually see the protons

moving around the circular track of the LHC, and that we are able

to measure their velocity, vL, in our local universe.

We would, using Newtonian physics, believe that the total energy of

the proton would be represented by

2

0

2

TT

m vE , EQUATION 168

where ET includes the velocity component in the fourth dimensional

direction, and also the velocity of the matter that is observable in the

three ordinary dimensions in excess of c. The rest mass of matter

used in Special Relativity, m0 is the mass of the proton and it does

not change as the velocity relative to any arbitrary coordinate

changes. The physicists would call it the “rest mass”, but in the local

universe, this is invariant. It is simply the mass, m, and nothing can

change it.

The local velocity has two vector components,

L Lsv v c uur uur r

, EQUATION 169

where LSv is the excess of velocity over c, the velocity of expansion

of the universe. The vL component is the only one we can observe

directly, and represents the velocity of the proton coming toward us


239

at our observation station along the perimeter of the LHC tube. It is

only the vL, or local spatial component we are going to be able to

measure, so it is only the local kinetic energy we will be dealing with,

2 22

22 2

L LL

mv vmcE

c

. EQUATION 170

Similarly, the kinetic energy of the proton in the LHC, when

translated to galactic coordinates, should be

2

22 2

22 2

1

K

v

cmv mcE

v

c

. EQUATION 171

The condition that the kinetic energy of a moving object is a

property of the object, and should be the same in both systems, if

calculated relative to the same observation point is

2

220

1

1

Lvm

m v v

c

. EQUATION 172

22

22

0

11

1

L Lvm v

m v cv

c

. Equation 173

This equation satisfies most of our prejudices with regard to the

appearance of the mass increase with increased velocity when viewed

as though the measurements had all been made in the galactic

reference system. When the velocity in the galactic system is zero,

the mass is m0, the rest mass. When it is accelerated, it moves faster,

but the velocity cannot appear to exceed c, so the mass increases to

account for the energy by the object in excess of the inherent rest

Les Hardison

240

energy, mc2/2, which is due to the expansion of the universe at

velocity c.

When the local velocity, vL, reaches c, the galactic velocity is c/2, etc.

and at a local velocity of 2c, the galactic velocity would be 2/3c. For

the galactic velocity to reach c, the local velocity would have to be

infinite.

Because the relationship between mass and velocity in the galactic

system does not agree with the values given in Equation 172, it seems

that the translation between the two systems is not handled properly

in Special Relativity (or, of course, I could be wrong, and the

remainder of the world right!)

But, if we consider for a moment what sort of correction would have

to be applied to the Special Relativity formulary if all of the

measurements were made in the local universe, which is the only

place they can be measured, and then treated as though they were

made in the galactic universe, the velocities would be in error by the

factor F, which is

2

2

1

1

Fv

c

. EQUATION 174

From this,

2 1

1 1

LvF

v v v

c c

, EQUATION 175

or

LvF

v . EQUATION 176


241

How does the F factor enter into Einstein’s equation for the increase

in mass with velocity?

Apparently, in all of the other instances in which the value of c, the

apparent speed of light, plays a role, it is really the actual speed of the

universe in the fourth dimensional direction. But the relationship

holds well even though the physical meaning of the value was not

what wa supposed. However, in the mass-energy relationship, c

actually signifies the velocity of light through a vacuum. The whole

purpose of this equation is to keep anything, including light, of

course, from moving faster than the actual speed of light. So, in this

case, the proper interpretation of the speed of light is that it is not

the value 300,000 /c kM Sec , but is, rather, infinite.

So, it is a different F that is used in equation 176; one where c is

infinitely large, and

20

2

11

1

m

m v

c

, EQUATION 177

for the value of c taken as infinite.

The velocity shrinkage, and that of the distance and time shrinkages

are, like the mass increase with velocity, artifacts of the mistaken use

of the local system for making measurements, and of the galactic

system for applying them.

But, of course, we really knew that to begin with. This is basically

what I derived in Chapter 7, when I pointed out that the result of

using measurements in the local system as though they had been

taken in the galactic system should be the appearance of the factor

F, where

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242

2 2

2 2

11 1

11 1

A A L

L

vt t t cF

vt t t v vcc c

.

EQUATION 178

So, my conclusion is that it would be better to stop trying to fit all

of the observed data (which was necessarily observed from the

viewpoint of a local observer) into the galactic reference system,

where it produces anomalous results when high velocities are

involved.

The basic energy equation of Special Relativity,

2

2

21

mcE

v

c

, EQUATION 179

should be replaced with

22

21

2

LvE mc

c

. EQUATION 180

The mass stays constant with acceleration, Newtonian physics seems

to hold for masses and accelerations. My lunch pail continues to have

two pounds of mass regardless of the motion of your reference

system, and it doesn’t get smaller if I move very fast relative to your

position.

And, the protons circulating around the track at Geneva Switzerland

don’t really get as heavy as butterflies. However, they have, when

moving at a velocity of 122 times the apparent speed of light, the same

impact a butterfly would have if he were moving at just the apparent

speed of light.


243

HOW DOES THE CERN LHC FUNCITION?

Surely, if there is a very great difference between the design velocities

for the LHC and the velocities actually achieved, there would be

problems in the operation that have not, presumably, surfaced.

One of these is the design of the superconducting magnet system

used to provide the magnetic field which bends the path of the

rapidly moving protons into the precise circular orbit they must

follow in order to stay within the vacuum tube in which they travel.

Another lies in keeping count of the number of bunches of protons

which pass a given detection station per unit time. If the velocity, in

terms of local time, is 122c instead of .98856c, would one not expect

the number of counts to be off by a factor of 122?

Each of these problems will be considered in the next few

paragraphs. There are, of course, many other such problems which

I am not aware of, but would be interested in learning about.

MAGNETIC FIELD STRENGTH

In order to make the protons follow a roughly circular path around

the 27 Km circumference of the LHC, rather than moving in a

straight line, a strong magnetic field must be present, with the poles

above and below the proton path. The field strength must be set

precisely to bring about the right amount of acceleration of the

protons toward the center of the Collider.

How, if both the values for both the mass and the velocity of the

protons are in error by a large factor, can the magnetic field strength

be anywhere near correct?

This is easily explained. The magnetic field exerts a force on the

particles which is equal to

MF qv B uur r ur

, EQUATION 181

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244

where:

q = proton charge

v= proton velocity

B=magnetic field strength,

and the v and B are both vector quantities. The cross product is equal

to the product of their magnitudes when they are at right angles to

each other, and is directed at right angles to both of them. In this

case, the force tends to bend them toward the center of the circular

orbit. This force must just equal the centrifugal force which tends to

keep them going straight, or outward from the center of the orbit.

The centrifugal force on the protons is proportional to the mass

times the velocity squared, divided by the radius of curvature of the

path

2

c

mvF

r . EQUATION 182

A stable circular path requires that these two forces be equal, so,

mvr

qB . EQUATION 183

Thus, for the known electrical charge on the proton, and radius of

the circular path, the momentum, mv, must be set correctly.

One would suppose that if the values of m and v were other than

they appear to the observer to bs, the magnetic field strength would

be set incorrectly at CERN, and the protons would follow a circular

path of the wrong radius. So, how can it be that the design actually

functions properly if the mass and velocity are both perceived

incorrectly?

I believe that the physical laws involved were all worked out on the

basis of experiments done before it was technologically possible to

accelerate particles to velocities greater than the apparent speed of light.


245

What the experimenters did was to make measurements of distance

and velocity in the local universe and attribute the values of local

velocity to the galactic universe without correction. Thus, the

development of Faraday’s l

Law, from which the force acting to bend the path of the proton

toward the center of the circular path, was based on measurements

made in the local universe, and was accurately defined by Equation

181 when the uncorrected rest mass was used with the local velocity,

0r

M LF qv B uur uur ur

, EQUATION 184

and

2

0 Lc

m vF

r . EQUATION 185

Thus the proper calculation of the magnetic field strength would

require

0 Lm vB

r . EQUATION 186

Because this simply doesn’t work if one uses the local velocity and

the rest mass, it is necessary to “correct” the rest mass upward by

the factor

2

2

1

1

Fv

c

, EQUATION 187

to compensate for the fact that the observed local velocity has been

“corrected’’ downward by this ratio.

The development of Faraday’s Law, and many of the other physical

laws was done at a time when it was not understood that the universe

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246

was expanding in a fourth dimensional direction, and that the

physical measurements being made were all relative to a different

coordinate system than they were actually using. A coordinate

system in which light moved from place to place at infinite velocity,

according to a consistent definition of the universe they were

observing.

The same appears to be the case for Newton’s laws of motion, and

for many other physical constants. They were developed using

observations relative to a local coordinate system, but using the

measurements of distance and time as though they had been

measured in reference to a coordinate system contained within the

galactic universe.

COUNTING THE PROTONS

Another seemingly puzzling problem about the difference between

the ordinary, galactic scheme for measuring times and velocities

involves the problem of how one could make a mistake in counting

the number of protons passing a particular observation station along

the perimeter of the LHC. On the one hand, the velocity is taken as

essentially c, and the time it takes to make a circuit is 88.9

microseconds. However, if one supposes that the velocity is 122c,

the time required for a full circuit is less than one microsecond.

This will take a bit of explaining, as one is used to physicists

reporting results accurate to one part in a billion when they are

measuring things, and not at all used to the idea that they might be

off by a large factor --- 122 in this case.

It all boils down, as I have repeated many times, to the concept of

how one regards the passage of time, and whether one makes

measurements in the local universe and presumes that they are,

instead, made in the galactic universe. .


247

FIGURE 57

SCHEMATIC OF CERN LARGE HADRON COLLIDER, SHOWING

THE UNIVERSE EXPANDING IN TO THE FOURTH DIMENSION

In Figure 57, it is apparent that the protons move around

substantially in a circle in the x – y plane in which the tubular ring is

located, and is shown as the lower perimeter of the vertical cylinder.

While the collider is located within this plane, the plane itself, along

with the rest of our entire universe, is moving in the vertical T

direction without limit as time passes. The cross sections of the

vertical cylinder represent the subsequent positions of the x – y plane

during each instant of time.

As photons move around the circular channel in the x – y plane, they

are following a helical path as the x – y plane moves in the T direction

at the velocity c. The protons move in bunches each containing

many protons. However, we can think of a single one of these

protons as being representative of one of a bunch.

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248

According to the example in table 6, with the protons moving at

very, very nearly the apparent speed of light, c, it takes about 0.09

seconds, or 90,000 nanoseconds for the proton to complete the

roughly 27 Km circuit. So, each proton should pass our checkpoint

about 11,245 times per second. However, there are 3705 bunches of

protons circulating in the ring, so the frequency of passage is 11,245

x 3705 = 41,670,000 sec-1, or a frequency of 41.67 MegaHz,

according to the time-clock of the galactic observer.

The local observer, on the other hand, has two times to deal with.

He has his local clock, which agrees at every instant with the galactic

timekeeper’s clock. However, he has his own local time clock, which

says that the time everywhere reads exactly the same along the 45

degree lines which are defined by the path radiant energy takes from

one point to another. His calculations of velocity, momentum and

energy are all based on the reading of his local clock.

Up until now, we have regarded the path of light as being in the local

time cone only, and therefore moving only in straight lines relative

to the observer who receives them. However, this is in the simplified

world of Special Relativity, where there are no gravitational, or

electrostatic and electromagnetic forces. In this world, protons

would also move in straight lines only.

What we must take into consideration is the enormously powerful

magnetic field in which the protons are moving in the LHC, in order

to force them to move in a circle when going at enormously high

velocities. These velocities lie completely outside the range of

comprehension.

It is my contention that the magnetic field warps the shape of the

galactic universe (and the historic picture of it we see in the local

universe) such that the cylinder pictured in Figure 57 represents a

segment of x - T space, which would ordinarily be a vertical flat

plane, wrapped around to form the cylindrical domain in which the

protons are circling. In this circular domain, light also would be bent

into a helical path through space-time, just as the protons are.


249

Our ordinary picture of the local universe could be examined by

unrolling the cylinder and laying it out flat, like a strip chart, where

the width of the chart represents the length of the proton’s path in

x – y space, and the vertical dimension represents the T dimension,

which stretches on far into the future.

The critical point here is that the observations on which the laws of

motion were formulated by Newton, were based on observations

made entirely within the local universe as he saw it. Because this

universe has been warped from the flat vertical plane, which would

represent the x – T universe with y = z = 0, into the shape of a

cylinder by the magnetic fields which cause the protons to follow a

cylindrical path, light would also follow the same cylindrical path.

The direction of the passage of time has been changed from a

straight vertical arrow pointing in the T direction to a helical curve,

pointing in a very nearly 45 degree angle to the galactic plane as

shown in Figure 58.

If we are to look at the protons from the standpoint of a real

observer, in his local universe, we can do so most easily by unrolling

the cylinder and laying the resulting strip chart out flat. This is akin

to unrolling a roll of toilet paper, where each square sheet width

represents the length of the circumference of the cylinder, and each

equal vertical distance represents an increment in the T Axis also

numerically equal to the circumference.

Les Hardison

250

FIGURE 58

CERN DIAGRAM WITH TWO CYCLES SHOWN

In Figure 58 the cylinder is shown with two complete orbits taking

place at essentially velocity c from the standpoint of the galactic

observer, so both the vertical and horizontal dimensions of the

unrolled sheet represent two orbits. It should be apparent that we

could unroll as many sheets as desired, so long as we kept the

diagram square, because as the protons moved around the cylinder

and from one sheet to the next in the horizontal direction, they

would also be passing upward in the T direction by the same

distance.


251

FIGURE 59

DEVELOPED SURFACE OF THE PROTON PATH

Figure 59 shows the developed surface, which contains the path of

the proton as it moves through two complete orbits and

simultaneously moves through the same physical distance in the

fourth, T dimension, as time passes.

Here the path of a proton moving around the circular CERN track

is indicated by the 45 degree line, which corresponds with a galactic

velocity essentially equal to c. However, the observations must be

made by a stationary observer, who has no visible communication

with the proton, and can only sense the location as the proton passes

the sensor in very close proximity. The 45 degree diagonal line

represents a galactic velocity of exactly c, the rate of expansion of

the universe in the T direction. Several other proton speeds are also

shown for reference. The sloping lines to the left of the 45 degree

line are the paths which would be followed by protons moving at

3c/4, c/2, c/4, c/8 and c/16, by galactic measure.

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252

However, the 45 degree line represents a velocity which corresponds

to c in the galactic system, where the vertical distance is the period

of rotation, to the local observer would involve the passage of no

time at all, and would correspond to an infinite velocity.

The proton, moving at 122.15c in local terms, or 0.99181c in terms

of the galactic reference system, would arrive at the second location

of the observer on his next cycle only a minute fraction of a cycle

later than would a light beam traversing the same distance. It is

apparent that the closer to the value of c the speed becomes, the

closer to the exact 45 degree path the trajectory becomes.

Now, the observer, located at the origin, is also moving in the x – y

plane as it moves upward in the T direction, and in which the proton

is moving according to the galactic frame of reference. However, the

observer cannot sense the location of the proton while it moves away

from his position. He can only tell where it has been, and sense the

velocity as it approaches. So, for each cycle, the observer must look

at the velocity as it approaches him from the left, and can never see

it as departing on the right, as it passes out of his sight at the moment

it passes his position.

It should also be apparent that the local observer is moving upward

in the T direction as the proton moves away from his position at, or

directly above the origin, but that it will begin to approach the

observer as it passes the point opposite the origin, as shown in

Figure 60.

However the observer will no longer be at the origin, as he was

moving in the T direction during the period of the cycle. As the

proton begins to approach the observer again, it will be as the

observer approaches, not point B in the diagram, but point B’.


253

.

FIGURE 60

THE DEVELOPED SURFACE FROM THE LOCAL OBSERVER’S

STANDPOINT

While the positions of the observer moves from Point A to Point B

to Point C as the universe moves in the T direction, Points A’, B’

and C’, and Points A’’, B’’ and C’’ also represent these same points

in spaced time. It is obvious that point A senses the passing of the

proton as it goes through the origin, at the beginning of the cycle,

while point B’ experiences the passing at the end of this cycle and

the beginning of the next one, while point C’’ experiences the third

passing,

Because the cycles are identical (or nearly so, if there is no further

acceleration or deceleration of the protons) the path from A to B’ to

C’’ could also be represented by a parallel path of the same electron

through points B and C’, and between A’ and B’’.

The number of crossings shown on the diagram will be exactly the

same as were presented on the diagram where the local observations

were attributed to the galactic coordinate system. However, the

difference is in the time assigned to the points. Points A, B’ and C’’

are all three in what an observer at C’’ would call the same local

Les Hardison

254

present. That is, he would see essentially no passage of local time

having taken place at all between the events recorded at A, B’ and

C’’. He would say that the protons were moving at near-infinite

velocity, just as light passing along this path would be moving at

infinite velocity according to a local observer.

The local observer at C’’ would presume that these events were

simultaneous if the galactic velocity were exactly c, and would

perceive that they were almost simultaneous, but not quite, if the

galactic velocity were, in fact, 0.99 times the apparent speed of light. In

fact, the local observer would report the velocity of the proton to be

121.15c, and the energy commensurate with that higher velocity,

with no change in the mass of the protons as they increase in speed.


255

CHAPTER 11 DO NEUTRINOS MOVE

FASTER THAN LIGHT?

No, they don’t. Not in the galactic reference system the physicists

are using.

Early in September, 2011, the OPERA Scientists announced that

they had measured the speed of neutrinos along a path between the

source at CERN and a receptor located about 725 Km away. I

immediately concluded that they must be mistaken, because,

according to my theory, light really moves at infinite speed, and only

appears to move at the apparent speed of light when the data are

incorrectly attributed to the wrong frame of reference. So, it really

is impossible for anything to exceed the apparent speed of light. That is

what “infinite” looks like the way physicists keep track of things.

There are two ways of looking at why neutrinos don’t move faster

than light, without bothering to go into the several ways in which the

experimenters could have been in error. I will start with these, and,

hopefully, convince you that they were in error because it is simply

not possible that their conclusion was correct.

The first, and simplest way is to convince you that the speed of light

is infinite, at least when measured by experiments conducted by

humans in the real world, which I have described as the local

universe. That is, light travels from place to place in zero time

without moving through the space between the source and the

receptor. In order for anything to go faster than that, it would have

to arrive at its destination at an earlier time than it left. In my picture

of the local universe, this is not possible.

The second way is to find some fatal flaw in their experiment which

would lead them to believe they had measured a velocity faster than

they actually did, granting that their measurements are made in the

local universe, as I have described, and used without correction in

their idealized galactic universe.

Les Hardison

256

I do have an idea of where the error might have been made, and also

a radical suggestion about the nature of neutrinos. I hit upon this

possibility a few days after the experimental results were announced,

and submitted my critique on the Vixra blog under High Energy

Particle Physics on September 26, 2011. Although I thought at the

time that my comment was far short of the typical high end physics

and mathematical comments which were being made, that I had

found the flaw in their experimental technique.

I got absolutely no comment of any sort on this submission, and

thought it appropriate to repeat it here, as long as I was already

making radical comments about relativistic physics.

THE FASTER THAN LIGHT NEUTRINO ERROR

Here is my critique of the Sasso experiments which indicated that

the speed of neutrinos passing through the earth had been observed

to traverse the distance between CERN and Gran Sasso slightly

faster than the apparent speed of light. It was made only a few days after

the popular media had broken the story, and before the

experimenters had published their paper detailing the results.

The news made quite a splash, and then died down. I had not had a

chance to read the original paper on which the story was based, but

I was convinced they were in error on general principles, as I don’t

think anything can be observed to go faster than the apparent speed of

light so long as the physicists use a coordinate system which I think

is incompatible with the measurements they make.

So, I was just taking a guess as to where they might have gone wrong,

based on the assumption that they had gone wrong somewhere.

I have since studied their paper, and have not found anything in it

to indicate that they took the problem I pointed out into account.

But they are a very big, very brainy group, and it seems likely that

they did make the correction for the shorter path length the


257

neutrinos took, as compared with light going through a fiberglass

cable, etc.

Anyway, here is my commentary, untouched since the initial

publication on the Vixra Blog Site11, which is specifically designed

for receiving just such comments.

September 26, 2011 at 2:50 pm

I think the experimenters might have used the wrong distance for

clocking the speed of the neutrinos.

Given that their distance measurement was quite precise, it was

done, according to reports, using GPS.

As a pilot, I know that the GPS does not give the linear distance

between two points, but rather the great circle distance connecting

them. That is, the distance as it would be measured by a tape measure

along the surface of the earth at sea level.

Neutrinos, reputedly, do not follow this curved path, but instead go

straight through the earth between the two points, which is a

significantly shorter distance. In this particular case, instead of 725

Km approximately, the chord of the arc distance is about 723. 8

11 Vixra Blog Site http”//www.vixra.com

http://blog.vixra.org/2011/09/19/can-neutrinos-be-superluminal/#comment-10819

Les Hardison

258

Km, using the mean radius of the earth as 6471 Km.

FIGURE 61

PROPOSED PATH LENGTH ERROR

Using the shorter distance and the roughly 60 nanoseconds sooner

arrival than light speed gave me a calculated speed of 299,638,769

m/sec, rather than 299,792,458 m/sec, or a velocity of about

0.99948735 times the speed of light.


259

ARE NEUTRINOS A FORM OF HIGH ENERGY

RADIATION?

If the experimenters did, in fact, neglect to correct the path length

in this way, it would not only leave the “laws of physics as we know

them” intact, but would also suggest some interesting things about

the nature of neutrinos. For example, consider that they might, like

photons, not really be particles, but rather attributes of a particular

kind of radiation.

That is, they would travel through Space just as light does, at the

“apparent speed of light” (when using the galactic coordinate

system) or at infinite speed (when using the local coordinate system),

but travel through matter more slowly, just as light does.

They would be to x-rays what x-rays are to visible light, passing

through all but the most energetic atoms of ordinary matter without

interaction, except for an occasional head-on collision with an

electron or proton. This is because only very heavy atoms can have

the inner electron pair so tightly bound by the electric field around

the nucleus to allow very high energy levels to exist.

This would account for the observation that the large flow of

neutrinos which seem to originate in space and pass through the

earth continuously comes from the interior of the sun, from super

novae, etc., all places where the energy levels are very high.

If this is the case, what the Sasso experimenters did was to measure

the refractive index of the radiation we describe as neutrinos through

dirt/rock/etc.

It would not, of course, be the first time radiation got mistaken for

particulate matter. In my opinion, exactly the same kind of error was

made in making up the photon to account for the quantum nature

of light. I do not believe there is any such thing as photons.

Les Hardison

260

THE OPERA EXPERIMENT PAPER

The following is a complete copy of the paper released by the

experimenters working at Gran Sasso Laboratories in Italy to

determine the velocity of a stream of artificially created neutrinos

passing between the source at the CERN Large Hadron Collider in

Geneva, Switzerland, and their detector installation at Sasso.

The paper is reprinted here in its entirety, as I think it may provide

some support for my arguments in favor of the apparent speed of light

being, in reality, the speed of expansion of the universe into a fourth

dimension which we cannot sense directly.

I invite the reader to look at:

1. My proposed explanation of the measurements of

velocity exceeding the apparent speed of light, and see

if it has any merit.

2. The possibility that the use of the conventional local

coordinate system for the interpretation of the

measurements is supported by these experiments, and

3. The suggestion that neutrinos are not particles at all, but

are instead, ultra high energy transfer events, much as

ordinary light is a transfer of energy from atom to atom,

rather than a stream of photons.


261

Measurement of the neutrino velocity

with the OPERA detector in the CNGS

beam

T. Adama

, N. Agafonovab

, A. Aleksandrovc,1

, O. Altinokd

, P.

Alvarez Sancheze

, S. Aokif

,

A. Arigag

, T. Arigag

, D. Autieroh

, A. Badertscheri

, A. Ben

Dhahbig

, A. Bertolinj

, C. Bozzak

,

T. Brugièreh

, F. Brunetl

, G. Brunettih,m,2

, S. Buontempoc

, F.

Cavannan

, A. Cazesh

, L. Chaussardh

,

M. Chernyavskiyo

, V. Chiarellap

, A. Chukanovq

, G. Colosimor

,

M. Crespir

, N. D’Ambrosios

,

Y. Déclaish

, P. del Amo Sanchezl

, G. De Lellist,c

, M. De Seriou

,

F. Di Capuac

, F. Cavannap

,

A. Di Crescenzot,c

, D. Di Ferdinandov

, N. Di Marcos

, S.

Dmitrievskyq

, M. Dracosa

,

D. Duchesneaul

, S. Dusinij

, J. Ebertw

, I. Eftimiopolouse

, O.

Egorovx

, A. Ereditatog

, L.S. Espositoi

,

J. Favierl

, T. Ferberw

, R.A. Finiu

, T. Fukuday

, A. Garfagniniz,j

,

G. Giacomellim,v

, C. Girerdh

,

M. Giorginim,v,3

, M. Giovannozzie

, J. Goldbergaa

, C. Göllnitzw

,

L. Goncharovao

, Y. Gornushkinq

,

G. Grellak

, F. Griantiab,p

, E. Gschewentnere

, C. Guerinh

, A.M.

Gulerd

, C. Gustavinoac

,

K. Hamadaad

, T. Haraf

, M. Hierholzerw

, A. Hollnagelw

, M.

Ievau

, H. Ishiday

, K. Ishiguroad

,

K. Jakovcicae

, C. Jolleta

, M. Jonese

, F. Jugetg

, M. Kamiscioglud

,

J. Kawadag

, S.H. Kimaf,4

,

M. Kimuray

, N. Kitagawaad

, B. Klicekae

, J. Knueselg

, K.

Les Hardison

262

Kodamaag

, M. Komatsuad

, U. Kosej

,

I. Kreslog

, C. Lazzaroi

, J. Lenkeitw

, A. Ljubicicae

, A. Longhinp

,

A. Malginb

, G. Mandrioliv

,

J. Marteauh

, T. Matsuoy

, N. Maurip

, A. Mazzonir

, E.

Medinaceliz,j

, F. Meiselg

, A. Meregagliaa

,

P. Migliozzic

, S. Mikadoy

, D. Missiaene

, K. Morishimaad

, U.

Moserg

, M.T. Muciacciaah,u

,

N. Naganawaad

, T. Nakaad

, M. Nakamuraad

, T. Nakanoad

, Y.

Nakatsukaad

, D. Naumovq

,

V. Nikitinaai

, S. Ogaway

, N. Okatevao

, A. Olchevskys

, O.

Palamaras

, A. Paolonip

, B.D. Parkaf,5

,

Parkaf

, A. Pastoreag,u

, L. Patriziiv

, E. Pennacchioh

, H.

Pessardl

, C. Pistillog

,

Polukhinao

, M. Pozzatom,v

, K. Pretzlg

, F. Pupillis

, R.

Rescignok

, T. Roganovaai

, H. Rokujof

,

Rosaaj,ac

, I. Rostovtsevax

, A. Rubbiai

, A. Russoc

, O.

Satoad

, Y. Satoak

, A. Schembris

, J. Schulera

,

Scotto Lavinag,6

, J. Serranoe

, A. Sheshukovq

, H.

Shibuyay

, G. Shoziyoevai

, S. Simoneah,u

,

Siolim,v

, C. Sirignanos

, G. Sirriv

, J.S. Songaf

, M.

Spinettip

, N. Starkovo

, M. Stellaccik

,

Stipcevicae

, T. Straussg

, P. Strolint,c

, S. Takahashif

, M.

Tentim,v,h

, F. Terranovap

, I. Tezukaak

,

Tioukovc

, P. Tolund

, T. Tranh

, S. Tufanlig

, P. Vilainal

,

M. Vladimirovo

, L. Votanop

, J.-L. Vuilleumierg

, G. Wilquetal

,

B. Wonsakw

, J. Wurtza

, C.S. Yoonaf

, J. Yoshidaad

, Y. Zaitsevx

,

Zemskovaq

, A. Zghichel

1 On leave of absence from LPI-Lebedev Physical Institute of

the Russian Academy of Sciences, 119991 Moscow, Russia 2

Now at Albert Einstein Center for Fundamental Physics,

Laboratory for High Energy Physics (LHEP), University of


263

Bern, CH-3012 Bern, Switzerland 3 Now at INAF/IASF,

Sezione di Milano, I-20133 Milano, Italy 4 Now at Pusan

National University, Geumjeong-Gu, Busan 609-735,

Republic of Korea 5 Now at Asian Medical Center, 388-1

Pungnap-2 Dong, Songpa-Gu, Seoul 138-736, Republic of

Korea 6 Now at SUBATECH, CNRS/IN2P3, F-44307

Nantes, France a

IPHC, Université de Strasbourg,

CNRS/IN2P3, F-67037 Strasbourg, France b

INR-Institute for

Nuclear Research of the Russian Academy of Sciences, RUS-

327312 Moscow, Russia c

INFN Sezione di Napoli, I-80125

Napoli, Italy d

METU-Middle East Technical University, TR-

06532 Ankara, Turkey e

European Organization for Nuclear

Research (CERN), Geneva, Switzerland f

Kobe University, J-

657-8501 Kobe, Japan g

Albert Einstein Center for

Fundamental Physics, Laboratory for High Energy Physics

(LHEP), University of Bern, CH-3012 Bern, Switzerlandh

IPNL, Université Claude Bernard Lyon I, CNRS/IN2P3, F-

69622 Villeurbanne, France i

ETH Zurich, Institute for

Particle Physics, CH-8093 Zurich, Switzerland j

INFN

Sezione di Padova, I-35131 Padova, Italy k

Dipartimento di

Fisica dell’Università di Salerno and INFN ”Gruppo

Collegato di Salerno”, I-84084 Fisciano, Salerno, Italyl

LAPP,

Université de Savoie, CNRS/IN2P3, F-74941 Annecy-le-

Vieux, France m

Dipartimento di Fisica dell’Università di

Bologna, I-40127 Bologna, Italy n

Dipartimento di Fisica

dell’Università dell’Aquila and INFN ”Gruppo Collegato de

L’Aquila”, I-67100 L’Aquila, Italy

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264

o

LPI-Lebedev Physical Institute of the Russian Academy of

Science, RUS-119991 Moscow, Russia p

INFN - Laboratori

Nazionali di Frascati, I-00044 Frascati (Roma), Italy q

JINR-

Joint Institute for Nuclear Research, RUS-141980 Dubna,

Russia r

Area di Geodesia e Geomatica, Dipartimento di

Ingegneria Civile Edile e Ambientale dell’Università di Roma

Sapienza, I-00185 Roma, Italy s

INFN - Laboratori Nazionali

del Gran Sasso, I-67010 Assergi (L’Aquila), Italy t

Dipartimento di Scienze Fisiche dell’Università Federico II di

Napoli, I-80125 Napoli, Italy u

INFN Sezione di Bari, I-70126

Bari, Italy v

INFN Sezione di Bologna, I-40127 Bologna, Italy w

Hamburg University, D-22761 Hamburg, Germany x

ITEP-

Institute for Theoretical and Experimental Physics 317259

Moscow, Russia y

Toho University, J-274-8510 Funabashi,

Japan z

Dipartimento di Fisica dell’Università di Padova,

35131 I-Padova, Italy aa

Department of Physics, Technion, IL-

32000 Haifa, Israel ab

Università degli Studi di Urbino ”Carlo

Bo”, I-61029 Urbino - Italy ac

INFN Sezione di Roma , I-

00185 Roma, Italy ad

Nagoya University, J-464-8602 Nagoya,

Japan ae

IRB-Rudjer Boskovic Institute, HR-10002 Zagreb,

Croatia af

Gyeongsang National University, ROK-900 Gazwa-

dong, Jinju 660-300, Korea ag

Aichi University of Education,

J-448-8542 Kariya (Aichi-Ken), Japan ah

Dipartimento di

Fisica dell’Università di Bari, I-70126 Bari, Italy ai

(MSU

SINP) Lomonosov Moscow State University Skobeltsyn

Institute of Nuclear Physics, RUS119992 Moscow, Russia aj

Dipartimento di Fisica dell’Università di Roma Sapienza, I-

00185 Roma, Italy ak

Utsunomiya University, J-321-8505

Utsunomiya, Japan al

IIHE, Université Libre de Bruxelles, B-

1050 Brussels, Belgium


265

Abstract

The OPERA neutrino experiment at the underground

Gran Sasso Laboratory has measured the velocity of neutrinos

from the CERN CNGS beam over a baseline of about 730 Km

with much higher accuracy than previous studies conducted with

accelerator neutrinos. The measurement is based on high-statistics

data taken by OPERA in the years 2009, 2010 and 2011.

Dedicated upgrades of the CNGS timing system and of the

OPERA detector, as well as a high precision geodesy campaign

for the measurement of the neutrino baseline, allowed reaching

comparable systematic and statistical accuracies. An early arrival

time of CNGS muon neutrinos with respect to the one computed

assuming the speed of light in vacuum of (60.7 ± 6.9 (stat.) ± 7.4

(sys.)) ns was measured. This anomaly corresponds to a relative

difference of the muon neutrino velocity with respect to the speed

of light (v-c)/c = (2.48 ± 0.28 (stat.) ±

0.30 (sys.)) ×10-5

.

1. Introduction

The OPERA neutrino experiment [1] at the

underground Gran Sasso Laboratory (LNGS) was designed to

perform the first detection of neutrino oscillations in direct

appearance mode in the νµ→ν

τ channel, the signature being the

identification of the τ−

lepton created by its charged current

(CC) interaction [2].

In addition to its main goal, the experiment is well

suited to determine the neutrino velocity with high accuracy

through the measurement of the time of flight and the distance

between the source of the CNGS neutrino beam at CERN

(CERN Neutrino beam to Gran Sasso)

[3] and the OPERA detector at LNGS. For CNGS neutrino

energies, <Eν> = 17 GeV, the relative deviation from the speed

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of light c of the neutrino velocity due to its finite rest mass is

expected to be smaller than 10-19

, even assuming the mass of the

heaviest neutrino eigenstate to be as large as 2 eV [4]. Hence,

a larger deviation of the neutrino velocity from c would be a

striking result pointing to new physics in the neutrino sector.

So far, no established deviation has been observed by any

experiment.

In the past, a high energy (Eν > 30 GeV) and short

baseline experiment has been able to test deviations down to |v-

c|/c <4×10-5

[5]. With a baseline analogous to that of OPERA

but at lower neutrino energies (Eν peaking at ~3 GeV with a tail

extending above 100 GeV), the MINOS experiment reported a

measurement of (v-c)/c = 5.1 ± 2.9×10-5

[6]. At much lower

energy, in the 10 MeV range, a stringent limit of |v-c|/c <2×

10-9

was set by the observation of (anti) neutrinos emitted by the

SN1987A supernova [7].

In this paper we report on the precision determination

of the neutrino velocity, defined as the ratio of the precisely

measured distance from CERN to OPERA to the time of flight

of neutrinos travelling through the Earth’s crust. We used the

high-statistics data taken by OPERA in the years 2009, 2010

and 2011. Dedicated upgrades of the timing systems for the

time tagging of the CNGS beam at CERN and of the OPERA

detector at LNGS resulted in a reduction of the systematic

uncertainties down to the level of the statistical error. The

measurement also relies on a high-accuracy geodesy campaign

that allowed measuring the 730 Km CNGS baseline with a

precision of 20 cm.


267

2. The OPERA detector and the CNGS neutrino beam

The OPERA neutrino detector at LNGS is composed of

two identical Super Modules, each consisting of an

instrumented target section with a mass of about 625 tons

followed by a magnetic muon spectrometer. Each section is a

succession of walls filled with emulsion film/lead units

interleaved with pairs of 6.7 × 6.7 m2

planes of 256 horizontal

and vertical scintillator strips composing the Target Tracker

(TT). The TT allows the location of neutrino interactions in the

target. This detector is also used to measure the arrival time of

neutrinos. The scintillating strips are read out on both sides

through WLS Kuraray Y11 fibres coupled to 4-channel

Hamamatsu H7546 photomultipliers [8]. Extensive

information on the OPERA experiment is given in [1] and in

particular for the TT in [9].

Fig. 1: Artistic view of the SPS/CNGS layout.

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The CNGS beam is produced by accelerating protons

to 400 GeV/c with the CERN Super Proton Synchrotron

(SPS). These protons are ejected with a kicker magnet

towards a 2 m long graphite neutrino production target in two

extractions, each lasting 10.5 µs and separated by 50 ms. Each

CNGS cycle in the SPS is 6 s long. Secondary charged

mesons are focused by two magnetic horns, each followed by

a helium bag to minimise the interaction probability of the

mesons. Mesons decay in flight into neutrinos in a 1000 m

long vacuum tunnel. The SPS/CNGS layout is shown in Fig.

1. The different components of the CNGS beam are shown in

Fig.2.

Fig.2: Layout of the CNGS beam line.

The distance between the neutrino target and the OPERA

detector is about 730 km. The CNGS beam is an almost pure νµ

beam with an average energy of 17 GeV, optimised for νµ→ν

τ appearance oscillation studies. In terms of interactions in the

detector, the ⎯νµ

contamination is 2.1%, while νe and ⎯νe

contaminations are together smaller than 1%. The FWHM of the neutrino beam at the OPERA location is 2.8 km.

The kicker magnet trigger-signal for the proton

extraction from the SPS is UTC (Coordinated Universal Time)

time-stamped with a Symmetricom Xli GPS receiver [10]. The

schematic of the SPS/CNGS timing system is shown in Fig. 3.

The determination of the delays shown in Fig. 3 is described in


269

Section 6.

The proton beam time-structure is accurately measured

by a fast Beam Current Transformer (BCT) detector [11]

(BFCTI400344) located (743.391 ± 0.002) m upstream of the

centre of the graphite target and read out by a 1 GS/s Wave

Form Digitizer (WFD) Acqiris DP110 [12]. The BCT consists

of toroidal transformers coaxial to the proton beam providing a

signal proportional to the beam current instantaneously

transiting through it, with a few hundred MHz bandwidth. The

start of the digitisation window of the WFD is triggered as well

by the magnet kicker signal. The waveforms recorded for each

extraction by the WFD are stamped with the UTC and stored

in the CNGS database.

The proton beam has a coarse bunch structure

corresponding to the 500 kHz of the CERN Proton Synchrotron

(PS) (left part of Fig. 4), on which the fine structure due to the

200 MHz SPS radiofrequency is superimposed, which is

actually resolved by the BCT measurement, as seen in the right

part of Fig. 4.

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Fig. 3: Schematic of the CERN SPS/CNGS timing system. Green boxes

indicate detector time-response. Orange boxes refer to elements of the

CNGS-OPERA synchronisation system. Details on the various elements

are given in Section 6.

Fig. 4: Example of a proton extraction waveform measured with the BCT

detector BFCTI400344. The five-peak structure reflects the continuous

PS turn extraction mechanism. A zoom of the waveform (right plot)

allows resolving the 200 MHz SPS radiofrequency.


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3. Principle of the neutrino time of flight measurement

A schematic description of the principle of the time of

flight measurement is shown in Fig.

5. The time of flight of CNGS neutrinos (TOFν) cannot be

precisely measured at the single interaction level since any

proton in the 10.5 µs extraction time may produce the neutrino

detected by OPERA. However, by measuring the time

distributions of protons for each extraction for which neutrino

interactions are observed in the detector, and summing them

together, after proper normalisation one obtains the probability

density function (PDF) of the time of emission of the neutrinos

within the duration of extraction. Each proton waveform is

UTC time-stamped as well as the events detected by OPERA.

The two time-stamps are related by TOFc, the expected time of

flight assuming the speed of light [13]. It is worth stressing that

this measurement does not rely on the difference between a

start (t0) and a stop signal but on the comparison of two event

time distributions.

The PDF distribution can then be compared with the

time distribution of the interactions detected in OPERA, in

order to measure TOFν. The deviation δt = TOFc -TOF

ν is

obtained by a maximum likelihood analysis of the time tags of

the OPERA events with respect to the PDF, as a function of δt.

The individual measurement of the waveforms reflecting the

time structure of the extraction reduces systematic effects

related to time variations of the beam compared to the case

where the beam time structure is measured on average, e.g. by

a near neutrino detector without using proton waveforms.

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Fig. 5: Schematic of the time of flight measurement.

The total statistics used for the analysis reported in this paper

is of 16111 events detected in OPERA, corresponding to about

1020

protons on target collected during the 2009, 2010 and 2011

CNGS runs. This allowed estimating δt with a small statistical

uncertainty, presently comparable to the total systematic

uncertainty.

The point where the parent meson produces a neutrino

in the decay tunnel is unknown. However, this introduces a

negligible inaccuracy in the neutrino time of flight

measurement, because the produced mesons are also travelling

with nearly the speed of light. By a full FLUKA based

simulation of the CNGS beam [14] it was shown that the time

difference computed assuming a particle moving at the speed

of light from the neutrino production target down to LNGS,

with respect to the value derived by taking into account the

speed of the relativistic parent meson down to its decay point

is less than 0.2 ns. Similar arguments apply to muons produced

in muon neutrino CC interactions occurring in the rock in front


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of the OPERA detector and seen in the apparatus (external

events). With a full GEANT simulation of external events it is

shown that ignoring the position of the interaction point in the

rock introduces a bias smaller than 2 ns with respect to those

events occurring in the target (internal events), provided that

external interactions are selected by requiring identified muons

in OPERA. More details on the muon identification procedure

are given in [15].

Fig. 6: Schematic of the OPERA timing system at LNGS. Blue delays

include elements of the time-stamp distribution; increasing delays

decrease the value of δt. Green delays indicate detector time-response;

increasing delays increase the value of δt. Orange boxes refer to

elements of the CNGS-OPERA synchronisation system.

A key feature of the neutrino velocity measurement is the

accuracy of the relative time tagging at CERN and at the

OPERA detector. The standard GPS receivers formerly

installed at CERN and LNGS would feature an insufficient

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~100 ns accuracy for the TOFν measurement. Thus, in 2008,

two identical systems, composed of a GPS receiver for time-

transfer applications Septentrio PolaRx2e [16] operating in

“common-view” mode [17] and a Cs atomic clock

Symmetricom Cs4000 [18], were installed at CERN and

LNGS (see Figs. 3, 5 and 6).

The Cs4000 oscillator provides the reference frequency

to the PolaRx2e receiver, which is able to time-tag its “One

Pulse Per Second” output (1PPS) with respect to the individual

GPS satellite observations. The latter are processed offline by

using the CGGTTS format [19]. The two systems feature a

technology commonly used for high-accuracy time transfer

applications [20]. They were calibrated by the Swiss Metrology

Institute (METAS) [21] and established a permanent time link

between two reference points (tCERN and tLNGS) of the timing

chains of CERN and OPERA at the nanosecond level. This

time link between CERN and OPERA was independently

verified by the German Metrology Institute PTB (Physikalisch-

Technische Bundesanstalt) [22] by taking data at CERN and

LNGS with a portable time-transfer device [23]. The difference

between the time base of the CERN and OPERA PolaRx2e

receivers was measured to be (2.3 ± 0.9) ns [22]. This

correction was taken into account in the application of the time

link.

All the other elements of the timing distribution chains

of CERN and OPERA were accurately calibrated by using

different techniques, further described in the following, in

order to reach a comparable level of accuracy.

4. Measurement of the neutrino baseline

The other fundamental ingredient for the neutrino

velocity measurement is the knowledge of the distance between


275

the point where the proton time-structure is measured at CERN

and the origin of the underground OPERA detector reference

frame at LNGS. The relative positions of the elements of the

CNGS beam line are known with millimetre accuracy. When

these coordinates are transformed into the global geodesy

reference frame ETRF2000 [24] by relating them to external

GPS benchmarks, they are known within 2 cm accuracy.

The analysis of the GPS benchmark positions was first

done by extrapolating measurements taken at different periods

via geodynamical models [25], and then by comparing

simultaneous measurements taken in the same reference frame.

The two methods yielded the same result within 2 cm [26]. The

travel path of protons from the BCT to the focal point of the

CNGS target is also known with millimetre accuracy.

The distance between the target focal point and the

OPERA reference frame was precisely measured in 2010

following a dedicated geodesy campaign. The coordinates of

the origin of the OPERA reference frame were measured by

establishing GPS benchmarks at the two sides of the ~10 Km

long Gran Sasso highway tunnel and by transporting their

positions with a terrestrial traverse down to the OPERA

detector. A common analysis in the ETRF2000 reference frame

of the 3D coordinates of the OPERA origin and of the target

focal point allowed the determination of this distance to be

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730534.61 ± 0.20) m [26].The 20 cm uncertainty is dominated

by the long underground link between the outdoors GPS

benchmarks and the benchmark at the OPERA detector [26].

Fig. 7: Monitoring of the PolaRx2e GPS antenna position at

LNGS, showing the slow earth crust drift and the fault displacement due

to the 2009 earthquake in the L’Aquila region. Units for the horizontal

(vertical) Axis are years (meters).

The high-accuracy time-transfer GPS receiver allows to

continuously monitor tiny movements of the Earth’s crust, such

as continental drift that shows up as a smooth variation of less

than 1 cm/year, and the detection of slightly larger effects due

to earthquakes. The April 2009 earthquake in the region of

LNGS, in particular, produced a sudden displacement of about

7 cm, as seen in Fig. 7. All mentioned effects are within the


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accuracy of the baseline determination. Tidal effects are

negligible as well. The baseline considered for the

measurement of the neutrino velocity is then the sum of the

(730534.61 ± 0.20) m between the CNGS target focal point and

the origin of the OPERA detector reference frame, and the

(743.391 ± 0.002) between the BCT and the focal point, i.e.

(731278.0 ± 0.2) .

5. Data selection

The OPERA data acquisition system (DAQ) time-tags

the detector TT hits with 10 ns quantization with respect to the

UTC [27]. The time of a neutrino interaction is defined as that

of the earliest hit in the TT. CNGS events are preselected by

requiring that they fall within a window of ± 20 µs with respect

to the SPS kicker magnet trigger-signal, delayed by the

neutrino time of flight assuming the speed of light and

corrected for the various delays of the timing systems at CERN

and OPERA. The relative fraction of cosmic-ray events

accidentally falling in this window is 10-4

, and it is therefore

negligible [1, 28].

Since TOFc is computed with respect to the origin of

the OPERA reference frame, located beneath the most

upstream spectrometer magnet, the time of the earliest hit for

each event is corrected for its distance along the beam line from

this point, assuming a time propagation according to the speed

of light. The UTC time of each event is also individually

corrected for the instantaneous value of the time link

correlating the CERN and OPERA timing systems.

The total statistics used for this analysis consists of

7586 internal (charged and neutral current interactions) and

8525 external (charged current) events. Internal events,

preselected by the electronic detectors with the same procedure

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used for neutrino oscillation studies [29], constitute a

subsample of the entire OPERA statistics (about 70%) for

which both time transfer systems at CERN and LNGS were

operational, as well as the database-logging of the proton

waveforms. As mentioned before, external events, in addition,

are requested to have a muon identified in the detector.

6. Neutrino event timing

The schematic of the SPS/CNGS timing system is

shown in Fig. 3. A general-purpose timing receiver “Control

Timing Receiver” (CTRI) at CERN [30] logs every second the

difference in time between the 1PPS outputs of the Xli and of

the more precise PolaRx2e GPS receivers, with 0.1 ns

resolution. The Xli 1PPS output represents the reference point

of the time link to OPERA. This point is also the source of the

“General Machine Timing” chain (GMT) serving the CERN

accelerator complex [31].

The GPS devices are located in the CERN Prevessin

Central Control Room (CCR). The time information is

transmitted via the GMT to a remote CTRI device in Hall

HCA442 (former UA2 experiment counting room) used to

UTC time-stamp the kicker magnet signal. This CTRI also

produces a delayed replica of the kicker magnet signal, which

is sent to the adjacent WFD module. The UTC time-stamp

marks the start of the digitization window of the BCT signal.

The latter signal is brought via a coaxial cable to the WFD at a

distance of 100 m. Three delays characterise the CERN timing

chain:

a) The propagation delay through the GMT of the time

base of the CTRI module logging the PolaRx2e 1PPS output to

the CTRI module used to time-tag the kicker pulse ΔtUTC =

(10085 ± 2) ns;


279

b) The delay to produce the replica of the kicker magnet

signal from the CTRI to start the WFD Δttrigger = (30

± 1) ns;

c) The delay from the time the protons cross the BCT to the

time a signal arrives to the WFD ΔtBCT = (580 ± 5) ns.

The kicker signal is just used as a pre-trigger and as an

arbitrary time origin. The measurement of the TOFν is based

instead on the BCT waveforms, which are tagged with respect

to the UTC.

The measurement of ΔtUTC was performed by means of

a portable Cs4000 oscillator. Its 1PPS output, stable to better

than 1ns over a few hour scale, was input to the CTRI used to

log the Xli 1PPs signal at the CERN CCR. The same signal was

then input to the CTRI that timestamps the kicker signal at the

HCA442 location. The two measurements allowed the

determination of the delay between the time bases of the two

CTRI, and to relate the kicker timestamp to the Xli output. The

measurements were repeated three times during the last two

years and yielded the same results within 2 ns. This delay was

also determined by performing a two-way timing measurement

with optical fibres. The Cs clock and the two-way

measurements also agree within 2 ns.

The two-way measurement is a technique used several

times in this analysis for the determination of delays.

Measuring the delay tA in propagating a signal to a far device

consists in sending the same signal via an optical fibre B to the

far device location in parallel to its direct path A. At this site

the time difference tA-tB between the signals following the two

paths is measured. A second measurement is performed by

taking the signal arriving at the far location via its direct path A

and sending it back to the origin with the optical fibre B. At the

origin the time difference between the production and receiving

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time of the signal corresponds to tA+tB. In this procedure the

optoelectronic chain used for the fibre transmission of the two

measurements is kept identical by simply swapping the

receiver and the transmitter between the two locations. The two

combined measurements allow determining tA and tB [32].

Δttrigger was estimated by an accurate oscilloscope

measurement. The determination of ΔtBCT was first performed

by measuring the 1PPS output of the Cs4000 oscillator with a

digital oscilloscope and comparing to a CTRI signal at the point

where the BCT signal arrives at the WFD. This was compared

to similar measurement where the Cs4000 1PPS signal was

injected into the calibration input of the BCT. The time

difference of the 1PPS signals in the two configurations led to

the measurement of ΔtBCT = (581 ± 10) ns.

Since the above determination through the calibration

input of the BCT might not be representative of the internal

delay of the BCT with respect to the transit of the protons, a

more sophisticated method was then applied. The proton transit

time was tagged upstream of the BCT by two fast beam pick-

ups BPK400099 and BPK400207 with a time response of ~1

ns [33]. From the relative positions of the three detectors (the

pick-ups and the BCT) along the beam line and the signals from

the two pick-ups one determines the time the protons cross the

BCT and the time delay at the level of the WFD. In order to

achieve an accurate determination of the delay between the

BCT and the BPK signals, a measurement was performed in

the particularly clean experimental condition of the SPS proton

injection to the Large Hadron Collider (LHC) machine of 12

bunches with 50 ns spacing, passing through the BCT and the

two pick-up detectors. This measurement was performed

simultaneously for the 12 bunches and yielded ΔtBCT = (580 ±

5 (sys.)) ns.


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The schematic of the OPERA timing system at LNGS

is shown in Fig. 6. The official UTC time source at LNGS is

provided by a GPS system ESAT 2000 [34, 35] operating at the

surface laboratory. The 1PPS output of the ESAT is logged

with a CTRI module every second with respect to the 1PPS of

the PolaRx2e, in order to establish a high-accuracy time link

with CERN. Every millisecond a pulse synchronously derived

from the 1PPS of the ESAT (PPmS) is transmitted to the

underground laboratory via an 8.3 Km long optical fibre. The

delay of this transmission with respect to the ESAT 1PPS

output down to the OPERA master clock output was measured

with a two-way fibre procedure and amounts to (40996 ± 1) ns.

Measurements with a transportable Cs clock were also

performed yielding the same result. The OPERA master clock

is disciplined by a high-stability oscillator Vectron OC-050

with an Allan deviation of 2×10-12

/s. This oscillator keeps the

local time in between two external synchronisations given by

the PPmS signals coming from the external GPS.

The time base of the OPERA master clock is

transmitted to the frontend cards of the TT. This delay (Δtclock)

was also measured with two techniques, namely by the two-

way fibres method and by transporting the Cs4000 clock to the

two points. Both measurements provided the same result of

(4263 ± 1) ns. The frontend card time-stamp is performed in a

FPGA (Field Programmable Gate Arrays) by incrementing a

coarse counter every 0.6 s and a fine counter with a frequency

of 100 MHz. At the occurrence of a trigger the content of the

two counters provides a measure of the arrival time. The fine

counter is reset every 0.6 s by the arrival of the master clock

signal that also increments the coarse counter. The internal

delay of the FPGA processing the master clock signal to reset

the fine counter was determined by a parallel measurement of

trigger and clock signals with the DAQ and a digital

oscilloscope. The measured delay amounts to (24.5 ± 1.0) ns.

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This takes into account the 10 ns quantization effect due to the

clock period.

The delays in producing the Target Tracker signal

including the scintillator response, the propagation of the

signals in the WLS fibres, the transit time of the

photomultiplier [8], and the time response of the OPERA

analogue frontend readout chip (ROC) [36] were overall

calibrated by exciting the scintillator strips at known positions

by a UV picosecond laser [37]. The arrival time distribution of

the photons to the photocathode and the time walk due to the

discriminator threshold in the analogue frontend chip as a

function of the signal pulse height were accurately

parameterized in laboratory measurements and included in the

detector simulation. The total time elapsed from the moment

photons reach the photocathode, a trigger is issued by the ROC

analogue frontend chip, and the trigger arrives at the FPGA,

where it is time-stamped, was determined to be (50.2 ± 2.3) ns.

Since the time response to neutrino interactions

depends on the position of the hits in the detector and on their

pulse height, the average TT delay was evaluated by computing

the difference between the exact interaction time and the time-

stamp of the earliest hit for a sample of fully simulated neutrino

interactions. Starting from the position at which photons are

generated in each strip, the simulation takes into account all the

effects parametrized from laboratory measurements including

the arrival time distribution of the photons for a given

production position, the time-walk of the ROC chip, and the

measured delays from the photocathode to the FPGA. This TT

delay has an average value of 59.6 ns with a RMS of 7.3 ns,

reflecting the transverse event distribution inside the detector.

The 59.6 ns represent the overall delay of the TT response

down to the FPGA and they include the above-mentioned delay


283

of 50.2 ns. A systematic error of 3 ns was estimated due to the

simulation procedure. Several checks were performed by

comparing data and simulated events, as far as the earliest TT

hit timing is concerned. Data and simulations agree within the

Monte Carlo systematic uncertainty of 3 ns for both the time

difference between the earliest and the following hits, and for

the difference between the earliest hit and the average hit

timing of muon tracks.

More details on the neutrino timing as well as on the

geodesy measurement procedures can be found in [38].

7. Data analysis

The data analysis was performed blindly by

deliberately assuming the setup configuration of 2006. In

particular, important calibrations were not available at all that

time, such as the BCT delay ΔtBCT, the trigger delay Δttrigger and

the improved estimate of the UTC delay ΔtUTC. Also TOFc was

not expressed with respect to the BCT position but referred to

another conventional point upstream in the beam line. DAQ

and detector delays were not taken into account either. This led

by construction to an unrealistically large deviation from TOFc,

much larger than the individual calibration contributions. The

precisely calibrated corrections applied to TOFν and yielding

the final δt value are summarized in Table 1.

For each neutrino interaction measured in the OPERA

detector the analysis procedure used the corresponding proton

extraction waveform. These were summed up and properly

normalised in order to build a PDF w(t). The WFD is triggered

by the magnet kicker pulse, but the time of the proton pulses

with respect to the kicker trigger is different for the two

extractions. The kicker trigger is just related to the pulsing of

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the kicker magnet. The exact timing of the proton pulses stays

within this large window of the pulse.

A separate maximum likelihood procedure was then

carried out for the two proton extractions. The likelihood

function to be maximised for each extraction is a function of

the single variable δt to be added to the time tags tj of the

OPERA events. These are expressed in the time reference of

the proton waveform digitizer assuming neutrinos travelling at

the speed of light, such that their distribution best coincides

with the corresponding PDF:

Near the maximum the likelihood function can be

approximated by a Gaussian function, whose variance is a

measure of the statistical uncertainty on δt (Fig. 8). As seen in

Fig. 9, the PDF representing the time-structure of the proton

extraction is not flat but exhibits a series of peaks and valleys,

reflecting the features and the inefficiencies of the proton

extraction from the PS to the SPS via the Continuous Turn

mechanism [39]. Such structures may well change with time.

The way the PDF are built automatically accounts for the beam

conditions corresponding to the neutrino interactions detected

by OPERA. The result of the maximum likelihood analysis of

δt for the two proton extractions for the years 2009, 2010 and

2011 are compared in Fig. 10. They are compatible with each

other.


285

Data were also grouped in arbitrary subsamples to look

for possible systematic dependences. For example, by

computing δt separately for events taken during day and night

hours, the absolute difference between the two bins is (17.1 ±

15.5) ns providing no indication for a systematic effect. A

similar result was obtained for a possible summer vs spring +

fall dependence, which yielded (11.3 ± 14.5) ns.

The maximum likelihood procedure was checked with

a Monte Carlo simulation. Starting from the experimental

PDF, an ensemble of 100 data sets of OPERA neutrino

interactions was simulated. Simulated data were shifted in

time by a constant quantity, hence faking a time of flight

deviation. Each sample underwent the same maximum

likelihood procedure as applied to real data. The analysis

yielded a result accounting for the statistical fluctuations of

the sample that are reflected in the different central values and

their uncertainties.

The average of the central values from this ensemble

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of simulated OPERA experiments reproduces well the time

shift applied to the simulation (at the 0.3 ns level). The

average statistical error extracted from the likelihood analysis

also reproduces within 1 ns the RMS distribution of the mean

values with respect to the true values.

.

Fig. 8: Log-likelihood distributions for both extractions as a

function of δt, shown close to the maximum and fitted with a parabolic

shape for the determination of the central value and of its uncertainty

The result of the blind analysis shows an earlier arrival

time of the neutrino with respect to the one computed by

assuming the speed of light δt (blind) = TOFc -TOFν = (1048.5

± 6.9 (stat.)) ns. As a check, the same analysis was repeated

considering only internal events. The result is δt (blind) =


287

(1047.4 ± 11.2 (stat.)) ns, compatible with the systematic error

of 2 ns due to the inclusion of external events. The agreement

between the proton PDF and the neutrino time distribution

obtained after shifting by δt (blind) is illustrated in Fig. 11. The

χ2

/ndf is 1.06 for the first extraction and 1.12 for the second

one. Fig. 12 shows a zoom of the leading and trailing edges of

the distributions given in the bottom of Fig. 11.

Fig. 9: Summed proton waveforms of the OPERA events corresponding

to the two SPS extractions for the 2009, 2010 and 2011 data samples.

Fig.

10: Results of the maximum likelihood analysis for δt corresponding to

the two SPS extractions for the 2009, 2010 and 2011 data samples.

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Fig. 11: Comparison of the measured neutrino interaction time

distributions (data points) and the proton PDF (red line) for the two SPS

extractions before (top) and after (bottom) correcting for δt (blind)

resulting from the maximum likelihood analysis.

The 17.4 ns correction in Table 1 takes into account all

the effects related to DAQ and TT delays, as well as the

difference between the value of Δtclock determined in 2006 from

a test-bench measurement and the one obtained on-site with the

procedure previously described. The 353 ns relative to the 2006

calibration assume the relative synchronisation of the CERN

and LNGS GPS systems prior to the installation of the two

high-accuracy systems operating in common-view mode. One


289

then obtains:

δt = TOFc –TOFν = 1048.5 ns – 987.8 ns = (60.7 ± 6.9 (stat.))

ns

The above result is also affected by an overall systematic

uncertainty of 7.4 ns coming from the quadratic sum of the

different terms previously discussed in the text and summarised

in Table 2. The dominant contribution is due to the calibration

of the BCT time response. The error in the CNGS-OPERA GPS

synchronisation has been computed by adding in quadrature the

uncertainties on the calibration performed by the PTB and the

internal uncertainties of the two high-accuracy GPS systems.

The final result of the measurement is (Fig. 13):

δt = TOFc -TOFν = (60.7 ± 6.9 (stat.) ± 7.4 (sys.)) ns.

We cannot explain the observed effect in terms of

presently known systematic uncertainties. Therefore, the

measurement indicates an early arrival time of CNGS muon

neutrinos with respect to the one computed assuming the speed

of light in vacuum. The relative difference of the muon neutrino

velocity with respect to the speed of light is:

(v-c)/c = δt /(TOF’c -δt) = (2.48 ± 0.28 (stat.) ± 0.30 (sys.)) ×

10-5

,

with 6.0 σ significance. In performing this last calculation a

baseline of 730.085 Km was used, and TOF’c corresponds to

this effective neutrino baseline starting from the average decay

point in the CNGS tunnel as determined by simulations.

Actually, the δt value is measured over the distance from the

BCT to the OPERA reference frame, and it is only determined

by neutrinos and not by protons and pions, which introduce

negligible delays.

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Fig. 12: Zoom of the leading (left plots) and trailing edges (right plots)

of the measured neutrino interaction time distributions (data points) and

the proton PDF (red line) for the two SPS extractions after correcting for

δt (blind).

A possible neutrino energy dependence of δt was

studied in order to investigate the physics origin of the early

arrival time of CNGS neutrinos. For this analysis the data set

was limited to νµ CC interactions occurring in the OPERA target

(5489 events), for which the neutrino energy can be measured

by adding the muon momentum to the hadronic energy. Details

on the energy reconstruction in the OPERA detector are

available in [15]. A first measurement was performed by

considering all νµ CC internal events. We obtained δt = (60.3 ±

13.1 (stat.) ± 7.4 (sys.)) ns, for an average neutrino energy of

28.1 GeV.


291

Table 2:

Contribution to the overall systematic uncertainty on the

measurement of δt.

Data were then split into two bins of nearly equal

statistics, including events of energy lower or higher than 20

GeV. The mean energies of the two samples are 13.9 and 42.9

GeV. The result for the low-and high-energy data sets are,

respectively, δt = (53.1 ± 18.8 (stat.) ± 7.4 (sys.)) ns and (67.1

± 18.2 (stat.) ± 7.4 (sys.)) ns. The above result was checked

against a full Monte Carlo simulation of the OPERA events.

The same procedure used for real data was applied to νµ CC

simulated interactions in the OPERA target. The comparison

between the two data sets indicates no energy dependence, with

a difference of ~1 ns. The simulation does not indicate any

instrumental effects on δt possibly caused by an energy

dependent time response of the detector. Therefore, the

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systematic uncertainties of the two measurements tend to

cancel each other out regarding the difference of the two

values, which amounts to (14.0 ± 26.2) ns. This result,

illustrated in Fig. 13, provides no clues on a possible energy

dependence of δt in the domain explored by OPERA, within

the statistical accuracy of the measurement.

Fig. 13: Summary of the results for the measurement of δt. The left plot

shows δt as a function of the energy for νµ CC internal events.

The errors attributed to the two points are just statistical in

order to make their relative comparison easier since the

systematic error (represented by a band around the no-effect

line) cancels out. The right plot shows the global result of the

analysis including both internal and external events (for the

latter the energy cannot be measured). The error bar includes


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statistical and systematic uncertainties added in quadrature.

Conclusions

The OPERA detector at LNGS, designed for the study

of neutrino oscillations in appearance mode, has provided a

precision measurement of the neutrino velocity over the 730

Km baseline of the CNGS neutrino beam sent from CERN to

LNGS through the Earth’s crust. A time of flight measurement

with small systematic uncertainties was made possible by a

series of accurate metrology techniques. The data analysis took

also advantage of a large sample of about 16000 neutrino

interaction events detected by OPERA.

The analysis of internal neutral current and charged

current events, and external νµ CC interactions from the 2009,

2010 and 2011 CNGS data was carried out to measure the

neutrino velocity. The sensitivity of the measurement of (v-c)/c

is about one order of magnitude better than previous accelerator

neutrino experiments.

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The results of the study indicate for CNGS muon

neutrinos with an average energy of 17 GeV an early neutrino

arrival time with respect to the one computed by assuming the

speed of light in vacuum:

δt = (60.7 ± 6.9 (stat.) ± 7.4 (sys.)) ns.

The corresponding relative difference of the muon

neutrino velocity and the speed of light is:

(v-c)/c = δt /(TOF’c -δt) = (2.48 ± 0.28 (stat.) ± 0.30 (sys.)) ×

10-5

.

with an overall significance of 6.0 σ.

The dependence of δt on the neutrino energy was also

investigated. For this analysis the data set was limited to the

5489 νµ CC interactions occurring in the OPERA target. A

measurement performed by considering all νµ CC internal

events yielded δt = (60.3 ± 13.1 (stat.) ± 7.4 (sys.)) ns, for an

average neutrino energy of 28.1 GeV. The sample was then

split into two bins of nearly equal statistics, taking events of

energy higher or lower than 20 GeV. The results for the low-

and high-energy samples are, respectively, δt = (53.1 ± 18.8

(stat.).) ± 7.4 (sys.)) ns and (67.1 ± 18.2 (stat.).) ± 7.4 (sys.))

ns. This provides no clues on a possible energy dependence of

δt in the domain explored by OPERA within the accuracy of

the measurement.

Despite the large significance of the measurement

reported here and the stability of the analysis, the potentially

great impact of the result motivates the continuation of our

studies in order to investigate possible still unknown

systematic effects that could explain the observed anomaly.


295

We deliberately do not attempt any theoretical or

phenomenological interpretation of the results.

Acknowledgements

We thank CERN for the successful operation and

INFN for the continuous support given to the experiment

during the construction, installation and commissioning

phases through its LNGS laboratory. We are indebted to F.

Riguzzi of the Italian National Institute of Geophysics and

Volcanology for her help in geodynamical analysis of the

high-frequency PolaRx2e data. We warmly acknowledge

funding from our national agencies: Fonds de la Recherche

Scientifique FNRS and Institut Interuniversitaire des Sciences

Nucléaires for Belgium; MoSES for Croatia; CNRS and

IN2P3 for France; BMBF for Germany; INFN for Italy; JSPS

(Japan Society for the Promotion of Science), MEXT

(Ministry of Education, Culture, Sports, Science and

Technology), QFPU (Global COE program of Nagoya

University, ”Quest for Fundamental Principles in the

Universe” supported by JSPS and MEXT) and Promotion and

Mutual Aid Corporation for Private Schools of Japan for

Japan; The Swiss National Science Foundation (SNF), the

University of Bern and ETH Zurich for Switzerland; the

Russian Foundation for Basic Research (grant 09-02-00300

a), the Programs of the Presidium of the Russian Academy of

Sciences ”Neutrino Physics” and ”Experimental and

theoretical researches of fundamental interactions connected

with work on the accelerator of CERN”, the Programs of

support of leading schools (grant 3517.2010.2), and the

Ministry of Education and Science of the Russian Federation

for Russia; the Korea Research Foundation Grant (KRF-2008-

313-C00201) for Korea; and TUBITAK The Scientific and

Technological Research Council of Turkey, for Turkey. We

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are also indebted to INFN for providing fellowships and

grants to non-Italian researchers. We thank the IN2P3

Computing Centre (CC-IN2P3) for providing computing

resources for the analysis and hosting the central database for

the OPERA experiment. We are indebted to our technical

collaborators for the excellent quality of their work over many

years of design, prototyping and construction of the detector

and of its facilities.


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CHAPTER 12 CONCLUSIONS

My conclusions from the analysis made here are very simple. The

world we live in, and the measurements we, and physicists, make are

all tied to what we see in the world when we look around us. The

measurements are dependent on light, or other forms of radiation as

they are perceived in our own local universe.

Prior to the beginning of the 20th century, the world was a simpler

place, where things moved relatively slowly, compared to the speed

of light, and we could well believe that what we were seeing was the

world as it really existed at that moment in time. Relationships

between the velocity of objects, their mass and the change in velocity

resulting from the application of some kind of force, seemed to be

straightforward and irrevocable.

But, physicists were experimenting with the only thing that moved

really fast --- light itself. And they were surprised to find that light

did not follow the rules that had been defined by Isaac Newton for

the relationship between velocities. When the speed of light was

measured accurately by a “stationary” apparatus, it came out the

same as it did when measured by a moving apparatus. That didn’t

seem right, but there was no way to deny the accuracy of the

experimenters who measured the velocity.

Albert Einstein was the first one to put the experimental data into a

framework which seemed to explain everything. He did it without

doing any experimentation at all, by simply applying some of the

mathematical techniques which were available to describe a model

of the universe in which a beam of light would appear to be moving

at the same speed if two observers moving relative to each other

measured it and got the same answer.

There were, of course, some complications. These included some

peculiar properties of time, which everyone had considered to be

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absolute and independent of anything else. Time had to be allowed

to expand, so that clocks would run more slowly if they were moving

with respect to the stationary observer. This, in turn, required that

the space had to appear differently to moving observers than to

stationary ones, and that physical objects had to get shorter as their

velocities increased. In terms of the equations of Special Relativity,

nothing could go faster than the apparent speed of light.

Finally, the coup de grace was that masses of objects had to increase

as they accelerated to higher velocities in order to avoid reaching

velocities which would exceed c, the apparent speed of light.

I have proposed that the experimenters who measured the apparent

speed of light from both “moving” and “stationary” vantage points

were, in fact, measuring the rate at which the universe is expanding

into a fourth spatial dimension. We are unaware of anything beyond

our normal three dimensions; although vaguely aware that time has

some properties like a fourth dimension.

If, in fact, they were measuring the a constant velocity at which we

(everyone and everything in the universe) are moving in this

direction, it would it would explain why light seems to be moving at

this rate, when it is actually being transferred from a source to a

receptor instantaneously.

This simple change in viewpoint would make much of the

complexity of the physical world as it is commonly regarded by

physical scientists go away. There would no longer be a limitation on

the speed at which material objects can travel. They wouldn’t get

shorter and become more massive as their velocity increases relative

to any fixed reference system. And, matter and energy are no longer

necessarily interchangeable.

Newton’s laws of motion would, once again, work and relativistic

correction factors would only have to be used if one chose to use

the particular galactic playing field in which most scientific

experiments are erroneously presumed to be conducted. Time


303

would, once again, be the same everywhere, but the measurement of

time would have to be done realistically, taking into account that o

These conclusions are of no consequence whatever to any of us in

the conduct of our ordinary lives. The people to whom this might

have some significant meaning are the scientists who are cooperating

on the biggest scientific project the world has even known, the

CERN Large Hadron Collider. I would be surprised but pleased if

any one of them showed sufficient interest to prove me wrong.

light in the local universe

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