mass theory

Mass and Gravitation - - 1 - Open and Closed Volumes 1

The Spacetime Model Part 1/5

Version 4.01 October 5th 2010

Author : Jacky JEROME Ingénieur Européen EUR-ING

Ingénieur DE, Ingénieur IPF, Ingénieur ITP-ECI

Tel: (0033) 615146741 Email: [email protected]

Mass and Gravitation An alternative to the Higgs

and Strings Theories


Patent Rights

This theory, the "Spacetime Model", was registered in different legal forms for Copyright and at INPI, the French Patent Institute, under the following references:

238268, 238633, 244221, 05 13355-2 895 559, 248427, 258796, 261255, 268327, 297706, 297751, 297811, 297928, 298079, 298080, 329638, 332647, 335152, 335153, 339797.

First deposit date at INPI: May 5th, 2005 Major deposit date at INPI: December 27th, 2005

In 2006, this theory was addressed to more than 7000 physicists worldwide by e-mail. Several paper copies were sent in October 2006 to the most important Academics of Science and Committees of Foundations for Research. The "Spacetime Model" was also published on November 30th , 2006, on 28 different web sites. It is also referenced on many sites like Google and Google Books, Yahoo, DMOZ... More than 145 000 Internet Users have read it with a satisfactory of 96,5%. The "Spacetime Model" is the intellectual property of its author, Jacky JEROME, and any illicit appropriation of the theory will be subject to prosecution.


Abstract

Introduction A close examination of the Einstein Field Equations conducts to a new explanation of mass and gravitation. In this paper, we show that replacing the well-known combination "Attractive force + mass" by "Pressure force + volume" perfectly solves the mass and gravitation enigma, staying in a 4D space with m = f(x,y,z,t). Mass It is not the mass of an object which deforms spacetime but its volume, more exactly its "closed volume", the later being explained in the text. This curvature of spacetime is convex. As a result, spacetime exerts a pressure force on the surface of the closed volume which acts as a "mass effect". Gravitation Two closed volumes inserted into spacetime make a convex curvature of it. Since spacetime is elastic (Einstein), this curvature produces an external pressure on these volumes, which tends to bring them closer to each other. So, contrary to what we think, gravitation is not an "attractive force between masses" but an "external pressure force exerted by spacetime on closed volumes". Mathematics This paper also gives the expression m = f(x,y,z,t) and calculates from scratch, with a great simplicity and without using tensors, the Newton Law of Universal Gravitation and the Schwarzschild Metric. Originality of these calculations is the fact that they are based on the new combination, "Pressure force + volume", instead of the well known "Attractive force + mass".

The table of contents is located at the end of this document


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1. Open and Closed Volumes

To solve the mass and gravitation enigma, it is necessary to redefine what exactly the volume is. So, this subject was divided into two chapters: Open and Closed Volumes, and Gravitation. Each chapter covers half of the solution.

1.1 Starting point The starting point of this new theory are some minor inconsistencies found in the Einstein Field Equations (EFE). Since tensors aren't easy to understand, this topic is covered in Supplementary Information D: "EFE vs Constraint tensor". This part may be bypassed for a first reading.

1.2 Current theory Einstein's equations connect mass to spacetime curvature. Scientific authors often represent the spacetime curvature by a drawing like that of figure 1-1. This representation is elegant but highly speculative since it does not answer the question:

“How is it possible for a mass to curve spacetime?”

Fig. 1-1


This figure was simplified to two dimensions for teaching purposes.

Fig. 1-2

1.3 Curvature of spacetime Let's drop a billiard ball into a container filled with water. The volume of the ball will produce a displacement of water.

The same phenomenon applies to spacetime, with some minor reservations described further (fig. 1-2). So, contrary to preconceived ideas, it is the volume, not the mass, which deforms spacetime1. This curvature is convex.

Any volume inserted into spacetime necessarily produces a curvature of it.

This simple explanation conducts to a question : What is the volume?

1.4 Definition of the volume Lets consider the two associations Sun-Jupiter (fig. 1-3 a) and nucleus-electron (fig. 1-3 b). 1 Whatever the dimension of the space is, 1D, 2D, 3D or 4D, we always have the same phenomenon. For example, let's imagine a simple line (1D). A small segment inserted into the middle of the line will push out its two ends to make room. Similarly, in 2D, a small surface inserted into a larger one will push out the surrounding surface to make room, and so on…. Spacetime shares the same principle. Any volume inserted in spacetime pushes out surrounding spacetime to get room. The word "volume" may not be exact since a volume has three dimensions, not four. In reality, according to special relativity, time and volume form a whole. Therefore, a 3D volume in everyday life becomes a 4D spacetime in physics.

a b

Fig. 1-3

Sun

Jupiter

Nucleus

Electron


Sun-Jupiter (fig. 1-3 a): The overall volume of this association is the sum of Sun + Jupiter. It would have no sense to take into account the volume of the Jupiter's orbit around the Sun.

Atom (fig. 1-3 b): Curiously, the overall volume of atoms is that of their orbitals, which is a nonsense.

So, in two identical situations, we have two different definitions of the word "Volume".

1.5 Open and closed volumes Let's replace the billiard ball of our example by an empty sphere having the same volume (fig. 1-4 a). Water produces a pressure on its surface. If we make some holes in this sphere (fig. 1-4 b), water goes inside and the pressure disappears. However, the sphere keeps the its original volume.

So, we have two different definitions of "volume": one is subject to an external pressure (a), the other not (b).

The same phenomenon also exists in spacetime. In reality, we have two classes of volumes:

Closed volumes (fig. 1-4 a): These volumes make a displacement of spacetime1, which produces a pressure on the surface of the volume. A "mass effect" appears, that is to say an effect having all characteristics of mass2. Fermions, their associations, empty volumes enclosed inside the nucleus (see § 3.5) etc… are examples of closed volumes. Only closed volumes deform spacetime, and since "spacetime curvature ≡ mass" (Einstein, see § 1.7), only closed volumes have a "mass effect".

1 Considering that spacetime is present anywhere, we could think that a closed volume is crossed itself by spacetime. Consequently, a closed volume could not curve spacetime itself. In reality, particles, atoms and molecules are continuously in movement. So, let's imagine a sphere of Minkowski spacetime, far from any mass, with a global volume equal to that of 1000000 protons. Following an interaction for example, a proton crosses this flat spacetime. When the proton will be in the centre of the sphere, we will have 1000000+1=1000001 protons for a volume of 1000000 protons. Due to the elasticity of spacetime (Einstein), the sphere will keep its original volume. As a result, spacetime of the bounds will not move, but spacetime near the proton will be compressed. So, we will have a curvature of spacetime near the proton (see fig. 3-2 b). 2 The "mass effect" [M] must not be confused with the pressure [M/LT²]. Paragraph 1.10 and Supplementary Information C cover this subject.

Yes Mass effect No No mass effect

Curvature of spacetime ?

a Fig. 1-4 b


Open volumes (fig. 1-4 b): These volumes exist but do not produce any displacement of spacetime. They are "porous" regarding spacetime. According to Einstein, if there is no curvature, there is no mass effect either. Orbitals of atoms and empty space between atoms or molecules are examples of open volumes. These volumes are massless.

1.6 Our view of the volume In reality, we are faced to two different points of view (fig. 1-5) :

• Everyday life - Mass and volume are two different definitions because people don't have to know the laws of physics.

• In Physics - Physicists must take into account exclusively closed volumes because only these volumes curve spacetime. Since "Spacetime curvature ≡ mass", only closed volumes have a mass. Open volumes, which are a vacuum, don't curve spacetime and, therefore, they can't have a mass. This means that open volumes must be ignored by physicists in mass calculations.

ClosedVolume

M ≠ V

Open volumes must be ignored

Mass

Physics

Volume Mass

Everyday life

M ≡ V

Fig. 1-5


1.7 Einstein Equations In special relativity, Einstein connects mass to energy by the well-known formula E = mc². In general relativity, he connects energy, therefore mass, to curvature of spacetime. If we replace "mass" by "mass effect", the Einstein Identity becomes:

Mass Effect ≡ Curvature of Spacetime Since the spacetime curvature comes from closed volumes exclusively, the Einstein Identity becomes:

1.8 Example: The twin paradox The twin paradox is a "thought experiment" in which a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on Earth. To explain this enigma, or time dilatation, let's consider two times, "t1" and "t2", in a flat Minkowski spacetime (fig. 1-6 a). We have t1 = t2. A closed volume inserted into this flat spacetime will curve it. According to special relativity, space and time form a whole. As a result, we will get t1 < t2 (fig. 1-6 b). If the volume is static with a spherical symmetry, the mathematical expression of t1 = f(t2) is given by the Schwarzschild Metric. Otherwise, the expression of t1 = f(t2) is a solution of the Einstein Field Equations, like that of Kerr, Reissner-Nordström, Robertson-Walker etc...

Fig. 1-6

t1

t2

a b

t1

t2

Mass Effect ≡

Curvature of Spacetime ≡

Closed volume


Please note that a new calculation of the Schwarzschild Metric is covered in Supplementary Information B. Originality of this calculation is that it is based on the convex curvature of spacetime by a closed volume, instead of the traditional "concave curvature + mass". To summarize, figure 1-6 and this new calculation of the Schwarzschild Metric fully explain the time dilatation enigma in the Twin Paradox.

1.9 Confirmation: Atoms Experimentation confirms the proposed theory since atoms are made of (fig. 1-7):

• A nucleus and electron(s): These closed volumes deform spacetime. Since "spacetime curvature ≡ mass effect", the nucleus and electron(s) have a mass1.

• Massless orbitals: It is obvious that orbitals, which are nothing but a vacuum, don't curve spacetime. Therefore, according to Einstein (spacetime curvature ≡ mass effect), orbitals are massless.

All components of the universe are combinations of these two classes of volumes: closed volumes (nucleus, particles…), having a mass, and open volumes (orbitals, a vacuum…), without mass. This proportion varies from one atom or molecule to another.

1 Theoretically, we must also take into account energy levels of atoms which are identical to mass since E = mc². Please see the two next paragraphs and Supplementary Information C about this topic.

Fig. 1-7

Open volume(s): Orbital(s)

Closed volumes: Electron(s) and

Nucleus

Spacetime

This is why we have the illusion, in everyday life on Earth, that mass and volume are two different concepts.


1.10 The reality of mass In our subconscious, the mass is "something material that has some weight", although one should not confuse mass and weight. In reality, the mass is a virtual entity produced by the curvature of spacetime. This is why, in this paper, we have replaced the word "mass" (meaning "material") with "mass effect" (meaning "virtual"). Speed, energy, pressure etc. are some virtual quantities which exist ... without existing in concrete terms. The mass effect is one of these virtual quantities. In our 4D universe, the only real quantities are space (x,y,z) and time (t). So, we have:

Speed = f(x,y,z,t) Energy = f(x,y,z,t) Pressure = f(x,y,z,t) Gravitation = f(x,y,z,t) Force = f(x,y,z,t) etc….

Some quantities contains the mass variable "m" and/or constants related to the mass, like G0, the universal constant of gravitation. These terms can be replaced by the equivalent expression of the "mass effect", m = f(x,y,z,t) (Supplementary Information C covers the real expression of mass), or by associations of constants. This conducts to represent all the laws of physics with only four dimensions: f(x,y,z,t).

1.11 Conclusions Replacing mass by closed volume provides the following advantages:

To have a consistent and scientific explanation of the curvature of spacetime,

To understand the time dilatation enigma as in the twin paradox,

To follow the view of Einstein who believed that the universe has only four dimensions. No extra dimension as in the Higgs and String Theories are necessary. Since mass effect ≡ closed volume, the expression of the mass effect "m" is that of a simple volume: m = f(x,y,z,t), with x,y,z = the coordinates of the closed volume, and t the time, as defined in special relativity.

To solve the inconsistency "Virtual ≡ Material" found in some laws of physics, as E = mc². In that equation for example, how can the mass be equal to energy ? Logically speaking, this equation is a non sense. Replacing "mass" (meaning "material") by "mass effect" (meaning "virtual") conducts to a new identity: "virtual ≡ virtual". So, each term of E = mc² becomes a 4D virtual expression:

E = f(x,y,z,t) m = f(x,y,z,t) c = f(x,y,z,t)


As a result, equation E = mc² becomes perfectly homogeneous and consistent. We can extend the same reasoning to laws of physics which includes variables or constants related to mass, and, in all cases, we obtain perfectly homogeneous and consistent equations "virtual ≡ virtual" or "material ≡ material ".

To have a consistent and scientific explanation of gravitation (see the next chapter).

Logical and consistent explanation

Closed Volume Proposed theory

No scientific explanation of the curvature of spacetime by mass

Mass

?

Spacetime is curved by:

Mass and Gravitation - - 2 - Gravitation 13

2. Gravitation

The precedent chapter demonstrates that spacetime is curved by closed volumes and not by mass. It also demonstrates that open volumes must be ignored in physics since they don't curve spacetime. Now, the challenge is to understand how such a spacetime curvature made by closed volumes can produce gravitation. This phenomenon is quite simple too.

2.1 Principle of gravitation Two closed volumes inserted into spacetime curve it. Since spacetime is elastic, this curvature produces an external pressure on these two volumes which tends to bring them closer to each other (fig. 2-1). So, contrary to what we think,

Since a pressure force is the opposite of an attractive force, result is unchanged:

Attractive force + Pressure force + Concave curvature of spacetime = Convex curvature of spacetime

Fig. 2-1

Gravitation is not an attractive force between masses but an external pressure force exerted

by spacetime on closed volumes


2.2 Principle of split To understand what gravitation is, we can also use the "principle of split" from the 1850's. This thought experiment comes from the fluid mechanics and is used to build the constraint tensor. Let's imagine a sphere, which has two opposite forces (fig. 2-2 a). Here, these forces comes from elasticity of spacetime. If we split this sphere down the middle (fig. 2-2 b), we have a movement of each half toward the other. Transposed to spacetime, this phenomenon is nothing but "gravitation".

2.3 Conclusions

a b

Fig. 2-2

Fig. 2-3

Gravitation ???

Mass ???Volume

Spacetime curvature ???

Today : No explanation of mass and gravity

Object


Fig. 2-4

Closed volumes curve spacetime

SpacetimeElasticity

(Einstein)

Closed volumes

Object

Proposed Theory

Mass effect

Gravitation

A "mass effect" due to the pressure of

spacetime on the surface is

associated with each closed

volume.

Only volume physically exists. Mass does not exist as such. Mass is an effect produced by the pressure of spacetime on closed volumes. This pressure on the surface of closed volumes also explains gravitation.

1

2

4Open volumes (ignored)

Spacetime exerts a pressure force on closed volumes

3

Mass and Gravitation - - 3 - Experimentations 17

3. Experimentations

This chapter presents some well-known applications which tend to confirm the theory proposed in this paper.

3.1 Higgs' Intuition One of the Higgs Basis is: "Particles get mass when they move in the Higgs Field". Peter Higgs' idea is correct but, in reality, the Higgs Field is nothing but …spacetime. The following experimentation confirms this point of view:

Why does the mass of a particle moving inside a crystal increase (fig. 3-1)? The lattice of a crystal is an array of tunnels. The particle moves inside one of these tunnels. Closed volumes of each atom of the crystal (nucleons, electrons) curve the spacetime located inside the tunnel, on the path of the particle. Therefore, the density of spacetime will be higher inside the tunnel than outside the crystal. The curvature of spacetime made by atoms is added to that made by the closed volume of the particle. Since the curvature of spacetime increases, the mass effect also increases since "spacetime curvature ≡ mass effect" (see § 1.7 : Einstein Equations).

Fig. 3-1

m (out of the crystal)

M

M > m Note

M, m = "mass effect" (not "mass")


3.2 The Von Laue Diagram1 A set of concentric circles is drawn on an expanded polypropylene (EPP) foam (fig. 3-2 a). These lines represent the geodesics of spacetime far from any mass (Minkovski space). If a static spherical symmetry closed volume is inserted in the centre, the EPP foam will be subject to a curvature (fig. 3-2 b). The Minkovski space becomes a Schwarzschild space.

Figure 3-2 b has been duplicated in fig. 3-3. The Von Laue Geodesics has been drawn over these circles. We see that the Von Laue Geodesics match EXACTLY the concentric circles. In other words, the Von Laue Diagram seems to confirm the theory described in this paper.

1 Von Laue, 1921, page 226, reported by Jean Eisenstaedt "Einstein and General Relativity", page 247.

Fig. 3-3 2GM/c²

3GM/c²

3◊3 GM/c² Von Laue Geodesics

Fig. 3-2

a b


3.3 Mass-volume equivalence he following basic example proves that mass and gravity are two phenomena produced by
T
closed volumes.

This simple thought experiment demonstrates that what we call "mass" is, in reality, a "mass-effect", which comes from the pressure exerted by the curvature of spacetime on the closed volumes of the pen and eraser (nucleons and electrons). In this example, for teaching purposes, gravitation has been taken into account, but this doesn't modify the reasoning because, far from any gravitation field, the curvature of spacetime also exists. It is produced by the closed volumes of the pen and eraser. 1 For teaching purposes, mass of electrons, binding energy etc… has been ignored. Moreover, we consider that the volume of protons is identical to that of neutrons.

On our left, we have an eraser and on our right, a pen that weighs two times more.

x2

If we remove the 99.999% of vacuum existing inside the atoms of the two objects, we obtain two heaps of nucleons. We will have two times more nucleons for the pen than for the eraser because protons are practically identical to neutrons1.

x2

Since all nucleons have the same volume, nucleons of the pen will have a total "closed volumes" two times greater to those of the eraser.

Therefore, the pen will produce twice more curvature of spacetime than that produced by the eraser. The spacetime curvature will produce a pressure two times stronger over the pen than over the eraser in the pen/eraser-Earth context. Therefore, the pen will be two times heavier than the eraser.

x2

x2P p


3.4 Relativistic particles Why does the mass of a particle increase when its speed approaches that of light? The proposed theory solves this enigma with a great simplicity (fig. 3-4). The speed of the particle produces a compression of spacetime. This phenomenon is identical to that described in paragraph 3.1 concerning particles in a crystal. In that case, the increase of spacetime density comes from the atoms of the tunnel. In relativistic particles, the increase of density comes from the compression of spacetime. So, in both cases we are faced with the same phenomenon: an increase of spacetime density. Therefore, contrary to what we think, at relativistic speed, the "mass" of a particle remains unchanged1. It is its "mass effect" due to the compression of spacetime that increases.

3.5 The mass excess The "mass effect" is function of closed volumes which produce the curvature of spacetime. The shape of the surface must also be taken into account, as in the Bethe-Weizsäcker formula, because spacetime acts on the surface of the volume.

1 When relativist particles are broken in an accelerator, sub-particles produced follow the same rule. As original particles, they curve spacetime giving us the illusion that they are massive. In reality, the mass of these sub-particles remains unchanged. It is the curvature of spacetime which is modified.

Current Theory Proposed theory

Fig. 3-4

V = 0

m0

Relativistic speed V

m0 1 – v2/c2m =

The speed of the particle produces a compression of spacetime, which gives us the illusion that the mass increases.

The particle curves spacetime Direction of movement

This point of view is wrong. Mass (closed volume) remains unchanged.


Figure 3-5 shows a very simplified view1 of a nuclide with 19 nucleons.

Independent nucleons (a) The total volume is 19V and the total surface 19S, V and

S being respectively the volume and surface of a nucleon.

Nucleus (b) The 19 nucleons are linked to make an atom. The grey surface represents a vacuum enclosed in the nucleus. Therefore, these open volumes become closed volumes and curve spacetime as closed volumes do.

Nucleus (c) From an external view, the figure (c) looks like (b), but the global volume of figure (c) is greater to that of (a), and the global surface (c) smaller than (a). As a result, the mass effect of (c) will be greater of that of (a).

3.6 A bomb (E = mc²) As we know, a tsunami is a large depression of water that causes tidal waves, or high-energy waves. The same phenomenon also exists in spacetime. In fig. 3-5, when the nucleus is broken from (c) to (a), the closed volume (shaded part of b) disappears, causing a large depression in spacetime. This can be identified to a kind of tsunami in spacetime. Finally, as in tsunamis, we get high energy waves (gammas). In E = mc², it is not the mass that is converted into energy, but the closed volume that becomes an open volume. This is exactly the tsunami sequence.

So, according to the current theory,

1 Up to day, we don't know exactly the arrangement of protons and neutrons inside a nucleus. This means that figure 3-5 is a simplified arrangement of nucleons.

a b c

Fig. 3-5

To understand E = mc², we must think "closed volume" instead of "mass". A closed volume is converted into an open volume or

conversely, but in all cases, a volume remains a volume.


3.7 The light deflection Every physicist is familiar with the observation of the light deflection by the sun made by Sir Arthur Eddington during a total solar eclipse in 1919. The following simulation is similar (fig. 3-6). A set of lines spaced 5mm appart is drawn on an expanded polypropylene (EPP) foam. Elasticity of the foam simulates that of spacetime. A half cylinder acting as a closed volume is placed under the lines. As we see on this photo, lines are curved. We have exactly the same phenomenon in spacetime. Contrary to what we think, the light is not "attracted" by the mass but follows convex geodesics of spacetime produced by the closed volume.

3.8 Conclusions

(*) Stars are combinations of open and closed volumes (large apparent volume, small "mass effect") whereas black holes are probably closed volumes exclusively (small apparent volume, large "mass effect").

Fig. 3-6

Light

Today Proposed Theory

??? Logical and consistent

explanation

• Twin paradox • Particles in a crystal• Light deviation • Mass excess • Relativistic particles• Von Laue graphics • Black holes (*)

What is mass?

What is gravitation?

What is Spacetime?


Supplementary Information

A – The Newton Law of Universal Gravitation This paper calculates the Newton Law of Universal Gravitation from scratch using only closed volume considerations.

B – The Schwarzschild Metric

This paper calculates the Schwarzschild Metric from scratch, using also closed volume considerations. Calculations are very simple and don’t require tensor knowledge as in EFE.

C – The Mass Effect Calculation

This paper calculates the expression of mass effect m = f(x,y,z,t).

D –EFE vs Constraint Tensor Proposes a study of EFE.

E – Equivalence Principle

This document demonstrates that the proposed theory also solves the Equivalence Principle.

F – Experimentation

This paper describes an interesting simulation. G – Black Holes Simulation

This document simulates a black hole behaviour. H – Miscellaneous

Predictions to validate the theory Objections to the theory Other original papers from the Author About the Author

Mass and Gravitation A - The Newton Law - S1 -

A. The Newton Law

Here we show that the Newton Law of Universal Gravitation can be easily obtained

Starting with a simple idea: it is the closed volume which makes a displacement, not the mass,

With few logical deductions, And using elementary mathematics that every one knows

(no tensors, no EFE, no weak field approximation).

A.1 Background: the Bulk Modulus The bulk modulus KB of a substance measures the substance's resistance to uniform compression. It is defined as the pressure increase needed to cause a given relative decrease in volume (fig. A-1).

Fig. A-1

V

∆V

∆P


Starting with the Fluid Mechanics, from 1850's, Einstein demonstrated in 1910's that spacetime is "elastic". Einstein identified spacetime to a fluid. The Bulk Modulus equation (1) is a part of the Fluid Mechanics and, therefore, can be applied to spacetime. The proposed theory states that a closed volume produces a displacement of spacetime. Since spacetime is elastic, this displacement makes a pressure on the surface of the volume, which conducts to a volume decrease, as shown in figure 1.

A.2 Background: Elasticity law Elasticity phenomena follows the well-known logarithmic law:

The Schwarzschild Metric gives an order of magnitude of the curvature of spacetime. This latter is infinitesimal. For example, the ratio "curvature of spacetime"/radius, or ∆R/R, is 1.4166 x 10-39 1 for the proton. Under that conditions, whatever the formulae used, logarithmic or not, we can consider that the curvature of spacetime is a linear function since we are working on an infinitesimal segment near to the point zero (limits of elasticity). So, this formulae becomes:

or, with volumes:

For the moment, coefficients of elasticity of spacetime εR and εv are unknown.

A.3 Curvature of spacetime ∆∆∆∆x A closed volume V inserted into a flat spacetime (Minkowski) "pushes" spacetime to make room (fig. A-2). So, the following volumes are identical.

1 M = 1.672 E-27, R = 8.768 E-16, G = 6.674 E-11, c² = 8.987 E+16, ∆R/R = GM/Rc². This formulae is the first order approximation of the square root of the r radius in the Schwarzschild Metric coefficient in polar coordinates.


Since the coefficient of elasticity of spacetime ev is constant (see the preceding paragraph), combining (4) and (5) gives:

A.4 Curvature vs displacement of spacetime There should not be any confusion between a simple displacement of spacetime V produced by the insertion of a closed volume into a flat spacetime, and the curvature ∆V=εvV due to the elasticity of spacetime. Figure A-3 shows this difference.

V V1 V2 V3

Vn

Fig. A-2

Curvature of spacetime: ∆Vx = εv Vx

Fig. A-3

Displacement of spacetime at the

distance "d" : Vx=V Vx

d

V


A.5 Curvature of spacetime ∆∆∆∆x at a distance d Since the ∆V's are infinitesimal, the volume ∆Vx is simply the product of ∆x by the surface Sx (fig. A-4):

On the same manner, the volume ∆VR is the product of ∆R by the surface SR:

Since, from (6):

Combining equations (7) and (8) gives:

Finally, at a distance "d" from the centre, the spacetime curvature is inversely proportional to d²:

Rd

Fig. A-4

∆∆∆∆VR :

VR ∆R

SR = 4πR² ∆VR = SR∆R

= 4πR²∆R

∆∆∆∆Vx : Vx ∆x Sx = 4πd² ∆Vx = Sx∆x = 4πd²∆x


Where:

R is the radius of the closed volume VR, assume it spherical, ∆R is the curvature of spacetime on the surface of the closed volume VR, d is the distance of the point of measurement from the centre of the closed volume VR, ∆x is the curvature of spacetime at the distance d.

A.6 Curvature (∆∆∆∆x) vs Mass (M) Figure 7 of the main text has been duplicated as figure A- 5. On this figure, we see that a relation exists between the curvature of spacetime, ∆R (or ∆x at a distance "d" from R), and the mass of the object, more precisely its "mass effect":

The mass effect acts as a pressure and, like any pressure, it is inversely proportional to the surface S, or [1/L²]. It is also proportional to the volume, or [L3]. Therefore, the dimensional quantity of the mass effect could be [1/L²][L3] = [L]. In other words, the proposed theory predicts that the mass effect is proportional to [L]. This deduction is in accordance with the Einstein Field Equations and their solutions (Schwarzschild Metric…).

Fig. A-5

Closed volumes curve spacetime

SpacetimeElasticity

(Einstein)

Closed volumes

Object

Proposed Theory

Mass effect

Gravitation

A "mass effect" due to the pressure of

spacetime on the surface is

associated with each closed

volume.

Only volume physically exists. Mass does not exist per se. Mass is an effect produced by the pressure of spacetime on closed volumes. This pressure on the surface of closed volumes also explains gravitation.

1

2

4Open volumes (ignored)

Spacetime exerts a pressure force on closed volumes

3


In referring to Einstein's works, we have good reason to believe that the relation between ∆R and M is a simple linear function like:

where K is an unknown constant having the dimensional quantity of [L/M].

The challenge, now, is to calculate K to get the Newton's law of Universal Gravitation.

A.7 The Newton Law Porting equation (13) in (11) gives:

or

Since x = ct, replacing R² by c²t² gives:

or :

The value ∆x/t² has the dimensional quantity of an acceleration [L/T²]. So, replacing this fraction by the acceleration symbol "a", we get:

On the other hand, the multiplication of a constant c² by a second constant K gives another constant. So, we can replace the product c²K by a new unknown constant, G for example:

or:

Expression (18) becomes:


To be consistent, this new constant G must have the same dimensional quantity as c²K. We have:

• G : Dimensional quantity = that of c²K • c² : Dimensional quantity = [L²/T²] • K : Dimensional quantity = [L/M] (see paragraph A-6).

So,

The dimensional quantity of this new constant G is [L²/T²][L/M] = [L3/MT²].

On the other hand, we know that the force is the product of an acceleration by a mass. Therefore, equation (19) can be written as follow:

About the unknown constant G, we remark: G is a constant, Its dimensional quantity is [L3/MT²].

So, we can identify G to the well-known constant of gravitation issued from experimentation: G = 6,67428.10-11. In other words,

A.8 ConclusionsAs we see, the Newtonproposed and obtained

• A volume inser• Since spacetime

object. • A very simple c• Using simple m

Finally, this chapter exof the Newton Law of U

Equation (22) can be identified to the Newton Law of Universal Gravitation.

Law of Universal Gravitation can be easily explained by the theory from the few following considerations:

ted into spacetime push it to make room. is elastic, this displacement make a pressure on the surface of the

alculation shows that the curvature of spacetime follows the 1/d² rule. athematics manipulations, we get the Newton Law.

plains, with some logical deductions and a great simplicity, the origin niversal Gravitation.

Mass and Gravitation B - The Schwarzschild Metric - S9 -

B. The Schwarzschild Metric

Here we show that the Schwarzschild Metric can be easily obtained Starting from a simple and low cost experiment (<$5.00), With logical deductions, And using elementary mathematics that every one knows instead of complex tensor manipulations.

B.1 The Minkowski Metric The expression of the Minkowski Metric, in spherical coordinates, is:

The Schwarzschild Metric concern a static object with a spherical symmetry. It is a Minkowski Metric, in spherical coordinates, with two unknown functions: A(r) and B(r) :

B.2 Determining A(r) and B(r) Remembering that the Minkowski Equation follows the Lorentz Invariance, the only way to get this invariance is to set A(r) = 1/B(r). From a mathematical point of view, we get the same result developing and simplifying the Einstein Field Equations. Details of calculations are described in many books concerning General Relativity1. This conducts to the following equality2:

1 For example, « Notes on General Relativity » - S. Carroll -. 2 Some authors prefer writing A(r)B(r) = K with K=c². In that case, the term c² must be excluded from the Minkowski Metric, equation (1). However, in both cases, result is the same. Please also note that, in order to simplify equations, some Authors replace c and G by 1. In this document, we don't follow this rule because a simple number, "1" in this case, doesn't have a dimensional quantity like c² or G, [L²/T²] or [L3/MT²] respectively. This conducts to get inconsistent equations from a dimensional quantity point of view.


B.3 The Schwarzschild Metric To calculate the Schwarzschild Metric from scratch, we use an expanded polypropylene (EPP) foam which simulates spacetime, and a closed volume placed under the foam (fig. B-1). A set of lines spaced 5mm. apart is drawn on the EPP. The theory shows that a flat spacetime is curved near a closed volume. This phenomenon is exactly what figure B-1 shows. Lines in bold simulate with a great realism the curvature of spacetime out and in the gravitational field simulated by the foam and the half cylinder. Since spacetime is "elastic" (Einstein), we can start with the well-known law of elasticity:

where: • ε is a coefficient of the increase of spacetime curvature at distance r, • ∆R is the curvature of spacetime1 produced by the closed volume, • r is the distance of the point of measurement.

The order of magnitude of ε is 10E-39. So, we can use the first order approximation:

The relation between two differential elementary radius drout and drin follows the law of elasticity L = (1 + ε) L0 :

1 Please note that the curvature of spacetime, ∆R, is not the displacement of spacetime. See Supplementary Information A.

Fig. B-1

drout

drin

r


Since ε << 1, we can write the equivalent formula:

or, elevating in square:

Developing the denominator (1 – ε)² = 1 - 2ε + ε² and ignoring the last term ε², we obtain:

This result is nothing but the radial component of the Schwarzschild Metric, that is to say the function A(r) of dr² in expression (2). The calculation of B(r) is immediate, taking into account that A(r) B(r) = 1 from (3). Hence:

So, equation (2) becomes:

In Supplementary Information A "The Newton Law", we have got the following result ∆R = KM (expression 13) where K = G/c² (20). So, equation (5) can be rewritten as:

Finally, porting this expression in (12) conducts to the well-known Schwarzschild Metric:


B.4 Conclusions Starting with a simple and low cost (< $5.00) experiment, this demonstration clearly shows that Spacetime is curved by a closed volume, not by a mass.

Mass and Gravitation C - The Mass Effect Calculation - S13 -

C. The Mass Effect Calculation

This supplementary information calculates the expression of the mass effect: m=f(x,y,z,t).

C.1 Expression of "m" We have seen, in Supplementary Information A (The Newton Law), that (fig. C-1) :

• The displacement of spacetime, VR, is equal to that of the closed volume, V, which produces this displacement (fig. C-1),

• The curvature of spacetime, ∆VR, is calculated from the displacement of spacetime VR, and the coefficient of elasticity εV,

• The radial distance of the curvature of spacetime, ∆R, is calculated dividing the volume by the surface: ∆R = ∆VR / S,

• Finally, since ∆VR = εvVR, the linear curvature of spacetime becomes:

On the other hand, we have calculated the Newton Law starting with the following expression where K is an unknown constant having the dimensional quantity of [L/M]:

R

Fig. C-1

VR = V ∆VR = εvVR

S ∆R = ∆VR / S

V

Mass and Gravitation C - The Mass Effect Calculation - S14 -

Porting (2) in (1) gives :

or

Combining equation (20) of Supplementary Information A and (4) gives the expression of the "mass effect": (5)

with: M = Mass effect (kg) V = Volume of the closed volume (m3) S = Surface of the closed volume (m²) εv = Coefficient of elasticity of spacetime 1 c = Speed of the light (m/s) G0 = Universal constant of gravitation

C.2 Case of a sphere In the particular case of a sphere, we have V = 4/3 πR3 and S = 4πR², and expression (5) becomes : (6)

C.3 Nuclei Nuclei aren't spherical. Therefore, it is not possible to apply (5) to calculate the mass effect since we don't know exactly the shape of the nucleus. Empirical formulae based on A, Z, N give accurate results because the shape of the nucleus, i.e. its volume and its surface, is function of A, Z, N 2. It is important to note that the law in A⅓ doesn't mean that the mass is proportional to the volume, but the rearrangement of nucleons inside the nucleus follows a law in A⅓. Results may be equivalent but the signification is totally different.

1 This coefficient can be calculated from spherical particles. However, this calculation is not easy to do because the only supposed spherical particles that we know are leptons. To have accurate data, we must take the muon and the tau which is a difficult task, or maybe nuclei having a null quadripolar moment. 2 A study on this topic is in hand.

Mass and Gravitation D - EFE vs Constraint Tensor - S15 -

D. EFE vs Constraint Tensor

This paper shows that a closed examination of the Einstein Field Equations (EFE) highlights some minor inconsistencies which are the starting point of the proposed theory.

D.1 Background EFE emphasize an identity between the properties of matter, mass-energy-momentum, and the geometry of spacetime. Einstein discovered equivalence between the stress-energy tensor Tjk and the geometrical tensor of curvature Rjk - (1/2) gjkR :

Geometry of spacetime ≡≡≡≡ Matter and energy

Hiding the cosmological constant Λ, the EFE, which must be read from right to left, becomes:

Rjk - (1/2) gjk R = (8πG/c4) Tjk

The member of left describes a representation of the geometry of spacetime. It is a geometrical tensor verifying a mathematical property of Lorentzian conservation. Rjk is the tensor of Ricci and R the scalar of Ricci.

The member of right represents the energy-momentum. It is the Tjk stress-energy tensor.

The simplest solution of Einstein's equations is the Schwarzschild Solution. Its metric describes the curvature of spacetime produced by a static object with a spherical symmetry. Setting down (x0, x1, x2, x3) = (ct, r, θ, Ω), this metric is written as follows:

0 0 0

0 0 0

0 0 r2 0

0 0 0 r2sin2θ

(gµν) =

²21 rcGM+−

²211

rcGM−


D.2 The Stress-Energy Tensor Einstein built his stress-energy tensor from the constraint tensor used in fluid mechanics since 1850's (fig. D-1). Constraint tensor

This tensor, from the Hooke Law, represents the dynamic pressures exerted by the fluid on an object. Elements of this tensor have the following significance:

• T01, T02, T12, T10, T20, T21 are viscosity • The trace T00, T11, T22, is the pressure.

Stress-energy tensor

The elements of this tensor have the following significance:

• T00 is the density of energy • T10, T20, T30 are the density of moments • T01, T02, T03 are the flow of energy • T12, T13, T23, T21, T31, T32 are viscosity, as with the constraint tensor • The trace, T11, T22, T33, represents an attractive force: gravitation.

T00 T01 T02 T03

T10 T11 T12 T13

T20 T21 T22 T23

T30 T31 T32 T33

Gravitation = Attractive force

Fig. D-1

Pressure

T00 T01 T02

T10 T11 T12

T20 T21 T22

Constraint tensor in fluid mechanics

Stress-energy tensor in General Relativity

In the original constraint tensor, thesignificance of the trace is a pressure.

The EFE tensor has been built from the constraint tensor. However, the initial pressure force (the trace) of the constraint tensor has been replaced by an attractive force.


D.3 Deductions This leads the following inconsistencies:

In fluid mechanics, since 1850's, constraint tensors are always built on volume, not on mass. Effectively, it is the volume – and not the mass – that produces the viscosity and pressure in fluid mechanics. Question: why has the mass replaced the volume?

Viscosity, in the Einstein's tensor, is the same as that of the constraint tensor. If the viscosity is the same, why would the trace be different? Why has an attractive force replaced the initial pressure force?

These two inconsistencies conduct to the four following combinations shown in figures 1-1 and 1-2 of chapter 1:

1. "Attractive force + Concave curvature of spacetime (Mass)", 2. "Attractive force + Convex curvature of spacetime (Volume)", 3. "Pressure force + Concave curvature of spacetime (Mass)", 4. "Pressure force + Convex curvature of spacetime (Volume)".

Let's replace the concave curvature of spacetime by the minus sign (-) and the convex by the positive sign (+). Likewise, let's replace the attractive force by (-) and the pressure force by (+). So, we can rewrite the four combinations as follows :

1. (- -) "Attractive force + Mass", 2. (- +) "Attractive force + Volume", 3. (+ -) "Pressure force + Mass", 4. (+ +) "Pressure force + Volume".

The first combination is that of Newton-Einstein. It works perfectly but has no sense since no one can explain how a mass can curve spacetime. The fourth combination has the same sign that the first one : (- -) = (+ +). This combination is much more credible because it fully explains many enigmas concerning mass and gravitation. To summarize: Combination 1: Since 1915's, physicists have tried to solve the mass and gravitation

enigma from the first combination "Attractive force + Mass". … One century later, we are still waiting for a logical and consistent explanation of this enigma.

Combination 4: On the contrary, this unknown combination 4, "Pressure force + Volume", perfectly solves the mass and gravitation enigma. Moreover, the Newton Law of Universal Gravitation and Schwarzschild Metric can be easily calculated from this combination, with logic and consistency. At last, this combination needs only 4D and is fully compatible with Einstein's works.


On the other hand, Einstein wrote his equations in 4D. Since the mass "m" is not a basic dimension of the Universe, a question arises :

What is the real nature of m in EFE ? It would seem logical to have a match between the theory and applications, as :

Theory 4D............... Applications 4D Theory 5D............... Applications 5D Theory 6D............... Applications 6D …………………………………….. Theory nD............... Applications nD

Since 1920's, all applications of general relativity, like the GPS, uses four dimensions. Therefore, the number of dimensions of the theory is probably four. This conducts to :

m = f(x,y,z,t) This deduction is in accordance with the theory presented here which uses only four dimensions. Effectively, the mass effect is function of the curvature of spacetime (see Supplementary Information C).

Mass and Gravitation E - Equivalence Principle - S19 -

E. Equivalence Principle

E.1 Demonstration Let’s consider an object on Earth (Fig. E-1). The volume of this object causes a curvature of spacetime which exerts a gravitational force on it of g = 9.81 m.s-2 on the surface of Earth. Let’s now consider the same object accelerated out of any gravitational field (fig. E-2). The acceleration, a, is supposed identical to g, i.e. a = 9.81 m.s-2.

Fig. E-1

g Note: For teaching purposes, in this figure, Earth has been omitted.

Fig. E-2

2a 2b

a a This figure is identical to fig. E-1 since g = a

Mass and Gravitation E - Equivalence Principle - S20 -

Without any reference, a local observer can’t say if the acceleration comes from the object or from the curvature of spacetime. In fact, figures E-2 a and E-2 b are identical and depend on where the observer stands, as described in Special Relativity. Since

• By definition, g = 9.81 m.s-2 (fig. E-1) is identical to a = 9.81 m.s-2 (fig. E-2). • These examples uses the same object. Therefore, the curvature of spacetime produced

by the closed volume of this object is identical. • So, the "mass effect" produced by these curvatures will be identical.

We deduce that the "gravitational mass effect" (fig. E-1) is identical to the "inertial mass effect" (fig. E-2). In other words:

Gravitational mass effect ≡

Inertial mass effect ≡

Spacetime curvature

Mass and Gravitation F - Experimentation - S21 -

F. Experimentation

This chapter shows that on Earth we can conduct experimentations which give similar results than those produced by gravitation. The following experimentation demonstrates that:

1) Gravitation is a pressure force, not an attractive force, 2) Made by volumes, not by masses.

Note : This experiment is only a simulation, nothing else, but great laboratories as the CERN often make similar simulations on unknown phenomena like the Big-bang or black holes.

F.1 Introduction Einstein demonstrated that spacetime has an elasticity behaviour. Therefore, it is possible to simulate spacetime replacing it by an EPP (expanded polypropylene) foam. Spacetime and EPP follow the same rules and the basic principle is identical (fig. F-1).

F.2 Basic material To conduct this experiment, we need:

• A piece of expanded polypropylene foam (EPP) measuring 30x21 cm, 2 cm thick • A drawing, on the EPP foam, of a set of lines spaced 5 mm apart. • Two cylinders with a 2 cm in diameter • Two Force Sensing Resistors (FSR) - see the following paragraph - • Some basic tools such as a soldering iron, a power supply, a multimeter, a cutter... • A few basic components such as wire, resistors, trimmers...

Fig. F-1


F.3 The FSR A Force Sensing Resistor (FSR) (fig. F-2) is a polymer thick film (PTF) device which exhibits a decrease in resistance with an increase in the force applied to the active surface.

The two FSR’s used in these experiments are manufactured by the Interlink Company, part # SS-U-N-S-00015 (price = $1.00 each). The pressure ranges from 0.007 to 7 bars, and the resistance decreases from 10 MΩ to 1 KΩ with an increase of force.

F.4 Experiment #1 Experiment #1 shows that far from any mass, the resistance of a FSR is 10MΩ (open circuit, fig. F-3). When a mass is placed on the FSR (fig. F-4), its resistance decreases to 35 KΩ. Since in the weight of a mass is directly related to gravitation (second Newton Law, Weight=mg), we can state:

Fig. F-2

Decrease of FSR resistance = Presence of a force (≡ gravitation)

Fig. F-3 Fig. F-4


F.5 Experiment #2 Two FSR’s measure the pressure produced by an expanded polypropylene (EPP) foam on each side of a volume V1. Figures F-5 and F-7 represent the first step of this experiment. In order to get an accurate measurement and to use only one galvanometer in this experiment, the two FSR’s are inserted in a Wheatstone Bridge. This setup is frequently used in strain gauge measurements. Figure F-6 represents the circuit diagram. The volume V1 is inserted in the EPP foam and the Wheatstone Bridge is adjusted by VR1 to obtain a zero voltage between the two midpoints A and B (fig. F-6). No current flows through the galvanometer Vg. The pressure of the EPP foam (or spacetime) on both sides of the volume V1 is identical.

A

FSR2 FSR1

R1 VR1

Vg B

C

D

Fig. F-6

Fig. F-5

FSR2 V1 FSR1

Pressure of the EPP foam (= spacetime) on the two FSRs

V1

Fig. F-7

FSR1

FSR2

CA

D

B


Without changing anything, a second volume, V2, is inserted near the first volume V1 (fig. F-8). We note a deviation on the galvanometer (fig. F-10), which indicates an additional pressure on FSR1. To summarize, with one volume, the galvanometer indicates no voltage (fig. F-9). With two volumes, it indicates a voltage proportional to the pressure produced by the second volume on FRS1 (fig. F-8 and F-10). This force between V1 and V2 can be identified to gravitation since "voltage on FSR = Presence of a force (≡gravitation)" (conclusion of paragraph F-4, "Experiment #1"). Fig. F-9 Fig. F-10

Fig. F-8

V2

FSR1

V1FSR2

C A

D

B


F.6 Deductions Out of any volume (or mass), the voltage in a Wheatstone Bridge is 0 V (fig. F-9).

When a second volume is inserted into the EPP foam, the voltage on FSR1 increases (fig. F-10).

Experiment #1 (fig. F-3 and F-4) shows that a decrease of resistance on a FSR indicates a "presence of gravitation".

Experiment #2 clearly shows that between V1 and V2 a force similar to gravitation has appeared.

It is obvious that this simulation doesn't prove the theory, but it shows that replacing elasticity of spacetime by elasticity of an EPP foam highlights two important phenomena:

1. We are faced with a pressure force, not an attractive force

2. The cylinders masses are irrelevant, only their volumes are.

Mass and Gravitation G - Black Holes Simulation - S27 -

G. Black Holes Simulation

The purpose of this experiment is to demonstrate that a simple EPP (expanded polypropylene) foam can simulate black holes. As indicated in the precedent chapter, this simulation is similar than those conducted in great laboratories as the CERN concerning simulation of the Big-bang or black holes.

G.1 Experimentation A set of lines, spaced 5 mm apart, has been drawn on an EPP foam simulating spacetime. A half cylinder with a radius of 22mm, or a closed volume, is inserted into the foam (fig. G-1).

The gaps between two adjacent lines are measured and plotted with ®Excel (fig. F-2).

0

1

2

3

4

5

6

1 3 5 7 9 11 13 15 17 19 21 23 25

Fig. F-2

This experiment has been conducted using low cost basic material (< $2,00). This is why some lines aren't regular. However, despite this poor accuracy of measurement, results of this experimentation are very interesting.

Fig. G-1

r

Base


G.2 Experimental plot r Distance measured between the base and the

point of measurement "r" (fig. F-1 on the previous page).

y(r exp) Curvature of spacetime calculated from the

distance "r" measured. The following formula comes from the Schwarzschild Metric (see supplementary information B), which have been reduced to the radial component:

The constant 2.2 comes from:

R = 22 mm. Radius of the closed volume, ε = 0.1, an arbitrary EPP foam coefficient, ∆R = εR = 0.1 x 22 mm = 2.2 mm.

The curve, from experimentation, is:

r y(r) 22

24,4 1,10 26,8 1,09 29,4 1,08 32,2 1,07 35,2 1,07 38,3 1,06 41,8 1,06 45,9 1,05 50,4 1,05 55,1 1,04 59,9 1,04 64,6 1,04 69,3 1,03 74,4 1,03 79,3 1,03 84,4 1,03 89,5 1,03 94,5 1,02 99,5 1,02 104,2 1,02 108,8 1,02 113,6 1,02 118,4 1,02 123,2 1,02 128 1,02

132,9 1,02

0,96

0,98

1,00

1,02

1,04

1,06

1,08

1,10

1,12

1 3 5 7 9 11 13 15 17 19 21 23 25Fig. G-3

Table of figure G-3


G.3 Theoretical calculation Now, we calculate data on a mathematical basis, using the same formula (1) as the precedent one, where: Col. 1: "n" is the rank of each line Col. 2: Lines "r0" are spaced 5 mm.

apart, out of gravitation, with an offset of 22, as that of the radius of the closed volume. Col. 3: ∆r is calculated using the

elasticity of spacetime, ε, supposed to be 0.1. Col. 4: Finally, the distance

between the base and the point of measurement of the spacetime curvature, r, is computed from ∆R and r0, Col. 5: Result.

The curve of function y(r theor.) is:

Col. 1 Col. 2 Col. 3 Col. 4 Col. 5 n r0 = 5n+22 ∆∆∆∆r = 0.1 r0 r = r0 - ∆∆∆∆r y(r) 1 27 2,70 24,30 1,10 2 32 3,20 28,80 1,08 3 37 3,70 33,30 1,07 4 42 4,20 37,80 1,06 5 47 4,70 42,30 1,05 6 52 5,20 46,80 1,05 7 57 5,70 51,30 1,04 8 62 6,20 55,80 1,04 9 67 6,70 60,30 1,04 10 72 7,20 64,80 1,04 11 77 7,70 69,30 1,03 12 82 8,20 73,80 1,03 13 87 8,70 78,30 1,03 14 92 9,20 82,80 1,03 15 97 9,70 87,30 1,03 16 102 10,20 91,80 1,02 17 107 10,70 96,30 1,02 18 112 11,20 100,80 1,02 19 117 11,70 105,30 1,02 20 122 12,20 109,80 1,02 21 127 12,70 114,30 1,02 22 132 13,20 118,80 1,02 23 137 13,70 123,30 1,02 24 142 14,20 127,80 1,02 25 147 14,70 132,30 1,02 26 152 15,20 136,80 1,02

0,96

0,98

1,00

1,02

1,04

1,06

1,08

1,10

1,12

1 3 5 7 9 11 13 15 17 19 21 23 25Fig. G-4

Table of figure G-4


G.4 Deductions As we see, the two tables (3) and (4) and their associated graphics are very close to each other. In particular, the last column in bold of the two tables are practically identical. This leads to two important conclusions:

1. The curve calculated from the Schwarzschild Metric (fig. F- 4), is very close to that plotted from experimentation using a simple EPP foam (fig. F-3) simulating spacetime,

2. In these two tables, once again, the volume, more exactly radius, replaces the mass.

G.5 The Schwarzschild Radius Rs If the elementary curvature of spacetime ∆R = εR = 0.1 x 22 mm = 2.2 mm. (see paragraph F-2) is increased to 40 mm., a singularity appears (fig. F-5).

We get a curve that match exactly that of the behaviour of the Schwarzschild Metric around Rs (Schwarzschild Radius). Effectively, the table and the curve (fig. F-5) show an asymptote when r = 40 mm.. We can also remark that the signature is changed from + to -, as inside a black hole. However, a question arises : Does that curve reflect the reality?

-30,00

-20,00

-10,00

0,00

10,00

20,00

30,00

1 3 5 7 9 11 13 15 17 19 21 23 25

Fig. G-5

r = Rs

-

+

Rank r y = f(r) 22 1 24,4 -1,56 2 26,8 -2,03 3 29,4 -2,77 4 32,2 -4,13 5 35,2 -7,33 6 38,3 -22,53 8 41,8 23,22 9 45,9 7,78 10 50,4 4,85 11 55,1 3,65 12 59,9 3,01 13 64,6 2,63 14 69,3 2,37 15 74,4 2,16 16 79,3 2,02 17 84,4 1,90 18 89,5 1,81 19 94,5 1,73 20 99,5 1,67 21 104,2 1,62 22 108,8 1,58 23 113,6 1,54 24 118,4 1,51 25 123,2 1,48 26 128 1,45 27 132,9 1,43

Table of figure G-5


G.6 Black holes From a mathematical point of view, it is possible to have r < R, R being the radius of the particle or object. From a physical point of view, r can't be less than R. It means that the validity of the Schwarzschild Metric is not proven with r < R. It is possible that, instead to have a singularity, we simply reach a limit of validation of the Schwarzschild Metric if r ≤ R. What happens if an electromagnetic wave goes near to R? The Von Laue Diagram (main text, fig. 3-3) partially gives the solution to this enigma:

Far from the volume that makes the displacement of spacetime (fig. G-6 A), the light is only deviated. It follows geodesics of spacetime.

Near the volume (fig. G-6 B), the light is captured. In this case, the light turns around the object and doesn't have the possibility of escaping.

In front of the volume (fig. G-6 C), the light comes in collision with the object (Compton Effect). In other words, the "famous" black hole capture could be nothing but …an ordinary Compton effect !!!

At last, we must note the two following remarks which are only suggestions:

Since a particle (electron, proton…) is a closed volume, its behaviour could be identical to that of a black hole.

If the light comes near to R (fig. G-6 B), it is possible that a resonance takes place if the circumference of the particle is a multiple of its wavelength. In that case, it is possible that particles of groups 2 and 3 of the Standard Model could be nothing but particles of group 1 in resonance. For example, the muon could be an electron in a "level 1 resonance". In the same manner, the tau could be an electron in a "level 2 resonance". It is even possible to have particles more heavy with "level 3, 4, 5…resonance". In all case, the resonance increases the closed volume (the mass) of the particles but keep their charge unchanged (-1 in this example). That is in accordance with the proposed theory.

A

B

Fig. G-6

C


G.7 Conclusions This simple and low cost experimentation simulates the black hole behaviour. Results are EXACTLY identical as in conventional physics using solutions of EFE. This experiment is very interesting because it proves, one more time, that Spacetime is curved by the volume, not by the mass. Effectively, during all these explanations, only lengths have been considered. Mass has been totally ignored. It is the radius, not the mass, which has been increased to 40 mm. to calculate a black hole behaviour.

Mass and Gravitation H - Miscellaneous - S33 -

H. Miscellaneous

H.1 Predictions The proposed theory can be confirmed by at least three simple experimentations:

1/ Particle behaviour near a surface Since the density of spacetime is higher near atoms, the "mass effect" of a particle moving near the surface of an high density object must increase too.

2/ The moon influence The curvature of spacetime produced by the moon is added to that produced by Earth. Therefore, the mass of a particle should depend of the position of the moon during the measurement since the spacetime density is not identical. If two accurate measurements of the mass of a particle are conducted a) when the moon is at zenith and b) 12 hours after, we should note a very light difference in results.

3/ Crystals The enigma of a particle crossing a crystal has been already discussed. The proposed theory predicts that the mass, more exactly the "mass effect" of the particle, is directly related with the density of spacetime inside a tunnel, more particularly: 1/ the structure of the lattice of the crystal, 2/ the number of nucleons of atoms of the crystal, 3/ the space between atoms. The density of spacetime can be theoretically calculated with different crystals. Appropriate experimentations should confirm this calculation and, therefore, the proposed theory too.

H.2 Objections Some physicists reject the proposed theory because they consider it too simple. They make a confusion. Consider, for example, a drum. A 5 years old child intuitively knows the principle, namely that by striking it, he makes noise. On the other hand, the mathematical description of the surface waves requires Bessel Functions, which are at the Master level. Mass, gravitation and modern physics share the same principle. It is advisable to distinguish the basic phenomena, generally very simple, like mass and gravity explained in this paper, from the mathematical laws governing them, which may be extremely complex: tensors, Schrödinger Equation, operators, Lie Groups, QCD etc….


Case 1: Stone-water A stone and a water wave are of different matter. In that case, the wave-particle duality can't be explained. It is an enigma.

Case 2: Water-water A drop of water (corpuscle) and a water wave are of identical matter. Water has either a corpuscle or a wave behaviour (duality). In that particular situation, wave-particle duality is explained with logic.

Fig. H-1

H.3 The Spacetime Model This document is a part of the "Spacetime Model", a new theory based on spacetime. Others parts can be download from the web site

www.spacetime-model.com

A summary of this theory is given below. However, some ideas are speculative and require a validation by experimentation. So, the reader must take this information with caution. This new theory is proposed as a possible way of research to solve enigmas of physics.

H.4 Wave-particle duality Contrary to a preconceived idea, duality isn't a "quantum effect". This phenomenon exists on Earth. For example, let's compare a stone falling in water and a drop of water (fig. H-1). So,

Wave–particle duality appears only in the very particular situation where the wave and

the particle are of identical matter

http://www.spacetime-model.com/


Antimatter is not located at the bottom of the universe but right before our

eyes, included in u and d quarks

H.5 Quarks and Antimatter This paper shows that we need two positrons to make three u quarks. A u quark with an electron becomes a d quark. Please note that the violation of the rule of fermions addition is covered in the "Spacetime Model". Finally, the 24 particles of the Standard Model come from only two basic particles: electrons and positrons. This conducts to solve the enigma of antimatter. Atoms are made up of an equal number of electrons and positrons, exactly 2A (A = atomic number). For example, the C12 is made of 24 e- and 24 e+, the latter being included into the u and d quarks of protons and neutrons. The following table shows isobars A = 16.

• uN: The number of u quarks in neutrons (= N) • dN: The number of d quarks in neutrons (= 2N) • uZ: The number of u quarks in protons (= 2Z) • dZ: The number of d quarks in protons (= Z) • Utotal: Since each d quark contains a u quark, the total of u quarks is:

Utotal = uN + dN + uZ + dZ • Positrons: Since three u quarks are made up of two positrons, the number of positrons is 2/3 of Utotal. This

number is e+. • Electrons: Each d quark contains one electron. Moreover, we have Z atomic electrons around the nucleus.

The total of electrons is therefore: dN + dZ + Z A calculation with Excel™ of the 2970 known isotopes shows that we have exactly the same number of positrons as electrons, i.e. 32 in this example. Matter strictly equals antimatter. So, contrary to preconceived ideas,

Nucleus A N Z uN dN uZ dZ Utotal e+ e-

Be 16 12 4 12 24 8 4 48 32 32

B 16 11 5 11 22 10 5 48 32 32

C 16 10 6 10 20 12 6 48 32 32

N 16 9 7 9 18 14 7 48 32 32

O 16 8 8 8 16 16 8 48 32 32

F 16 7 9 7 14 18 9 48 32 32

Ne 16 6 10 6 12 20 10 48 32 32

Antimatter MatterNeutrons

u d dProtons

u u d


H.6 Extensions of the theory Other discoveries of the author are:

• Explanation of electromagnetism • The constitution of matter • The strong nuclear force • Unification of the three forces in two basic forces • A new explanation of the birth of universe, replacement of the Big Bang

Please note that all these explanations are logic and consistent. They only need a validation by experimentation. So, waiting this validation, the reader must take this information with caution.

H.7 About the Author This document can be downloaded from the following sites:

www.spacetime-model.com www.theory-of-everything.com www.mass-gravity.com www.higgs-boson.org

If you are a follower of this theory, or should you have any question, you can contact the author1 by email at:

[email protected]

Tel: (0033) 615 146 741

1 The author does not work in an institutional establishment. The writing of the Spacetime Model has been done entirely on his own money and time, with no help from the scientific community. If you find some error in this document, please let him know. On the other hand, if this paper has been of interest to you, thanks to insert the above website addresses in your blog or your web page (Face Book …).

http://www.spacetime-model.com/

http://www.theory-of-everything.com/

http://www.mass-gravity.com/

http://www.higgs-boson.org/

mailto:[email protected]


Table of contents

1 - Open and Closed Volumes 1.1 Starting point ...................................................................................5 1.2 Current theory..................................................................................5 1.3 Curvature of spacetime....................................................................6 1.4 Definition of the volume ................................................................6 1.5 Open and closed volumes................................................................7 1.6 Our view of the volume...................................................................8 1.7 Einstein Equations...........................................................................9 1.8 Example: The twin paradox ............................................................9 1.9 Confirmation: Atoms ......................................................................10 1.10 The reality of mass ..........................................................................11 1.11 Conclusions .....................................................................................11

2 - Gravitation

2.1 Principle of gravitation ....................................................................13 2.2 Principle of split ..............................................................................14 2.3 Conclusions .....................................................................................14

3 - Experimentations

3.1 Higgs' Intuition ................................................................................17 3.2 The Von Laue's diagram..................................................................18 3.3 Mass-volume equivalence ...............................................................19 3.4 Relativistic particles ........................................................................20 3.5 The mass excess ..............................................................................20 3.6 The light deflection..........................................................................21 3.7 Conclusions .....................................................................................22

Supplementary Information

A – The Newton Law A.1 Background: the Bulk Modulus.......................................................S1 A.2 Background: Elasticity law..............................................................S2 A.3 Curvature of spacetime ∆x ..............................................................S2 A.4 Curvature vs displacement of spacetime .........................................S3 A.5 Curvature of spacetime ∆x at a distance d.......................................S4 A.6 Curvature (∆x) vs Mass (M)............................................................S5 A.7 The Newton Law .............................................................................S6 A.8 Conclusions .....................................................................................S7


B – The Schwarzschild Metric

B.1 The Minkowski Metric ....................................................................S9 B.2 Determining A(r) and B(r)...............................................................S9 B.3 The Schwarzschild Metric...............................................................S10 B.4 Conclusions .....................................................................................S12

C – The Mass Effect Calculation

C.1 Expression of "m"............................................................................S13 C.2 Case of a sphere...............................................................................S14 C.3 Nuclei ..............................................................................................S14

D – EFE vs Constraint Tensor

D.1 Background......................................................................................S15 D.2 The Stress-Energy Tensor ...............................................................S16 D.3 Deductions.......................................................................................S17

E – Equivalence Principle E.1 Demonstration .................................................................................S19

F – Experimentation F.1 Introduction .....................................................................................S21 F.2 Basic material ..................................................................................S21 F.3 The FSR...........................................................................................S22 F.4 Experiment #1 .................................................................................S22 F.5 Experiment #2 .................................................................................S23 F.6 Deductions.......................................................................................S25

G – Black Holes Simulation G.1 Experimentation ..............................................................................S27 G.2 Experimental plot ............................................................................S28 G.3 Theoretical calculation ....................................................................S29 G.4 Deductions.......................................................................................S30 G.5 The Schwarzschild Radius Rs .........................................................S30 G.6 Black holes ......................................................................................S31 G.7 Conclusions .....................................................................................S32

H – Miscellaneous H.1 Predictions .......................................................................................S33 H.2 Objections........................................................................................S33 H.3 The Spacetime Model......................................................................S34 H.4 Wave-particle duality ......................................................................S34 H.5 Quarks and antimatter......................................................................S35 H.6 Extensions of the theory ..................................................................S36 H.7 About the Author.............................................................................S36

The Spacetime Model Version 3.02 4 March 2009

Jacky JEROME Ingénieur Européen EUR-ING

Ingénieur DPE (Diplômé Par l'Etat) Ingénieur IPF

Ingénieur ITP-ECI Email: [email protected]

ISBN 97829531234-0-2 Editions Arts et Culture 42

4, square Kennedy 42120 LE COTEAU (France)

Cover: On the left of the photo of Einstein: Maxwell, Feynman, Max Planck, Schrödinger On the right: Pauli, Niels Bohr, Marie Curie, De Brogglie, Dirac, Heisenberg

A step toward the Theory of Everything

Part 2

Constitution of Matter

The Spacetime Model - - Part 2 - Introduction

II

Patent Rights

This theory, the “Spacetime Model”, was registered at INPI, the French Patent Institute, under the following references:

238268, 238633, 244221, 05 13355-2 895 559, 248427, 258796, 261255, 268327, 297706, 297751, 297811, 297928, 298079, 298080, 329638, 332647, 335152, 335153, 339797.

This list is not exhaustive and some recent registrations at INPI are not mentioned. The “Spacetime Model” was also registered in other legal forms for Copyright.


In 2006, the two versions of this document, English and French, were addressed to more than 7000 physicists worldwide by e-mail. Several paper copies were sent in October 2006 to the most important Academics of Science and Committees of Foundations for Research.

The “Spacetime Model” was also published on November 30, 2006, on 31 different web sites.

The “Spacetime Model” is the intellectual property of its author, Jacky JEROME, and any illicit appropriation of the theory will be subject to prosecution.


III

Before reading… To fully understand this part, the reader must be familiar with the deductions and results developed in Part 1. These results are summarized below:

The curvature of spacetime Let's fill up a container with water. We drop a billiard ball into the container. The volume of the ball produces a displacement of water.

The same phenomenon applies to spacetime. Contrary to generally accepted ideas, it is not mass which deforms spacetime, but volume, more exactly “closed volume”.

Mass = Volume? In our world, mass and volume seem to be two different quantities because in atoms, the mass is not proportional to the volume. So, we have a large range of atoms with different masses and volumes. However, at the particle level, mass = volume (with some reservations explained in Part 1).

In reality, we have two main classes of volumes:

! Closed volumes (A): These volumes make a displacement of spacetime. Thus, a pressure force appears on the surface of the volume. This pressure produces a “mass effect”, an effect having all mass characteristics. Nucleons and electrons are examples of closed volumes.

! Open volumes (B): These volumes exist but do not produce any displacement of spacetime. If there is no curvature, there is no mass effect either. Orbitals of electrons in atoms are examples of open volumes.

Each atom has a particular proportion of open and closed volume. This is why mass and volume give us the illusion of being two different quantities.

A B


IV

What is Gravity? Two volumes inserted into spacetime curve it. Since spacetime is elastic, its curvature produces pressures on these two volumes. This tends to bring them closer to each other. So, contrary to what we think:

Gravity is not an attractive force between masses but a pressure force exerted by spacetime on closed volumes.

Since a pressure force is the inverse of an attractive force, there is no difference between the current theory and this new explanation of mass and gravity:

Attractive force (Newton) + Concave curvature of spacetime (Einstein) = Pressure force + Convex curvature of spacetime

Validation by experimentation Part 1 describes a simple experimentation, which proves that the curvature of spacetime produces a pressure force, not an attractive force. Moreover, this simple experiment highlights a black hole behavior when R = Rs.

Validation by mathematics In Part 1, the Schwarzschild Metric and Newton Law aren’t calculated using the Einstein Field Equations but using this new explanation of Mass and Gravity, from the Hooke Law. Moreover, the proposed theory is in perfect accordance with the Von Laue Diagram.

Please note that the Higgs Theory is far to propose to the Physicists Community a simple explanation, an low-cost experimentation and a full mathematical validation (Schwarzschild-Newton-Einstein-Hooke) as those explained in Part 1.

The Spacetime Model - Part 2 - - 1 - Wave-Particle Duality

1

1 Wave-Particle Duality

Matter presents the particularity of having a wave and particle behavior. This phenomenon is known as "wave-particle duality", or "complementarity". However, this enigma, which has been challenged by so many physicists, has still not been solved.

This chapter solves the mystery of wave-particle duality.

1.1 Current definition of duality It is generally accepted that wave-particle duality is two different visions of a single object (fig. 1-1). Usually, physicists take a cylinder to explain duality. We observe either a rectangle or a circle depending on where we stand. This metaphor is very interesting but it doesn't explain anything. It does not explain what really occurs at the particle level. As a physicist, it is necessary to leave this philosophical aspect to the philosophers and to try to solve this enigma in a scientific way, with a logical and rational explanation.

1.2 Explanation of the duality A toy boat is in the middle of a swimming pool. If you want to capsize it, you have two possibilities: to launch stones (particle concept) or to make waves (waves concept).

Let's replace the stones with a high-pressure washer. The water that is emitted from it can be considered a particle and has a corpuscular behavior. In fact, we can capsize the small boat by pointing the hose towards it.

Now let's put the nozzle in the water in the swimming pool. The water emitted from the hose, which was like a particle in the air, will also be like a particle in the water. This operation does not change the corpuscular nature of the water that is emitted from the nozzle.

We can observe that the water is transformed gradually into waves.

Fig. 1-1


2

Example 1A stone and a water wave are of different matter. In that case, the wave-particle duality can't be explained. It is an enigma. Example 2 A drop of water (corpuscle) and a water wave are of identical matter. Water has either a corpuscle behavior or a wave behavior. In this particular situation, wave-particle duality is explained with logic and consistency.

Fig. 1-2

If, moreover, we activate the pressure washer for a short time, comparable to the action time of a particle, we can see that the small jet of water emitted from the nozzle becomes a single wave.

As we can see in this example, the water has either a corpuscular or a wave behavior.

Nature offers us identical situations: the water of Niagara Falls has a particle behavior during its fall and, once it has reached the river down below, the particles become "eddies", or waves. The opposite situation also exists: let's consider the example of an almost empty swimming pool. If we make only one wave in the residual water, some amount will spill out of the drain valve. Thus, the wave is transformed into a short filament of water, or "particle". The water coming out of the drain valve is obviously not a wave. Yet, it is the same water that, a few seconds ago, was a wave. Another example that anyone can conduct is a stone falling into a container filled with water (example 1, fig. 1-2). In example 2, a drop of water replaces the stone. The same object (water) has either a particle behavior (drop) or a wave behavior. We are exactly in a wave-particle duality situation. This photograph proves that the wave-particle duality also exists on Earth.


3

1.3 First principle of duality To summarize, when the particle and the wave are of different matter, like a stone and water, the mystery of wave-particle duality can't be explained. It is a true enigma. On the contrary, if the particle and the wave are of identical matter, like water/water in our examples, the wave can be transformed into particles and the converse. However, in our first example, water coming out of the nozzle can't be transformed into waves if the experiment is done in the air. This transformation is possible only if the medium is also water. The same condition can be applied in the example of a drop of water. The wave exists only if the medium is also water. In other words, the medium must also be in the same composition as the particle and the wave. This is a necessary condition. To summarize, as figure 1-3 shows:

Wave – particle duality appears only in the very particular situation where the wave, the particle and the medium are of identical matter.

Thus, we can have a duality in the following cases: water/water/water, air/air/air, or spacetime/spacetime/spacetime, the latter being useful later. If one of these three objects is different from the others, the duality can't be explained logically and becomes a true mystery.

Note Medium and waves are obviously of identical matter. However, we will separate them for teaching purposes. Sometimes, we will use the wave concept, for example when we are talking about 511 KeV gammas, and sometimes we will use the medium concept.

wood stone metal water glass plastic carbon

air water water water water water air

Fig. 1-3

Duality ? No No No YES No No No

Particle

Wave

Duality is fully explained in this particular case

water water water water water water water

Medium

Impossibility Impossibility


4

1.4 Important deduction In other words, if a duality is observed in quantum mechanics, it means that the medium, particles and waves have the same internal constitution. For example, if the medium is spacetime, particles and waves are made of spacetime too. This is a necessary condition. This deduction will be utilized in the following chapters to explain the constitution of the particles.

1.5 Second principle of duality As we saw in the preceding example, the water of the pressure washer is transformed gradually, in intermediate phases, from a particle state into a wave state. Obviously, all these states of transition between particle and wave cannot coexist. It is either one or the other but not several states together.

Experimentations on particles confirm this fact. Indeed, particle and wave states never appear simultaneously.

We can thus state a second principle of duality, resulting from experimentation, based on the “OR EXCLUSIVE” conjunction:

Wave-particle duality can exist if, and only if,

! the particle, ! the wave, ! the medium,

have the same constitution.

1

When the conditions of the first principle of duality are met, the element concerned can exclusively take one, and only one, of the three following states:

1 - Particle state, when it is motionless 2 - Wave state, when it is moving 3 - Halfway state between wave and particle, during the transition (the particle is moving at a very low speed).

2


5

1.6 Third principle of duality As we saw in the preceding example of the pressure washer, the wave state appears only if the particle is moving. Otherwise, if the particle is motionless, it remains in a corpuscular state. Therefore, the third principle of duality is: This principle is very important since it solves many enigmas of modern physics. For example, in accordance with experimentations, magnetism only appears when the charged particle is moving. The reason, covered in Part 4 "Electromagnetism", is quite simple:

When the particle is motionless, it is a corpuscle in a spherical symmetry1. When it is moving, the particle becomes a wave, and the spherical symmetry disappears to be replaced by a complex wave with magnetic (and spin) components. In other words, the simple electric field becomes a electromagnetic field.

So,

Electromagnetism is nothing but a consequence of wave-particle duality.

1.7 Polymorphism All elements that meet the criteria of duality are polymorphic. Their form can be transformed from a particle form into a waveform and conversely. We have arrived at the concept of polymorphism that will be used further in Parts 3 and 5. Even if it is obvious, like the three preceding principles, it is interesting to formalize this concept as follows:

1 Only the "r" radius is relevant in the explanation of ‘electric field’. The angles ϕ et θ are not relevant.

Elements that meet the duality criteria are necessarily polymorphic

3

When the particle is moving, it becomes a wave

Note: This proposal is not commutative. Any polymorphic element does not present a duality, particularly if it doesn't produce waves (modelling clay for example)


6

1.8 History Why, since 1905, has this enigma never been solved? In fact, the real question arising is: “Is there not the possibility that we are in the particular case where waves, particle and medium are of the same constitution?”.

The answer is YES. There is perhaps a probability of 1 per 1000, but this possibility exists. Unfortunately, since 1905, physicists have great difficulty solving this enigma because they have generalized a particular case. Indeed, trying to understand the wave-particle duality with, for example, a stone and water, leads to a true enigma. As we see, the only way to explain logically the wave-particle duality is to consider that, in quantum mechanics, we are in the particular case where waves, particles and medium are of the same constitution.

1.9 Conclusions Duality has always been regarded as a burden for the physicists because no one has been able to explain it rationally. This enigma is summarized as follows:

“We note a wave-particle duality, which is very strange. However, this is a normal situation since quantum mechanics is, by definition, illogical and irrational”.

This document does not share this "theory of irrationality" of some physicists concerning quantum mechanics. It transforms this disadvantage into an advantage. Instead of regarding duality as a burden, it regards it as fortuitous, the great opportunity to solve the mystery of matter. Indeed, this enigma, which is no longer a mystery, is summarized as follows:

“Since we note a wave-particle duality in quantum mechanics, we can deduce from this that waves, particles and medium have the same constitution. This is a necessary condition. Thus, if we find the constitution of the medium, we will know the constitution of waves and particles and the converse".

-o-o-o-o-o- Note It is obvious that wave-particle duality only applies to waves and particles. Is the photon a particle? It is far from being proven. As Einstein (in 1920’s), many physicists think that photons aren’t “traditional particles” but, rather, mathematical objects, like vectors, used to describe waves. It means that wave-particle duality doesn’t apply to photons. This is why the Young Slits Enigma is not solved with the above explanation. In reality, this mystery has a different explanation, which is covered in Part 4 “Electromagnetism”.

The Spacetime Model - Part 2 - - 2 - EM radiations

7

2 EM radiations

EM radiations are mathematically described with a high degree of accuracy, but no one is able to explain the constitution of photons and EM waves. To solve the mystery of EM waves, we will proceed by an indirect method. Initially, we will try to understand why "c", the velocity of light, is invariant. There is a good probability that the solution to this enigma will lead us to the constitution of EM waves. Since the first principle of wave-particle duality shows that waves and particles have, necessarily, the same constitution, the knowledge of the waves leads us directly to the knowledge of the particles. So, the resolution of the c invariance enigma, although interesting, is not an end per se but rather a method of investigation by which to solve the mystery of the constitution of particles. Note: The photon concept is covered in Part 4 “Electromagnetism”.

2.1 History The nature of EM radiations has always been the "pet peeve" of physicists. To this day, this problem has not been solved. • Newton, during his time, thought that light was made of particles.

• In the nineteenth century, physicists favoured the wave concept. EM waves were propagated in aether, an unknown propagation medium.

• In 1905, continuing the works of Max Planck (Nobel Prize - 1918), Albert Einstein (Nobel Prize - 1921) built a particle theory of EM radiations. The concept of aether became obsolete since photons do not need any aether to be propagated. However, some problems, like Young's experimentations for example, were still not solved with the photon concept.

• Later, in 1922, Einstein returned to aether. He was confronted with the problem of duality since the photon is incompatible with the wave, and therefore with aether.

• In 1959, 39 years later, Louis de Broglie (Nobel Prize - 1929) proposed the idea that aether was made of neutrinos.

• Around 1980, physicists verified once more the constant speed of light with quasars, using embedded systems and telescopes in satellites.


8

These recent experiments show that the propagation of EM waves and the enigma of the constant speed of light are still not solved. The aether concept would help but no one is able to give an exact definition of it. Finally, since 1905, the enigma of the constitution of light has been so persistent it prompted Louis De Broglie to say: “Science will make a great step ahead the day that it can explain a simple ray of light”.

2.2 Nature of EM radiations One of the peculiarities of the EM wave is that it can be propagated in a vacuum. But in a vacuum… there is nothing… and the EM wave cannot exist in the absence of a propagation medium. The introduction of the photon partially solves this problem. Indeed, like any particle, the photon can move in a vacuum. However, if an EM radiation behaves like a particle in 90% of the cases, it also behaves like a wave in the remaining 10% of cases, as in Young's slits experimentation. The enigma thus remains unsolved for these cases. When a hard drive periodically makes one, two, three or more errors, it must be formatted. Of course, this leads to a waste of time, but there is no other solution. In quantum mechanics, errors or inconsistencies don't occur in one’s, two’s or three’s, …but in ten’s. In such a case, the only thing to do is to "format" the quantum mechanics. The best approach is to start from scratch, ignoring the few laws of quantum mechanics that are inconsistent, but keeping experimentations in mind. Therefore, to understand the nature of EM radiations, we must return to the early 1900’s, when Einstein explained the photoelectric effect and discovered special and general relativity. As stated, the particle aspect of EM radiations, namely photons, will be discussed in Part 4 “Electromagnetism”.

2.3 Separation of media The problem of velocity additions suggests that we are in the presence of two distinct media:

1- “Apparent medium” This is the visible medium that carries out the experimentations, and from where the EM wave is emitted.

For example, in Fizeau Experimentation, this medium is water, and in Michelson’s, it is the Earth's atmosphere moved by the Earth itself.


9

2- “Real medium” EM waves are propagated in a “real medium”. For example, this "Real Medium" could be De Broglie "Neutrinos Sea". The "apparent medium" and the "real medium" are overlaid (fig. 2-1).

2.4 Properties of the "Real medium" The "real medium”, if it exists, must have at least the following two properties:

1- To be present everywhere Since EM waves are propagated everywhere, the "real medium” must also be present everywhere, in air, in water … and even in a vacuum. Spacetime is an excellent candidate to be this "real medium” since it is present everywhere, even in a vacuum1. 2- To have propagation properties We know that any wave needs a propagation medium to move. Since spacetime is elastic and can be deformed (Einstein), it could be an excellent propagation medium.

Therefore, spacetime could be used without any problem as a support for EM waves. This being said, gravity and EM waves do not curve spacetime in the same manner. Please read the three following documents, Part 1, Parts 3 and Part 4 concerning these subjects.

1 Spacetime is not this unknown aether for which we are looking. Spacetime is spacetime. There is no other correct definition and spacetime can’t be identified with aether. In order to avoid any confusion, we will use the term “real medium” instead of "aether”.

"Apparent medium": Air, water, vacuum…, in which the experimentations are carried out

"Real medium" of propagation of the light Fig. 2-1

In this figure, points A and A', as well as the apparent and real media, are separated for teaching purposes but, obviously, they share the same place. Any apparent medium has, necessarily, a subjacent real medium that is associated with it. A’

A


10

2.5 Constant speed of light Let's imagine the emission of a beam, L, from a laser diode (fig. 2-2). The diode, A, is fixed on an "apparent medium" moving with the velocity "V". In fact, the laser beam L is not emitted from the apparent medium as this figure shows, but from the point 'A' located in this "real medium" which is spacetime of the universe.

Since light is propagated in the real medium, its speed depends only on the nature of this medium, and nothing else. In reality, the permittivity of free space ε0 is not a "vacuum permittivity" but rather a "spacetime permittivity", a physical constant that defines the spacetime propagation characteristics, as the "spacetime permeability" µ0. Fizeau, Michelson and other physicists thought that light is propagated in this apparent medium which is moving, water, air, vacuum etc…, whereas, in fact, it is propagated in this real medium which is the "motionless" spacetime of the universe. Note 1 We should not have any confusion between the word “motionless” used in the context of the universe, which is correct, and the same word used in Special Relativity, which is not relevant in that study. Note 2 The spacetime of the universe, sometimes called "global spacetime structure", is the one that was created about 13.9 billion years ago, and not the local spacetime of special relativity. So, in this document, the word "spacetime" will always refer to "global spacetime structure of the universe", as in Friedman-Robertson-Walker Definition. Note 3 There should not be any confusion between the apparent medium, from where the EM wave is emitted, and its propagation medium, the real medium, which is spacetime of the universe.

"Apparent medium":Moving support holding the laser diode.

"Real medium": Motionless spacetime. Fig. 2-2

A

A'

L

L'


11

2.6 Case of two reference spaces Figures 2-3 and 2-4 show that the presence of a "real medium" does not affect the principles of Special Relativity.

Fig. 2-3

A

B

Current Theory

A photon is emitted from A to B, or the converse, to synchronize the two reference spaces, which are both moving. The points A and B belong to the apparent media. In this case, no one can explain why the speed of light is constant. Logically, the velocities should be added. Since this is not the case, this diagram must be revised (…but not the experimentations!!!), despite the fact it has been used since 1905.

Photon

Light is not propagated in the apparent medium, which supports the sources of light A and B, but in the real medium, which is global spacetime of the universe. EM radiations do not consist of photons but of EM waves (please see Part 4 “Electromagnetism” concerning this assertion). As a result, the constant speed of light is easily explainable. The velocity of light is a function of the real medium characteristics, i.e. spacetime permittivity ε0, and spacetime permeability µ0. Thus, the speed of light is always 300 000 km/s, whatever the velocity of the reference space, or the apparent medium, from where the light is emitted.

Real medium: spacetime of the universe

B

B'

A

A'

Fig. 2-4

Proposed Theory

EM wave


12

2.7 Conclusions Therefore, although it amounts to the same thing, it would be more accurate to write:

“The speed of light is 300 000 km/s in spacetime”

rather than:

“The speed of light is 300 000 km/s in a vacuum”

Note: Under certain conditions, EM waves may move at a speed different than 300 000 km/s. For example, using Bose Einstein Condensate made up with sodium atoms at -273.15°, Lene Vestergaard Hau, from Harvard University, USA, slowed down EM waves to 17 m/s. In the same way, EPR also is an exception to the theory. See Part 1, "Mass and Gravity", and Part 4, “Electromagnetism”, to understand these few exceptions.

• EM waves are emitted from an apparent medium but are propagated by the real medium, which is global spacetime of the universe.

• In this real medium, the speed of light is 300 000 km/s. Its invariant velocity is only a function of the permittivity ε0 and the permeability of spacetime µ0

• EM waves are a succession of spacetime vibrations.

The Spacetime Model - Part 2 - - 3 - Movements in Spacetime

13

3 Movements in Spacetime

This chapter affords the reader a more concrete vision of the role of spacetime in EM waves. The deduction developed in chapter 2, i.e. EM waves = spacetime movements, will lead us directly to the knowledge of the constitution of the elementary particles.

3.1 EM waves The spacetime vibrations of an EM wave are shown in figure 3-1. This is a simplified figure, which is not necessarily the real representation of an EM wave. These vibrations are variations of spacetime density. The universe is filled with EM waves of all kinds. Thus, spacetime is not motionless but is vibrating continuously. In this chapter, we only consider the vibrations of EM waves, not those due to gravitational waves.

3.2 Movements in spacetime Variations of density are “movements” in spacetime, like "whirlpools" or "eddies" in water. The propagation of EM waves is similar to that obtained by a stone that makes rings when thrown into the water. The only difference is the medium that is spacetime instead of water. In figure 3-1, wave 1 is the main wave, and waves 2, 3, 4… are secondary waves (if they exist). In this figure, the wave is propagated from left to right.

Fig. 3-1

1234


14

3.3 Mathematical formalization From a quantum mechanics point of view, we have a "wave packet" (fig. 3-2). In reality, the form of EM waves depends on the phenomenon that created it. For our further demonstrations, we will take the simple form of a damp sinusoid (fig. 3-3 and 3-4), even if these schematics are not fully exact. Figure 3-3 represents the periods, from 1 to 4, of the wave in figure 3-1. Figure 3-4 is the same wave but with only one period. Important: The reader must keep in mind that these graphs are only for teaching purposes.

3.4 Polarity of spacetime The following graphics (fig. 3-5 and 3-6 on the next page) are identical to the preceding ones (fig. 3-3 and 3-4). Sign "+" was inserted in areas of high relative density of spacetime and sign "-" in areas of low relative density. The "reference" is the density of spacetime before the arrival of the wave. The positive and negative variations of the wave densities, i.e. spacetime densities, are relative to this reference. This is why the word "relative" was used.

Fig. 3-2

x

Ψ

Fig. 3-3

t

d (spacetime density)

1 2 3 4

Fig. 3-4

t

d (spacetime density)


15

3.5 Example Let's imagine that ambient air is divided into small cubes. In this example, the EM wave is replaced by a soundwave. Each cube has a density of air. When a soundwave arrives, the pressure of the air inside each cube changes in a combination of positive and negative pressures, or high and low pressures. After the passage of the soundwave, the pressure of cubes falls back to its initial value. It is this initial value of density of air that is called "reference" on figures 3-5 and 3-6.

Important note

In this example, a sound wave makes a periodic displacement of air into each cube, which can be identified to EM or Matter waves. The presence of an object, like a house, also makes a displacement of air. The phenomenon is different and can be identified to gravity. In reality, these two displacements of air are two different phenomena. They can be assimilated to electromagnetism (the soundwave) and the curvature of spacetime in general relativity (the house). The difference between these two phenomena is fully explained in two other documents, Part 1 “Mass and gravity”, and Part 4 “Electromagnetism”.

+

Reference

Fig. 3-5

t

d

Fig. 3-6

t

d

+ + ++

- - - -

Reference


16


The Spacetime Model - Part 2 - - 4 - Forces in Spacetime

17

4 Forces in Spacetime

Physicists think that nature has three fundamental forces: gravity, electroweak force (unified in 1972 by Weinberg and Salam, Nobel Prize – 1979) and strong nuclear force. This chapter covers one of these three forces. Differences of high and low densities of spacetime necessarily produce a force. We have the same phenomenon in air: the difference of pressure produces wind. We do not know the character of the force described below, or its properties. At the present moment, we will simply be satisfied to understand it. We will try to identify this force later, in the following two chapters.

4.1 Elasticity of spacetime A material is said to be elastic if it is deformed under stress, e.g. external force, and then returns to its original shape when the stress is removed. This is the case of spacetime.

The Einstein Field Equations, EFE or "Einstein Equations", demonstrate that matter curves spacetime and, since 1916, many experiments have proven that spacetime is elastic.

4.2 Principle of "Least curvature" The principle of Maupertuis1 in 1744 indicates that nature always tends towards the least action. Transposed to spacetime, this principle becomes: This principle goes hand in hand with the Einstein's concept of elasticity. Indeed, like any elastic material, spacetime naturally tends to minimize its curvature.

1 Koenig, De Fermat, Liebniz, Euler, Lagrange, Jacobi and Helmholtz have written similar principles.

Spacetime tends naturally towards the least curvature


18

4.3 Principle of "Least relative density of spacetime" Let's imagine a space far away from masses or waves (fig. 4-1, on the left). Following a disturbance, the spacetime is curved (fig. 4-1, on the right). As we see in this figure, the word “curve” is synonymous with “density”. Any part of spacetime that is curved necessarily produces variations of density. These two words express the same phenomenon.

Thus, the principle of least curvature can be stated in a different way, which will be useful for us, later in this document: (*) Paragraph 3.4 covers the definition of "relative density".

4.4 Density of spacetime For teaching purposes, the two figures in the preceding chapter, fig. 3-1 and 3-5, are grouped in figure 4-2 which represents an EM wave, on the left, and its simplified mathematical representation, on the right. We do not know if a low density produces a negative polarity or the reverse. Further in this document, we will presume that a high density of spacetime corresponds to a positive polarity, and a low density to a negative polarity.

Spacetime tends naturally towards

its least relative density (*)

Fig. 4-1

Variations of spacetime

density


19

4.5 Annihilation process Let's imagine that we take the two “pieces” A and B of the EM wave (spacetime vibrations) in figure 4-2. These two small parts are represented in figure 4-3. What happens if we put these two areas, A and B, in contact? Intuitively, we might think that these two areas will cancel out each other. The area of high density of spacetime in A will annihilate the area of low density of spacetime in B.

Fig. 4-3

Reference: zero relative

density

A B

t

d (relative spacetime density)

+

-+

- - +

Fig. 4-2

Reference: zero relative density

A

B

EM wave


20

We can also demonstrate this phenomenon with the "spacetime curvature" concept (fig. 4-4). Since spacetime is elastic, the two areas A and B will not remain motionless. In any case, spacetime tends towards a null relative curvature. The Maupertuis Principle adapted to spacetime states: The only way to get the least curvature of spacetime is when areas A and B annihilate each other. To better understand the phenomenon, let's consider the example of an acoustic wave. As we know, it is a succession of pressures and depressions in air. Let's isolate two small cubes of air, one in a pressure half period (A), and the other in a depression half period (B). Now, let's put them in contact. Intuitively, we might think that these two areas, A and B, will mutually cancel out each other. The result will be two neutral areas with zero relative density, like our "reference" in fig. 4-2 and 4-3 or 3.5 and 3.6. The same phenomenon occurs in spacetime when we put together two areas, one with a high density of spacetime, and the other with a low density.

4.6 Attractive force Each area of pressure A and depression B of spacetime is delimited by a kind of virtual line called the “horizon of influence” which is marked L (fig. 4-5). If the two areas are far away from each other, nothing occurs. One area doesn't have any influence on the other. If their horizon of influence comes into contact, the high density of spacetime in A tends to cancel the low density of spacetime in B. As we have seen before, the two areas, A and B, will cancel out each other. When the annihilation begins, the two areas continually approach each other, and finally disappear completely if they have exactly the same volume.

Fig. 4-4

B A


21

This “attraction” of the two areas towards each other until complete annihilation is like an attractive force. The principle of least relative density of spacetime, or its twin principle of spacetime curvature, confirms this attraction. Since the attraction process is identical to the annihilation process, it is not necessary to go over the preceding explanation again.

Two areas with opposite polarity, at short distance, tend to a mutual annihilation, thus producing an attractive force.

4.7 Repulsive force In the same manner, two areas with the same polarity of density of spacetime will tend to push each other away (fig. 4-6). When the two areas approach each other, their horizons of influence (L line in fig. 4-6) come into contact.

Fig. 4-5

BA

L

A A

L

Fig. 4-6


22

Just before the contact, the relative density of spacetime on this line L was zero. If the two areas continue to approach each other, this relative density will increase or decrease depending on the polarity but, obviously, will no longer remain null. A repulsive force appears between the two areas A and B since the line L must remain null. The principle of least relative density of spacetime or its twin principle of curvature of spacetime confirms this repulsive force. Thus:

Two areas with the same polarity, at short distance, tend to push each other back thereby producing a repulsive force.

4.8 Fusion Under certain conditions, two areas of identical polarity can merge (fig. 4-7). For example, if the energy of one area is higher than the "barrier" of another, this barrier can be crossed over and fusion becomes possible. We know this phenomenon on Earth in nuclear fusion with light nuclei. Thus, under some conditions of proximity, repulsion can become a fusion.

Fig. 4-7

The Spacetime Model - Part 2 - - 5 - Electron-Positron Annihilation

23

5 Electron-Positron Annihilation

In this chapter, we propose a scenario using the attractive and annihilation forces seen in the preceding chapter, including the explanation of wave-particle duality seen in chapter 1. More precisely, we will try to imagine what occurs when two areas of opposite density of spacetime are put together. For the moment, we do not know the character of this interaction. In the following chapter, we will try to describe the phenomenon and compare it to something known.

5.1 Scenario Let's imagine two areas of spacetime, A and B, of the same dimension (fig. 5-1 on the right). These areas are two small pieces taken from an EM wave (fig. 5.1 on the left) and are made of high and low density of spacetime respectively. Area A comes from a positive half-period and B from a negative one (fig. 5.1 down).

A

B

EM wave

A B

Movements in spacetime

Movements in spacetime

Fig. 5-1

t+ -

+ +- -


24

In the previous chapter we saw that when two areas of opposite polarity meet, they annihilate each other. As we can imagine, this annihilation produces movements in surrounding spacetime. We have the same process when an anticyclone comes into contact with a depression; annihilation always produces wind and disturbances in surrounding space. We must note that all the elements of figure 5-1 are made up of spacetime:

• The areas A and B are “parts” of the EM wave, therefore areas of spacetime • Surrounding space is also made up of spacetime • Since everything is spacetime, movements produced by annihilation are also made up

of spacetime. As we saw, these movements are like an eddy or whirlpool in water. They are EM waves.

The loop is thus closed:

1. The two “pieces” of waves, areas A and B, are annihilated, 2. … which produces movements in spacetime, 3. … movements which are EM waves.

5.2 Different volumes Let's complicate the problem slightly. Let’s suppose that one of the areas has a volume of 0.1% superior to the other (not represented in the figure). What would occur? It is simple: the excess 0.1% will not be annihilated. For example, let's take an area of a volume equivalent to 511 KeV1, and the other 509 KeV. After annihilation, it will remain an area of 2 KeV. This area will be ejected in a direction that preserves the momentum, in relation to the two other disturbances.

1 It would seem strange to relate mass or energy to volume. Explanation of this assertion is given in Part 1 “Mass and Gravity”.

Static areas of

spacetime (Particles?)

Movements

in spacetime (EM waves)


25

5.3 Interpretation This scenario, purely intuitive, coincides curiously with that of an e+e- annihilation.

• The two areas of high and low density of spacetime could be the positron and the electron.

• The movements of spacetime due to annihilation could be the two gammas of 511 KeV created during an e+e- annihilation.

• The volumes A and B disappear. In physics, the positron and electron disappear too.

• The volume of the movements in spacetime corresponds to the volumes destroyed.

• The remainder, if volumes are slightly different, could be the neutrino. Indeed, we don't have the proof that the positron has exactly the same mass as that of the electron1, but we have proof that the neutrino exists. Further discussion of the neutrino is covered in Part 3 “Quarks and Antimatter”.

• If the neutrino comes from an electron or positron, it must also have a spin = 1/2. This is exactly what the experimentation proves.

Such a coincidence in the experimentation is disconcerting but not sufficient to validate a theory. We will make further deductions in the following chapter. As you will see, our conclusions confirm that the present scenario describes, word for word, an e+e- annihilation.

Note: If this scheme is correct, the neutrino should have a very light charge, so light that it could be very hard to detect. This eventuality is covered in chapter 8.2 "The Neutrino", in Part 3 "Quarks and Antimatter".

1 The accuracy of measurement is: |me+ - me-| /m < 8.10-9, with a CL of 90%.


26


The Spacetime Model - Part 2 - - 6 - Nature of Particles

27

6 Nature of Particles

We know of about 300 elementary particles. Among those, physicists have favored the electron. It seems that the electron, and its antiparticle the positron, are the basic particles of the universe. For this reason we have also chosen the electron and the positron with which to continue our research into the constitution of particles. This chapter synthesizes the preceding deductions.

6.1 Constitution of particles The following deductions, made in five different ways, always lead to the same conclusions: particles are areas of spacetime.

1) 1st principle of duality This principle, which fully explains the enigma of wave-particle duality, states that particles, waves and medium must have the same constitution. Since the medium is spacetime, particles and waves are also made of spacetime.

2) Electron-positron pairs production We know that a high-energy gamma, which passes near a nucleus or any charged particle, can decay into an electron-positron pair. This phenomenon is very simple to explain. The positive Coulomb Field of the nucleus attracts the negative areas of the EM wave and pushes back the positive areas, namely the areas of low and high density of spacetime. Thus, the wave decays in two parts (fig. 6-1 and 6-2). These two “pieces of wave” are e+e- pair(s). Obviously, it is impossible to create particles or any other object from nothing1. The electron and positron originate somewhere, and this “somewhere” can only be the original EM wave, i.e. spacetime vibrations.

1 Spacetime is not considered as "nothing".


28

Since the original EM wave is made up of spacetime, the electron and the positron are necessarily made up of spacetime too. We can deduce that:

3) Electron-positron annihilation We have studied, in the previous chapter, the annihilation of an electron and a positron. Since the result, two gammas of 511 KeV, are a movement in spacetime, the origin, or the electron and the positron, is made up of spacetime too. This experimentation is a simple conversion from spacetime (particles) to spacetime (gammas), in accordance with the wave-particle duality explanation of chapter 1.

4) De Broglie Waves

In 1924, Louis De Broglie had the idea that any particles could have an associated wave similar to the EM wave. For De Broglie, all the waves have a comparable constitution. The experimentations of Davisson (Nobel Prize - 1937) and Germer in 1927 confirmed De Broglie's theory. So:

! Particles and matter waves are of the same constitution (first principle of duality).

! "Matter waves1" and EM waves and are of comparable constitution (De Broglie).

By association, we deduce that particles have the same constitution as EM waves, i.e. they are made of spacetime.

1 The subject of EM and matter waves is covered in the two following documents: Part 3 “Quarks and antimatter”, and Part 4 “Electromagnetism”.

+

Fig. 6-1

t

d

+ + +- - -

e+

e-

Fig. 6-2

t

d

+

-

e+

e-

-

The electron and the positron are made up of spacetime


29

5) Coulomb's Force

Let's return to the scenario discussed in the preceding chapter and try to identify this force. What is this unknown force that brings closer the two areas A and B until their complete annihilation? We have four possibilities:

• Gravity? The scenario of chapter 5 couldn't work with two areas of identical polarity. Since gravity disregards polarity, this unknown force is not gravity.

• The strong nuclear force? In chapter 5, we never mentioned nuclei or quarks. Thus, this unknown force cannot be the strong nuclear force.

• The weak nuclear force? In the same way, it is not a question of interactions with bosons Z°, W+ or W-. This unknown force is not a weak nuclear force or, more precisely, the weak nuclear component of the electroweak force.

• The EM force? By elimination, it must be the EM force.

We deduce that the unknown force discussed in the preceding chapter is the Coulomb component of EM force. This conclusion seems logical since the two areas, A and B, are "pieces of EM waves", which are related to EM force. Since the Coulomb Force acts only on charged particles, we deduce that the two areas A and B are charged particles. However, these two areas are “pieces” of an EM wave, i.e. spacetime. We naturally conclude that the particles are made up of spacetime.

6.2 Conclusions The conclusion is that Nature is founded on only one basis, which is summarized below.

Note: the concept of polymorphism has been added to the following definition for reasons that will be discussed in Part 3 “Quarks and Antimatter”.

EM waves and elementary particles are made of

Polymorphic areas of high and low densities of spacetime

Particles = Static areas of spacetime EM waves = Dynamic areas of spacetime (vibrations)


30

6.3 Einstein's Point of view Let's note this remark by Einstein, which tends to confirm our deductions: "Matter cannot exist without spacetime". Thus, the proposed theory is far from being unrealistic since, in the 1920's, this great physicist thought that Nature was directly connected to spacetime.

Waves = Particles = Medium Spacetime = ??? = Spacetime

Wave-particle duality can exist if, and only if, ! the particle, ! the wave, ! the medium,

have the same constitution. (see paragraph 1.3)

Particles Have necessarily the same internal

constitution as waves and medium, i.e.

Spacetime

Medium isknown

Waves are known

Medium is spacetime (chapter 2)

Waves Medium Particles ???

EM waves are movements in

spacetime (chapter 3)


31

6.4 The fifth dimension? This conclusion also corroborates our simple model of the universe based upon spacetime and using only four dimensions. Indeed, we are faced with the following alternative:

• Either the charge is independent of the four known dimensions and thus cannot be expressed by the form q = f(t,x,y,z). It is then necessary to envisage a fifth dimension, independent of the others four. This new dimension is the charge, q. In this way, the universe variables would be t,x,y,z,q.

• Or, the charge is a function of four known dimensions and can be expressed by the form q = f(t,x,y,z). In this case, we can remain in these four well-known dimensions. All particles are then expressed with the four spacetime variables: t,x,y,z.

Except for the few years of his life when Einstein was interested in the Kaluza Theories, he believed the universe had only 4 dimensions. The previous demonstration shows that he was right. It is not necessary to add a fifth dimension to explain the charge.

The observation that the charge is nothing but differences in density of spacetime is in full agreement with Einstein's ideas.


32


The Spacetime Model - Part 2 - - 7 - Clarification

33

7 Clarification

As the discussion stands now, the reader may take the following stance:

"This does not mean anything… When I take a hammer, I see that this hammer is made of matter, and not of the so-called polymorphic areas of high and low densities of spacetime…”.

This chapter is probably the most difficult to understand of the theory since it tries to explain to the reader that all the matter of the universe is made up of spacetime areas and that we are living in a virtual world. This is far from being obvious.

7.1 What we know For the past 50 years, what we have known is particularly disconcerting:

1 - Inside the atom It has been known for a long time that if the atom was one meter in diameter, the nucleus would have 100 microns and the electron less than one micron. Thus, if we eliminate all the vacuum of the atom (99.999%), the size of the human body would be reduced to a pinhead… 2 - Waves In accordance with De Broglie, matter and waves are identical. Thus, the human body, at least the 0.001% that remains after all the vacuum is removed, would be nothing but waves… 3 - Energy As we know, E = mc². So, this pinhead would be identical… to pure energy… We will further reconsider this equation in Part 4 “Electromagnetism”.

To summarize, as we know, matter is made of:

! A vacuum: 99.999% (experimentations) ! Waves or matter-energy: 0.001% (De Broglie, Einstein, experimentations)

Under these circumstances, is it logical to continue considering matter as a physical concept? Of course not. It is obvious that we can’t continue to call “matter” something that is 99.999% vacuum and 0.001% waves or energy…


34

It would be more reasonable to consider that what we call “matter” is nothing but a virtual concept since a vacuum and waves don't exist in concrete terms. So, if a vacuum and waves are both virtual concepts, we are living in a virtual world. Please, note that this is not a new idea. These conclusions were well known in the last century, in particular when Davisson and Germer demonstrated in 1927 that matter and waves are identical. Note: This enigma (99,999% of an object is a vacuum) is fully explained in Part 3 “Quarks and Antimatter”.

7.2 The Spacetime Model contribution The current theory doesn't change our point of view about objects, which are always made up of a vacuum (99.999%) and waves (0.001%). Nothing has changed and matter, or its counterpart waves, remains a virtual concept. The Spacetime Model is a little more precise regarding the nature of waves (fig. 7-1). So, the major difficulty doesn't arise from the Spacetime Model but from what we have known for 50 years: 99,999% of matter is made of a vacuum. We already know that gravity has its origin in spacetime. The Spacetime Model demonstrates that spacetime is also "curved" by EM and De Broglie Waves. The Spacetime Model simply extends the Einstein Concept to all components of the universe, stating that

It seems that we have great difficulty accepting the idea that we are living in a virtual world made of two virtual elements: 1. A vacuum (99.999%) 2. and waves or energy (0.001%)

All is spacetime


35

(1) At the present time, no one knows exactly the constitution of De Broglie Waves (2) The constitution of matter and many enigmas of quantum mechanics are fully explained if we

consider that De Broglie and EM Waves are spacetime variations. This is the only contribution of this new theory.

7.3 Explanation In reality, we must not think in terms of “matter” but in terms of “forces”. Indeed, forces alone generate all forms of communication experienced in human life:

• Intelligence: chemical interactions in neurotransmitters and glial cells (Coulomb Force),

• Sound, music, speech… (vibrations of air), • Heat (infra-red EM waves), • Pain (electrical currents in the sensory nerves), • Joy (hormones which are specific molecules issued from the Coulomb Force), • Human power (electrical currents in the motor nerves),

…and what we call "matter" is:

• What we see: light, or EM waves, • The weight of objects: gravitational force, • The touch: Coulomb Forces between molecules.

Of course, all these forces are invisible, as those of two magnets, but they exist and must be taken into consideration in any explanation of what we call “matter”.

De Broglie Waves (1)

A vacuum

+

A vacuum

+

Current theory

Proposed theory

Fig. 7-1

De Broglie Waves (2)


36

7.4 Importance of forces in spacetime Let's try to understand the importance of these forces in life. If we remove all these forces from the human body, what would remain?

• If all the EM force disappeared, we would not have any more light. We would be blind.

• Acoustic waves are propagated in the air by forces. If these forces did not exist, we could not hear noises, music, or speech.

• We know that nerves propagate electric potentials. If our hands were disconnected from our brain, we would not have any feelings (sensory nerves), or movements (motor nerves).

• But the chemical interactions between neurotransmitters and glial cells of our brain are Coulomb Forces. Thus, our brain would no longer function.

• Molecules are associations of atoms thanks to the Coulomb Force. Thus, the human body, life, and all the objects that surround us would not exist since there would be no association of atoms in molecules.

• Moreover the atoms themselves could not exist since it is still the Coulomb Force that maintains the electrons on their orbital. If we remove the Coulomb Force from the nucleus, what would become of the Schrödinger Equation?

• At last, nucleons are quarks associations thanks to the nuclear force. Thus, if all of these forces did not exist, the universe would only be made of free electrons and positrons1. In other words, the universe would be made of areas of low and high densities of spacetime. Finally, these polymorphic areas of spacetime that we call “matter”, that is to say atoms, which are made of a vacuum and waves or energy, have only a passive role to play in Nature. On earth, we encounter the same situation. For example, on a CD, it is not the material, or PVC, which is relevant, but the data or music registered on it, i.e. a virtual concept. To summarize, we can say that Nature = Forces. Forces are a virtual concept produced by spacetime which, by various combinations, make up atoms, molecules, and finally the universe and life.

"As a magician makes us believe that an object is on our right whereas it is on our left, nature makes us believe that all is matter whereas all is forces produced by spacetime."

1 We will confirm later, in Part 3 “Quarks and Antimatter”, that quarks are made up of positrons.

The Spacetime Model - Part 2 - - Complements

I

Complements

Predictions According to paragraph 5.3, the neutrino could have a very slight charge. Partitioning the theory The five parts of the Spacetime Model can be downloaded at the following URL address:

Part 1 ....... Mass and gravity................... www.spacetime-model.com\mass.pdf Part 2 ....... Constitution of Matter .......... www.spacetime-model.com\matter.pdf Part 3 ....... Quarks and Antimatter ......... www.spacetime-model.com\quarks.pdf Part 4 ....... Electromagnetism................. www.spacetime-model.com\electromagnetism.pdf Part 5 ....... Forces, the Universe ............. www.spacetime-model.com\forces.pdf

Part 1 - Mass and Gravity

Mass In our world, mass and volume seem to be two different quantities because in atoms, the mass is not proportional to the volume. So, we have a large range of atoms with different mass and volume. However, at the particle level, mass = volume. In reality, we have five classes of volumes. The two main classes are:

1. Closed volumes. These volumes produce a displacement of spacetime. As we know, the spacetime curvature produces gravity, but it also produces a "mass effect". Electrons are examples of closed volumes. Indeed, electrons have a mass.

2. Open volumes. These volumes exist but do not produce any displacement of spacetime. If there is no curvature, there is no "mass effect" either. Orbitals in atoms are examples of open volumes. Indeed, orbitals are massless.

/



II

Quarks This part demonstrates that we need two positrons to make three u quarks. A u quark with an electron becomes a d quark (please note that the rule of addition of fermions is covered in Part 4). This deduction, from the wave-particle duality and spacetime, has been extended to all particles. Finally, u quarks, d quarks, antiquarks, muons, antimuons, taus, mesons, baryons etc... can be made with only two basic particles: electrons and positrons.

Antimatter From this discovery, we can deduce that antimatter is not located at the bottom of the universe but right before our eyes, embedded in u and d quarks. A simple calculation demonstrates that any atom is made up of an equal number of electrons and positrons, exactly 2A, with A = atomic number. For example, the C12 is made of 24 electrons and 24 positrons, the latter being embedded in quarks. The calculation is fully explained in this Part and is 100% accurate for all 2930 known isotopes.

Part 3 – Quarks and Antimatter

/

Each atom has a particular proportion of open and closed volume. This is why mass and volume seem to be two different quantities but this is an illusion. At the particle level, more exactly at the electron and positron level, mass equals volume. Composite particles, like mesons, are combinations of other classes of volumes.

Gravity Contrary to a preconceived idea, spacetime is not curved by mass but by closed volume. This phenomenon is the same as when a ball is immersed into water: It is the volume of the ball, and not its mass, which produces the displacement of water.

A particle also produces a displacement of spacetime. Since spacetime is elastic (Einstein), the curvature of spacetime produces a pressure on volumes. This tends to bring them closer to each other. It means that gravity is not an attractive force between masses, but a pressure force on closed volumes.


III

The mystery of the wave-particle duality solved in Part 2 leads to a full knowledge of electromagnetism. This phenomenon is quite simple to understand. In short, when a charged particle is motionless, its electric field has a spherical symmetry. When it moves, it becomes a wave and its spherical symmetry disappears. Its 1D space is transformed into a 2D/3D space. A magnetic component (2D/3D) is added to the electric field (1D) of the particle. This phenomenon is exactly what experimentation proves (∆q/∆t).

Part 4 - Electromagnetism

Nuclear force Electrons or positrons, which surround other particles as a spacetime wave, produce a recall force toward the center of the particle, like a rubber band. This force is nothing but the "strong nuclear force".

Unification of forces This part unifies the three basic forces (gravity, electroweak and strong nuclear force) in two generic forces: the Coulomb Force and the Hooke Force.

The Universe A suggestion regarding the creation of the universe is proposed. In reality, the Big-Bang Theory does not explain the electron mystery" and this enigma is discussed. This Part offers two suggestions, much more credible than the Big-Bang, regarding the creation of the universe.

Part 5 - Forces, the Universe


IV

Contact You can contact the author1 by email at:

[email protected]

or writing to:

M. Jacky JEROME Editions Arts et Culture 42 4 square Kennedy 42120 LE COTEAU (France)

1 Note: The author is a physics hobbyist and does not work in an institutional establishment. The writing of the Spacetime Model has been done entirely on his own money and time, with no help from the scientific community. If you find some error in this document, please let him know.


V

Table of content

Introduction........................................................................................I IV

1. Wave-Particle Duality

1.1 Current definition of duality.............................................................1 1.2 Explanation of the duality ................................................................1 1.3 First principle of duality...................................................................3 1.4 Important deduction .........................................................................4 1.5 Second principle of duality ..............................................................4 1.6 Third principle of duality .................................................................5 1.7 Polymorphism ..................................................................................5 1.8 History..............................................................................................6 1.9 Conclusions......................................................................................6

2. EM Radiations

2.1 History..............................................................................................7 2.2 Nature of EM radiations...................................................................8 2.3 Separation of media ........................................................................8 2.4 Property of the Real Medium ......................................................9 2.5 Constant speed of light ....................................................................10 2.6 Case of two reference spaces ...........................................................11 2.7 Conclusions......................................................................................12

3. Movements in Spacetime 3.1 EM waves.........................................................................................13 3.2 Movements in spacetime..................................................................13 3.3 Mathematical formalization .............................................................14 3.4 Polarity of spacetime .......................................................................14 3.5 Example ..........................................................................................15

4. Forces in Spacetime 4.1 Elasticity of spacetime ....................................................................17 4.2 Principle of "Least curvature" ..........................................................17 4.3 Principle of "Least relative density of spacetime" ...........................18 4.4 Densitiy of spacetime ......................................................................18 4.5 Annihilation process ........................................................................19 4.6 Attractive force ................................................................................20 4.7 Repulsive force ................................................................................21 4.8 Fusion...............................................................................................22


VI

5. Electron-Positron Annihilation 5.1 Scenario............................................................................................23 5.2 Different volumes ............................................................................24 5.3 Interpretation ....................................................................................25

6. Nature of Particles

6.1 Constitution of particles ...................................................................27 6.2 Recapitulation ..................................................................................29 6.3 Conclusions......................................................................................29 6.4 Einstein's Point of view....................................................................30 6.5 The fifth dimension? ........................................................................31

7. Clarification

7.1 What we know .................................................................................33 7.2 The Spacetime Model contribution..................................................34 7.3 Explanation ......................................................................................35 7.4 Importance of forces in spacetime ...................................................36 Complements.......................................................................................I - IV









Part 3

Quarks and Antimatter

The Spacetime Model - Part 3 - - Introduction

II

Patent Rights


238268, 238633, 244221, 05 13355-2 895 559, 248427, 258796, 261255, 268327, 297706, 297751, 297811, 297928, 298079, 298080, 329638, 332647, 335152, 335153, 339797.







III

Before reading… To fully understand this part, the reader must be familiar with the deductions and results developed in Parts 1 and 2. These results are summarized below:

The curvature of spacetime (Part 1) Let's fill up a container with water. We drop a billiard ball into the container. The volume of the ball produces a displacement of water.

The same phenomenon applies to spacetime. Contrary to generally accepted ideas, it is not mass which deforms spacetime, but volume, more exactly “closed volume”.

Mass = Volume? (Part 1) In our world, mass and volume seem to be two different quantities because in atoms, the mass is not proportional to the volume. So, we have a large range of atoms with different masses and volumes. However, at the particle level, mass = volume (with some reservations explained in Part 1).

In reality, we have two main classes of volumes:

! Closed volumes (A): These volumes make a displacement of spacetime. Thus, a pressure force appears on the surface of the volume. This pressure produces a “mass effect”, an effect having all mass characteristics. Nucleons and electrons are examples of closed volumes.



A B


IV

What is Gravity? (Part 1) Two volumes inserted into spacetime curve it. Since spacetime is elastic, its curvature produces pressures on these two volumes. This tends to bring them closer to each other. So, contrary to what we think:

Gravity is not an attractive force between masses but a pressure force exerted by spacetime on closed volumes.

Since a pressure force is the inverse of an attractive force, there is no difference between the current theory and this new explanation of mass and gravity:

Attractive force (Newton) + Concave curvature of spacetime (Einstein) = Pressure force + Convex curvature of spacetime

Validations (Part 1) This part describes a simple experimentation, which highlights a black hole behavior when R = Rs. The Schwarzschild Metric and Newton Law are also calculated using this new explanation of Mass and Gravity, from the Hooke Law. Moreover, the proposed theory is in perfect accordance with the Von Laue Diagram.

Wave-Particle duality (Part 2) Since 1905, the wave-particle duality has been one of the greatest enigmas of physics. Indeed, nobody can explain this phenomenon, but there is one particular case where wave-particle duality becomes logical and rational. That is when waves and particles are of identical constitution.

For example, a drop of water (corpuscle) and a water wave are of identical matter. Water has either a corpuscle behavior or a wave behavior.

This explanation of wave-particle duality leads to a major deduction: when the particle is motionless, it remains in a corpuscular state, and when it is moving, it becomes a wave.

Matter and charge (Part 2) Parts 2 and 4 cover explanation of EM waves, which are nothing but spacetime vibrations. Linking this discovery, the wave-particle duality explanation, and experimentations like the 511 KeV production from e+e- annihilations, we deduce that matter is made of spacetime. More exactly, what we call "matter" is areas of low (electrons) and high (positrons) densities of spacetime. So:

Waves = Matter (Spacetime variations) (Spacetime areas)

The Spacetime Model - Part 3 - 1 - 1 - MicroDomains

1 MicroDomains

It seems that spacetime would be parcelled out in a kind of "neutral electrons" called µDomains in this document.

When Pasteur discovered invisible microorganisms, no one believed him. Like microorganisms, µDomains are invisible since they have no charge. Therefore, like neutrinos, they can't be moved. Is that a reason to reject this concept? Of course not. So, instead of saying "Since I don't see µDomains, they don't exist", it is wise to say "Why not? Let's study this possibility".

This chapter covers the µDomains concept and gives arguments in their favour: why they are necessary, their use, how to verify their existence etc...

1.1 The basic particles At the origin of the universe, what were the basic particles? Physicists consider that electrons and u/d quarks, from the Standard Model, are the basic building blocks of the universe. It is impossible, or highly improbable, that the universe was created at an intermediate stage with so many different charges: - 1, - 2/3, -1/3, 0, +1/3, +2/3 and +1, taking into account both particles and antiparticles of the Standard Model, including the three neutrinos.

Seven different charges are too many to make this point of view credible It is obvious that the universe was created in a very simple state. It is a necessary condition. The simplest is the best. Its symmetry was elementary, probably originating with only one particle.

The original particle remains to be determined. If physicists were to choose a particle among the 300 known, it would almost certainly be the electron. It is a logical choice. Since the electron charge is - 1, we need at least an opposite charge of +1 to preserve the symmetry. Moreover, it is not possible to build anything with only one charge. Thus, the second particle to be considered is, of necessity, the positron, with a charge of +1. It is, therefore, logical to think that the creation of the universe required only two particles, the electron and the positron. This means that ALL PARTICLES are made up with Electrons and Positrons. The reader will have confirmation of this assumption in the following chapters.


1.2 µDomains The physicist Pierre Weiss discovered the existence of microscopic magnetic fields, called “Weiss Domains”. Later, Felix Bloch (Nobel Prize - 1952) discovered that walls, called "Bloch Walls", surrounded the Weiss Domains. It would seem that global spacetime1 of the universe is divided into quanta called "microdomains", analogous with the Weiss Domains. These µDomains are electrons (or positrons) without charge. Each µDomain could thus have an mass of 511 KeV.

Wouldn't spacetime also be made of µDomains,

possibly surrounded of µWalls?

It is a simple assumption but we will see that it can be verified, at least for the µDomains, (possibly not for the walls). This leads to interesting conclusions. In particular, µDomains explain perfectly the Coulomb Force, magnetism, quarks, antimatter etc…. Let's examine the following table 1-1, which summarizes the well-known particles. In this table, the muon and tau are missing since they are some kind of electron. 1 For a definition of "Global Spacetime", please see Part 2 "Constitution of Matter", paragraph 2.5, footnote #2

Positron/ --- /Electron

Proton/neutron/antiproton

π+/π°/π−

K+/K°/K-

B+/B°/B-

D+/D°/D-

∆+/∆°/∆−

Σ+/Σ°/Σ−

Ξ+/Ξ°/Ξ−

+ 0 -

+ 0 -

+ 0 -

+ 0 -

+ 0 -

+ 0 -

+ 0 -

+ 0 -

+ -

Fig. 1-1

Charge


We note that a particle is missing, the neutral electron.

With this neutral electron, or "µDomain", the table is complete and homogeneous

All the particles are grouped in three’s. It should be noted that a similar approach has already been used in physics with Lie Groups.

1.3 Existence of µDomains The existence of µDomain seems be confirmed in multiple ways:

• In the particle table (fig. 1-1), the "neutral electron" is missing. • The process of the creation of the universe is, necessarily, very simple. The most

simple is the best. However, we already know two structures of 511 KeV: the electron and the positron. A third neutral structure is necessary to fill the empty space of the universe. The immediate idea is that this unknown structure also be of 511 KeV. It is not credible to think that the universe has been created with two different structures, one concerning the electrons and positrons (511 KeV), and another one, a neutral structure, with a different volume, or built on a continuum basis.

• According to Max Planck (Nobel Prize 1918 ), all components of the universe could be quantified. It doesn't mean that spacetime is also quantified, but it is an interesting indication.

• It is impossible to build particles having a fractional charge of 1/3 or 2/3 with integers charges of –1 (electrons) and +1 (positrons). µDomains are a necessity (see chapter 4).

• µDomains are also a necessity in cosmology (see Part 5 "Forces, the Universe"). Many enigmas of astrophysics are fully explained by µDomains.

• µDomains are the basis of the EM field, and probably of the spin too (Part 4 "Electromagnetism").

• µDomains explain the "distributed charge" model (chapter 2). • This leads us to the explanation of quantum levels in atoms (chapter 3). • µDomains also explain the significance of the Schrödinger Model (chapter 3). • µDomains explains the muon and pion masses (see paragraph 1.6). • This leads us to the quark model (chapter 2). • This new quark model gives the solution to one of the greatest enigmas of physics:

where is the antimatter in the universe? (chapter 5) • The quark model also explains one of the major enigmas of physics: why the proton

has exactly the opposite charge of the electron? (chapter 6). • µDomains explain the E0 energy level in atoms (chapter 3, paragraph 3.2). • µDomains fully explain the paradox of photons and EM waves when they decrease in

1/r ² (Part 4 "Electromagnetism"). • µDomains also explain the non-linearity of time in general relativity1, • The resolution of some enigmas like EPR (Part 4 "Electromagnetism"), • Or the Heisenberg Uncertainly Relation (Part 4 "Electromagnetism"), • Or Young Slits (Part 4 "Electromagnetism") etc...

1 Paragraph 3.7 in Part 1 "Mass and Gravity" explains the deviation of light thank to µDomains which are the support to this phenomenon.


We may reasonably consider that:

At the present time, µDomains have never been detected because, like neutrinos, they have no charge1. The existence of the neutrino is obvious when we examine the conservation laws of momentum. This is not the case with µDomains. That is the difficulty.

1.4 Properties of µDomains Since the existence of the neutral electron must not be excluded, we will suppose that it exists. Further, we will have confirmation of its existence. For the moment, let's imagine its assumed properties:

• Its mass (or its closed volume), must be 511 KeV. • Its relative density of spacetime, i.e. its charge, must be that of its environment. It is

regarded as having a null relative density of spacetime (see Part 2 "Constitution of Matter").

• A µDomain can be charged or not. If it has a low density of spacetime, it becomes an electron, and if it has a high density of spacetime, it becomes a positron. Let's remember that this choice is arbitrary, the reverse being possible.

• Since a µDomain doesn't have any charge, it is not possible to move it or to detect it. We have the same problem with neutrinos and any neutral particles.

• If one or more µDomains are included in a particle, the volume of the particle increases. The latter gets more mass. Therefore, the enclosed µDomains are considered as closed volumes. See Part 1.

• Free µDomains have a volume of 511 KeV each but, since they can't be moved, they don't curve spacetime to make room. They are massless. See Part 1.

1.5 Basic components of the universe The basic components of the universe could be those of the following figure 1-2. We will also see that it is possible to build any particles with only these three particles.

1 Not exactly. The Spacetime Model predicts that the neutrino has a very little charge. See § 8.2.

If µDomains solve so many enigmas of physics (quarks, orbitals, antimatter etc), it can't be

merely a simple coincidence.


Note: We will see, in Part 5 "Forces, the Universe", that the charge of a µDomain may shift to another µDomain making electron-positron or matter-antimatter pairs.

1.6 Example of verification It is impossible to prominently display free µDomains since they are neutral. However, it is possible to detect them when they are included in some particles. For this purpose, the following example is proposed. The central particle is the π° meson. An electron surrounds it in order to build a π - meson1. The outer-shell electron charge is distributed in µDomains surrounding the central π° meson. Some µDomains are locked up in the mass difference π -- .π°.

1 See the following chapter. For the rule of addition of spins, please see paragraph 2-6, Part 4 "Electromagnetism".

-1 +1

Fig. 1-2

µDomain(511 KeV)

Positron (511 KeV)

Electron (511 KeV)

Charge 0

ππππ−−−− meson

Fig. 1-3

π° meson

Electron µDomains

muon

Electron


It would seem that the µDomains, electrons and positrons, gather in multiples of 3 or 91. The following calculation (data from PDG) is based on groups of 9 µDomains. The abbreviated form below is µD for one µDomain and µD9 for 9 µDomains. ! The muon, including the outer-shell electron, consists of 23 µD9. Each µD9 has a

volume, i.e. mass, of 105.658369/23 = 4.5938 MeV.

! The difference between the π+/− and π° meson is 4.5936 MeV. This difference seems to be equal to one µD9 calculated from the muon.

The tau would have 387 µD9. Each µD9 of the tau has a volume of 1776.99/387 = 4.5917 MeV. We can note that 387 is also a multiple of 9. However, the tau volume (mass) is 17 times more important than the muon mass. An adjustment of the µDomains according to the volume may be necessary2. The following table summarize the calculation. The CL between the muon and the pion, and the tau and the pion, are:

As follows:

• The theory predicts that a µDomain has a volume close to 511 KeV. Calculations give 510,4 KeV for these three particles. It is a normal result since the volume (the mass) of each particle is compressed due to the curvature of spacetime (see Part 2 "Mass and Gravity").

• The CL of correlations obtained is very interesting: - Between the muon and the pion: 99.9948 % - Between the adjusted tau and the muon: 99.9972 %, with a measurement error

of 0.0309%. At last, these results are close to the center of tolerance of each particle.

1 This is not a rule but only a simple remark by the author. 2 This calculation isn't described in this document but the Author can send his study by email upon request.

µD9 µD CL

π meson 4.5936 MeV 510.400 KeV (reference)

Muon 4.5938 MeV 510.427 KeV 99.9948% Tau (adjusted) 4.5937 MeV 510.412 KeV 99.9972% Tau (not adjusted) 4.5917 MeV 510.189 KeV Not relevant

The Spacetime Model - Part 3 - 7 - 2 - The "Distributed Charge" Model

2 The "Distributed Charge" Model

Contrary to a preconceived idea, in atoms, the electron is not moving around the nucleus as a punctual particle. Its charge is distributed into quanta, making a kind of "cloud of charges" around the nucleus. This is a consequence of wave-particle duality. This new model can also be applied to composite particles such as neutrons or mesons and its application is of considerable interest.

2.1 Electron in the atom Let's imagine a drop of oil on the top of an eggshell. What happens? This drop of oil spreads over the eggshell.

We have seen, in Part 2 chapter 1, that the electron is not moving as a punctual particle but rather as a wave. Its charge is distributed in several µDomains. When the wave, i.e. the electron, approaches the nucleus, it takes the form that any polymorphic object, in similar circumstances, does: it spreads out over its orbital, like a drop of oil does over the eggshell. Its form will resemble a thin shell of spacetime density surrounding the nucleus (fig. 2-1).

2.2 The distributed charge" model In reality, we don't have a "thin shell" but rather a "distribution of spacetime density". The charge of the electron is distributed inside µDomains (fig. 2-2). This is confirmed by experimentations, in particular that of the electron diffusion by a neutron (see paragraph 6-3).

Fig. 2-1


2.3 The Schrödinger Model Let's imagine, for example, that the electron wraps up the nucleus in 50 µDomains. Instead of having a continuous moving electron around the nucleus with a charge of -1, we will have 50 µDomains with a charge of –0.02 each. This is what is called the "distributed charges" model or, in other words, a sort of "spacetime distribution", since charge is spacetime.

Current theory The Schrödinger Equation could say that the probability of finding the electron at a given position and at a given time, in this example, is 0.02. Since, around the nucleus, we have 50 µDomains, the total probability of finding the electron on its orbital is 0.02 x 50 = 1.

Proposed theory In the Spacetime Model, the measurement1 does not relate to the electron as a particle, but to a negligible part of its charge. The probability of finding the electron is always 1 (100%) in each µDomain, but the charge measured is –0.02 instead of -1. Since we have 50 µDomains, we obtain the same result.

As we see, from a mathematical point of view, nothing is changed. However, the explanation of this phenomenon is different. In both cases, the whole probability is 1. Therefore, the Schrödinger Equation can continue to be used, but it would be more correct to replace "probability density" with "charge distribution".

1 We mention “measurement” making the theory comprehensible, but it is obvious that a real measurement of the electron under the above conditions must be in accordance with the Heisenberg Uncertainly Relation.

Fig. 2-2

µDomains


Note: Einstein never agreed with this probabilistic explanation posed by Max Born (Nobel prize 1954). All things considered, the Spacetime Model is more close to Einstein's view than to its opposite Max Borns and Schrödingers view.

2.4 The vacuum enigma No one is able to explain why 99,999% of matter is a vacuum. However, this enigma becomes very simple to undesrtand if we consider that electrons, in atoms, follow the distributed charge model. For example, let’s consider a “ball pit”, also known as “ball pool” (fig. 2-3). Each ball is empty. Therefore, the amount of PVC in each ball is very small, so small that we can consider that 99% of the pit is a vacuum. In atoms, the phenomenon is the same. If the electron is that particle moving around the nucleus, no one can explain why 99.999% of the atom is a vacuum (fig. 2-4A). If electrons are distributed in µDomains as figure 2-2 shows, the amount of "matter" (0.001%) is the same but we have the perception that "matter" exists (fig. 2-4B).

Fig. 2-3

Fig. 2-4A Fig. 2-4B


2.5 The PE effect The PE effect offers additional proof. If the electron is that particle moving around the nucleus at a great distance from it (fig. 2-4A), the probability that a photon has to meet the electron is practically zero. Today, under these circumstances, why does the PE yield reach 95%? If the electron is distributed in µDomains all around the nucleus (fig. 2-4B), this enigma becomes clear. In such a case, the PE yield may reach 100%. Note: the footnote of paragraph 3.1, in Part 4, offers more information concerning this enigma.

2.6 U and d quarks If quarks are built according to the "distributed charge" model, we could have the following scheme (fig. 2-5)1. This model is confirmed in chapter 5 by a formula that calculates the antimatter in the universe.

For the moment, let's say that the central charge of both quarks is +2/3. The outer-shell electron of the d quark has a double effect: it decreases the charge from +2/3 (u quark) to –1/3 (d quark), and it increases the volume, i.e. the mass (see Part 2 "Constitution of Matter"). This explains the mass difference between the d and u quarks. It should be noted that the volume of the d quark is considerably smaller than that of any atom; it is a closed volume. Since this overall volume is hermetic to spacetime, it is mass-like.

1 The rule of addition of spins is discussed in chapter 2-6, Part 4 "Electromagnetism".

u quark +2/3

d quark2/3 – 1

-1/3

Fig. 2-5 Electron

Note: The peripheral electron may not be spherical and homogenous.

u quark

The Spacetime Model - Part 3 - 11 - 3 - Atom

3 Atom

Niels Bohr (Nobel Prize - 1922) thought that electrons were continually moving around the nucleus inside the atom. Around 1930, Schrödinger (Nobel Prize - 1933) created another concept: "probability density". In this concept, the electron is a particle, as the third postulate of quantum mechanics indicates: the probability of locating the particle is described by the wavefunction. The word "particle" is not ambiguous and doesn't mean a wave or anything else. This new concept was an improvement on Bohrs idea but did not solve the enigma of the quantification of orbitals.

Since atoms are built according to the "distributed charge model, this chapter is the continuation of the preceding one which covers this subject. We will try to bring logical answers to those questions that are mathematically verified but, so far, remain unanswered.

3.1 Energy levels of orbitals The Schrödinger Equation gives the mathematical solutions to orbitals with great accuracy but no one can rationally explain this principle. We can take the example of satellites orbiting around Earth. Of course, many satellites may share the same orbit. Why, in quantum mechanics, would it be different? If the electron is a particle which “is moving in all directions” around the nucleus, the quantification of orbitals can't be explained. Moreover, if the electron is a punctual particle, the Pauli Principle also can't be explained. If the charge of the electron is distributed in several µDomains around the nucleus, according to the "Distributed Charge Model", the quantification of orbitals becomes obvious. The following example explains this phenomenon.

Let's place five magnets, all oriented in the same direction (fig. 3-1), in a vertical rail. Each magnet is subject to gravity, which attracts it toward Earth, and to a repulsive force due to the adjacent magnets.

The lower magnets carry the total weight of the upper ones. This is why spaces between magnets are not equally drawn. The levels E1, E2, E3 are, thus, dynamically built.

By repeating the same experiment any number of times and under the same conditions, we will always find the same spaces E1, E2, E3 We could think that these magnets are systematically placed on imaginary rails, or quantum rails, E1, E2, E3 In other words, we could think that the position of each magnet E1, E2, E3is "quantified".


This example explains the origin of the quantification of orbitals in atoms1. If the electron is distributed in the µDomains surrounding the nucleus, according to our "distributed charges" model, this enigma no longer exists. The above example explains the construction of orbitals inside the atom. In particular, we must note that the orbitals are dynamically built. In the example, if the magnet E1 is removed, the magnet E2 drops down and takes the empty place of the removed magnet (fig. 3-2).

1 In quantum mechanics, there is often confusion between “discrete” and “quantified”. In the Schrödinger Equation, we have both definitions. On one hand, the Laguerre Polynomials are discrete and, on the other hand, the Planck Constant is quantified. In this document, when the two concepts are simultaneously present, we will use the qualifier of “quantified”, even if this word is not entirely correct.

SN

SN

SN

SN

SN

E0

E1

E2

E3

E4

Fig. 3-1

Quantumenergy levels

SN

SN

SN

E0

E1

E2

E3

Fig. 3-2

Next energy level to be occupied

Energy level E4 doesn't exist


Fig. 3-3 shows the principle of the “distributed charge” model inside the atom. This diagram is only for illustration since, as we know, orbitals are not spherical. To summarize, we can state:

• Levels are dynamically built, one after the other. • An atom cannot have high-level orbitals if low-level ones do not exist. There are,

however, a few exceptions1. • Since the levels are dynamically built, electrons always tend to fill empty layers. • If an external disturbance occurs, it modifies the overall magnetic field. In such a

case, all the levels may be displaced (level degeneration).

To sum up, the quantification of orbitals is a mathematical illusion. Orbitals are not quantified but are dynamically built taking into account electrons that are still in place. New electrons, distributed in several µDomains, take their natural place on orbitals having the most favourable Coulomb Force.

3.2 The E0 energy level In quantum mechanics, we have another enigma regarding the atom: why doesn't the electron drop on the nucleus yielding its energy? If the electron was a punctual particle moving around the nucleus, this enigma exists and can't be solved. The E0 energy level was imagined to solve such a phenomenon, but this theory is only a theory, nothing more. In the Spacetime Model, since the charge is distributed in many µDomains, the overall charge surrounding the nucleus is stable. This problem doesn’t exist.

1 Sometimes, some orbitals are far from each other. This is the case of the "p" layer orbitals. We can also have coinciding energy levels of layers, like "s" and "p" for example (layers known as "sp").

Fig. 22-3

n=1

n=2

n=3

Next orbital to be filled: n=4. Orbital n=5 doesn't exist. It will be built dynamically when orbital n=4 will be filled. Note: for teaching purposes, other levels (l, p) have been omitted.


3.3 Schrödinger Equation The Schrödinger Equation introduces another enigma: the probability of the presence of electrons is maximal at the center of the nucleus. Why does this curiosity exist? In the Spacetime Model, the Schrödinger Equation doesn’t relate to a probability but to a charge. Since the nucleus (the main charge) is precisely located in the center of the atom, the maximum charge is obviously focused in the center. That is the explanation of this enigma.

3.4 The Pauli Principle (proposal) The Pauli Principle is fully demonstrated but no one can explain it. Indeed, if electrons are those punctual particles moving around the nucleus, the Pauli Principle remains a true enigma. For example, would it not be logical to consider that more than two satellites may share the same orbit around Earth. Why would it be different in quantum mechanics? Around the nucleus, we can have either one or two electrons distributed in several µDomains (fig. 3-4). If two electrons fill the orbital, the spin locks them up1. However, a more accurate explanation of the spin is necessary to fully understand this enigma, but it is obvious that the current model, which is based on a punctual particle moving around the nucleus, is far from reality. Important note: The following explanation is only a suggestion and must be taken with great care.

1 Chapters 2-6, Part 4 "Electromagnetism" cover the spin.

Fig. 3-4

The Spacetime Model - Part 3 - 15 - 4 - U and d quarks

4 U and d quarks

We saw that electrons and positrons are charged µDomains, i.e. µDomains containing a spacetime density higher and lower than the average density (see Part 2 "Constitution of Matter"). Would u and d quarks follow the same model?

This chapter covers the constitution of u and d quarks. In particular, it proposes a logical explanation of the mysterious charge of 2/3 and -1/3. Applying our "distributed charge" model to the quarks, we obtain relevant conclusions.

4.1 Starting points The starting points of our quark theory are: ! The universe is made of spacetime. It has only four dimensions. Not one more. ! µDomains include various relative densities of spacetime: the negative densities, by

convention, are electrons, and the positive ones are positrons (see Part 1). ! These electrons, positrons and µDomains make up quarks ! The "distributed charge" model also applies to quarks.

It is interesting to see that we have two means by which to verify this theory:

1. If this theory is correct, we should find as many electrons as positrons in the universe. This leads to the resolution of the antimatter enigma.

2. If this theory is correct, it should also solve the enigma of the proton's charge. Indeed, the proton’s and electron's charges are both strictly equivalent, with a remarkable accuracy of 10-21. This is a true mystery for physicists.

4.2 U and d quarks construction (proposal) A suggestion of the construction of u and d quarks is represented in figure 4-1. The following sequence is detailed for teaching purposes. This sequence may not be exact. We will see, in chapter 6, that protons, neutrons and hydrogen atoms have a simpler construction. At last, it should be noted that a confirmation of this quark model is done in the following chapters, in particular concerning the proton enigma and location of antimatter.


Note 1 Experimentation gives a value different from 511 KeV for a u quark. Several explanations are possible. For example, the two positrons may merge with a µD10, that is to say a group of 10 µDomains. In this case, the overall volume will be equal to 12 µD (µD10 + two positrons), and each u quark would have a volume, or a mass, of (12 x 511 KeV)/3 = 2 044 KeV.

It is possible that the volume (the mass) of the u quark is:

(n x 511KeV)/3, with n = integer value ≥ 3.

It would be premature trying to solve this problem because it is impossible to isolate quarks and, therefore, results of experimentations (from 1.5 MeV to 3 MeV for the u quark) are inaccurate..

Note 2 The scheme of figure 13-1 is probably not exact and needs some adjustments, but there is no longer any doubt about the construction of the u and d quarks from electrons and positrons. If this quark configuration solves so many enigmas, it is not a simple matter of chance.

Fig. 13-1

Phase 1: Fusion Two positrons merge with one or many µD(s) to make a three-particle group. The µD(s) is(are) necessary to bind the two positrons, to avoid the Coulomb Repulsion. The result is an intermediate particle having a charge of +2.

Phase 2: Separation The charge of +2 tends to be uniformly distributed. When the Coulomb Repulsion appears, the particle decays into three sub-particles. The charge of +2 is then divided into three parts. Each sub-particle, therefore, has a charge of +2/3. These sub-particles are u quarks.

Phase 3: d quarks When a free electron, in its waveform, meets a u quark, it surrounds the quark according to the “distributed charge” model. The electron closes up one or many µDomains. Thus, we obtain a charge of +2/3 - 1 = -1/3. The volume, or the mass, of the d quark is necessarily larger than that of the u quark. Please note that the fermions/bosons law of addition is covered in paragraph 2-6, Part 4.

e+ µD(s) e+

+ +

u u u

µDs

+

d quark

u e-

u


4.3 Conclusions

We think having:

(matter) (antimatter) electron positron u quark u antiquark d quark d antiquark neutrino antineutrino muon antimuon tau antitau etc…

Nature is not so complicated. In reality, we have:

(matter) (antimatter) electron positron

All particles are combinations of electrons, positrons and empty space (µDomains)

What gets us into trouble is not what we don't know. It's what we know for sure that just ain't so.

Mark Twain

The Spacetime Model - Part 3 - 19 - 5 - Antimatter

5 Antimatter

If the Quark Model previously described is correct, it must provide the solution to one of the greatest enigmas of physics: where is the antimatter in the universe? Initially, from the Quark Model, we will calculate the quantity of antimatter inside atoms. Then, we will extend this calculation to the antimatter in the universe

5.1 Starting points If we consider that the basic universe is composed of electron-positron pairs, which are the two basic particles, we may state the two following remarks. 1/ Location in atoms ! If electron-positron pairs were created at the same time and in the same place,

positrons are, necessarily, close to electrons.

! We already know where the electrons are.

! Since the atoms are neutral, the positrons we are looking for are probably in the positive part of the atom, the nucleus. That these positrons are associated in quarks or in one form or in another does not matter. One thing is sure, positrons are not far from electrons. In other words, we can say: Search the electron, and you will find its companion, the positron1, which, by necessity, is close to it (probably in the positive part of the atom).

It is obvious that, if at a given time, an electron was created in the universe, its counterpart, the positron, is certainly not 14 billion light-years from the event.

2/ ββββ+ radioactivity

Let's imagine that each nucleus is a type of balloon filled with helium. We know that, in the universe, we must have a large amount of helium, but we don't know where it is. At the bottom of universe? In extra-dimensions (string theory)? In SUSY?

1 As on Earth: "Search the woman, and you will find her companion, the man"… It is obvious that women and men, necessarily, live on the same planet. It would be strange to consider that women live on Earth, whereas men live on a planet located 14 billion light-years away from Earth.


Inside any atom, the number of electrons is strictly equal to the number of positrons

After accurate investigations, we note that one part per million of helium flows out of each balloon. What should we think? Of course, the immediate thought is: "The little amount of helium that flows out of the balloons leads us to suppose that the balloons are filled with the helium for which we are searching". It is obvious.

In physics, we are faced with the same problem. We know that a very small amount of antimatter flows out of the nucleus by way of β+ radioactivity. Whatever the name given to the internal particles, bosons, gluons, X, Y or Z… we can strongly suppose that antimatter is enclosed inside the nucleus. This means that we must undertake our investigations to find antimatter starting with the nucleus1.

To summarize, these two starting points let's consider that we have a strong probability of finding antimatter inside the nucleus, and not 14 billion light-years from Earth.

5.2 Homogeneity of the atom It has been pointed out that we need two positrons to make three u quarks. We saw also that a d quark is made up of a u quark and an electron. It is, therefore, easy to calculate the number of electrons and positrons inside any atom. The calculation is done in the flowchart (fig. 5-1) on the following page.

Whatever the chemical element is, this calculation indicates that, in any atom, we have exactly the same number of positrons as electrons. Therefore, the antimatter, i.e. positrons, is strictly equal to the matter, i.e. electrons.

This conclusion is in accordance with Feynman's Formalism (Nobel Prize 1965) and QED in which the electron and positron have symmetrical roles in quantum mechanics.

The flowchart of figure 5-1 gives the following formula:

1 In reality, the β+ radioactivity is not directly related to quarks (see Part 5). However, the reasoning given here is correct. Without good reason, it is not logical to think that antimatter is located in the deepest universe.

ke+ = ke- = 2A (5-1)

k = number of electrons or positrons inside an atom A = atomic number (A=N+Z)


Total

(3Z+3N) u quarks (Z+2N) electrons

Z protons 3Z ..... u quarks Z........ electrons

Conclusion:

Positrons ..... 2AElectrons ..... 2A

Fig. 5-1

Writing A = N + Z, with A = atomic number

u u u

Proton 3 u + 1 e-

u u

Neutron3 u + 2 e-

ud d d

(*) We need 2 positrons to make up 3 u quarks

N neutrons 3N...... u quarks 2N...... electrons

u

u quark = 2/3 of positron d quark = u quark + electron

du

Electrons Nucleus....................... 2N+Z Atomic electrons ......... Z Total electrons ......... 2N+2Z

Positrons U quarks ..................... 3N+3ZConverted in positrons (*): Total Positrons .........2N+2Z

Electrons Inside d quarks............Z+2N Atomic electrons..........Z Total ........................2Z+2N

Spacetime

e+ µD e-

Atom with Z protons and N neutrons

Electron

See fig. 1-2, in chapter 1


5.3 Example The table below (fig. 5-2) shows the isobars A = 16. This table must be read as follow:

• uN: The number of u quarks in neutrons (= N) • dN: The number of d quarks in neutrons (= 2N) • uZ: The number of u quarks in protons (= 2Z) • dZ: The number of d quarks in protons (= Z) • Utotal: Since each d quark contains a u quark, the total of u quarks is: Utotal = uN + dN + uZ + dZ • Positrons: Since three u quarks are made up of two positrons, the number of positrons

is 2/3 of Utotal. This number is e+. • Electrons: Each d quark contains one electron. Moreover, we have Z atomic electrons

around the nucleus. The total of electrons is therefore: dN + dZ + Z

Conclusion: We see that we have exactly the same number of positrons as electrons. Matter strictly equals antimatter. This number of electrons or positrons is, in any case, and in any atom, the double of the mass number A. This means that antimatter is located into the nucleons' quarks. We obtain the same result with any atom or isotope. 1. The "exotic" Li3 is the only exception but its existence is not proven. Its acknowledgement depends on published works. In any case, this exception can't be retained as a valid objection. The problem comes from the lack of a neutron. In the Spacetime Model, as we will see, each nucleus needs at least one neutron. The Li3 doesn't have any. If this isotope does indeed exist, it should decay immediately into three protons. The author doesn't have detailed information about Li3.

This rule, which is verified within the 2930 known isotopes1, confirms the Spacetime Model

Fig. 5-2

Nucleus A N Z uN dN uZ dZ Utotal e+ e-

Be 16 12 4 12 24 8 4 48 32 32

B 16 11 5 11 22 10 5 48 32 32

C 16 10 6 10 20 12 6 48 32 32

N 16 9 7 9 18 14 7 48 32 32

O 16 8 8 8 16 16 8 48 32 32

F 16 7 9 7 14 18 9 48 32 32

Ne 16 6 10 6 12 20 10 48 32 32

Antimatter Matter Neutrons

u d dProtons

u u d


The universe contains strictly the same quantity of matter (electrons) as antimatter (positrons)

5.4 Antimatter in the universe Given our current knowledge and depending on theories, the main elements in the universe are neutrons, hydrogen, and various atoms resulting from the Bethe Cycle or others. Black holes and dark matter are not taken into account since we don’t know the exact constitution of these elements. Neutrons Each neutron is made up of three “u” quarks and two electrons (see the following chapter, paragraph 6-2). The three “u” quarks are made up of two positrons. Two positrons and two electrons mean that we have a perfect equivalence of matter and antimatter in the neutron. Hydrogen and various atoms We simply apply the formula (5-1). For hydrogen, since A=1, we have two positrons and two electrons (= 2A). To summarize, the formula of the antimatter in the universe is:

With: ke-, ke+ Number of electrons or positrons in the universe nn Number of neutrons in various elements. The “2” factor comes from formula (5-1). NH Number of hydrogen atoms1 in the universe. As in the neutron calculation, the “2” factor comes from the formula (5-1). Index A Atomic number of the various atoms in the universe. The limit “m” is the maximum atomic number supposed in the universe. “A” serves as an index too. It starts from 2 since we have already taken hydrogen into account. NA Number of atoms, of index A, in the universe. 2A Number of electrons or positrons of the atom of index A. The “2” factor comes from the same formula (5-1). εεεε Free electrons and positrons in various forms in the universe, other particles, free electrons from ionized atoms etc.. This quantity is negligible when compared to the other terms.

1 Excluding the hydrogen isotopes, which are calculated in the following term.

ke- = ke+ = 2nn + 2nH + ∑A=2m nA2A + εεεε

(5-2)


5.5 Validation of the Spacetime Model The confirmation of the theory on the antimatter of the universe, which is applied to the 2930 known elements without exception, is of considerable interest: it validates the entire Spacetime Model. Indeed, this conclusion is the synthesis of all preceding discoveries. The following flow chart (fig. 5-3 ) clearly states that, before coming to this important conclusion, it was necessary to find the solution to many unsolved enigmas of contemporary physics.

-o-o-o-o-

The greatest joke that Nature has played on us was to have us believe that antimatter is at the edge of the universe when it is right before our eyes, into the quarks.

3 quarks u = 2 positrons 1 quark d = 1 quark u + 1 electron

Atoms, neutrons, particles As much matter (electrons)

as antimatter (positrons)

Distribution of charges

Only one possible particle, with its

antiparticle

Particles are made up of spacetime

! Electron ! Positron

Birth of the universe? (Part 5)

Mass = volume

Antimatter in the universe Inside the quarks:

2/3 of positrons into each quark

Fig. 5-3

Waves are propagated in spacetime Wave-particle duality (Part 2) (Part 2)

(Part 2)

(Part 1)

(Part 3)

(Part 3)

(Part 3)

The Spacetime Model - Part 3 - 25 - 6 - Nucleons

6 Nucleons

The explanation of the enigma of the antimatter in the universe confirms the quark model described in chapter 4. Are the nucleons affected by this structure? This chapter covers the proton and neutron schemes according to the "distributed charge" model. A scenario of the creation of nucleons is proposed.

6.1 Proton The (u u d) quark structure of the proton in figure 6-1A is not exact and must be replaced by the (u u u) + electron structure (fig. 6-1B), which is in perfect accordance with experimentations. That does not change any previous calculations of antimatter. Indeed, the three quarks (u u d) are not bound by a hypothetical strong nuclear force whose origin is unknown. Nature made things a lot simpler. A free electron surrounds the three u quarks and keeps them locked up. This electron acts as a rubber band: the more one moves away from the center, the stronger the force becomes. When the proton interacts, its electron surrounds a u quark, which becomes a d quark. This makes us believe that the d quark exists inside the proton. This, however, is an illusion. Examination of some interactions and logical deductions let’s suppose that the d quark is built during the interaction with the proton’s electron of one of its three u quarks.

Fig. 6-1

Electron from the d

quark The electron leaves the d quark, which becomes a u quark, and surrounds the three u quarks to make a proton. This electron acts as the strong nuclear force.

u u

uRepulsive Coulomb

Force

A - Current Model

u

u d

No one can explain the origin of the strong

nuclear force

B - Spacetime Model


6.2 Neutron The neutron is a proton surrounded by an electron (fig. 6-2). Please note that the fermions/bosons law of addition is covered in paragraph 2.6, Part 4. This electron has two effects:

! It cancels the positive charge of the proton making it neutral ! It increases the volume, i.e. the mass, of the proton.

These effects are confirmed by experimentation. However, µDomains are probably kept closed between the two electrons surrounding the three quarks. If that were the case, the pressure made by the outer-shell electron, due to the Coulomb Force, would decrease the µDomains volume, which would be lower than 511 KeV.

…And, as we could expect from experimentation,

The decay of the neutron gives a proton and an electron1

6.3 Confirmation by experimentation The shape of the neutron reflects exactly our “distributed charge” model (fig. 6-3). The neutron is neutral only at 1.5 to 2.10-15 m.. A negative charge appears at a distance of 0.5 fermi. No one can give a rational explanation of this phenomenon. The Spacetime Model offers a very simple explanation of this enigma. The negative charge comes from the electron surrounding the proton to make up a neutron (fig. 6-2). Therefore, this well known experimentation confirms that:

1. The neutron is made of an electron, which surrounds a proton, 2. Since this experimentation is a reality, the “distributed charge” model is a reality too.

1 Since the antineutrino is a secondary effect (see chapter 8), it is not mentioned here.

Fig. 6-2

u u

u

Neutron

Electron from the additional d quark of the neutron (udd)

Proton

µDomain(s)

Electron from the d quark of the proton (uud)


6.4 Direct proton creation The scenario of the creation of protons described here, at the very first moments of the universe, is more probable than other scenarios because it is simpler. It is also perfectly logical. Its description is given in figure 6-5 on the following page. It should be noted that the creation of protons is immediate and only requires one phase. It was pointed out, earlier, that the universe, at the time of its creation, was necessarily very simple. By no means is this an assumption or a conjecture. It is a necessity. Any phenomenon during its creation, whatever it is, is necessarily very simple too.

The simplest is the best. As an alternative scenario, figures 6-4A and 6-4B require two stages. The u and d quarks are initially built separately. Then, a d quark attracts two u quarks. The electron leaves the d quark and surrounds the three u quarks to make up a proton.

0.5 1 1.5 d(f)

Fig. 6-3

Proton

Neutron

Charge

Outer shell electron of the neutron

Fig. 6-4

u u u

d Proton

u u

u

Electron A B

This scenario is provided for information only. This scheme is less probable than the scenario of figure 6-5 on the next page, which is immediate.


Building H atoms and neutrons from spacetime

u u

u

Proton

u uu

Fig. 6-5

e+ e+

Hydrogen atom or neutron

The electron surrounds the three quarks.

µD

The proton volume (mass) is large because the three u quarks have a mutual repulsive Coulomb Force.

IMPORTANT Here, the process is illustrated for teaching purposes. In reality, it may be immediate. The quarks, the proton and the H atom or neutron are probably built instantaneously. Other schemes are also possible.

e- e-

Spacetime

Spacetime (µDomains) creates e+e- pairs. For more information, see Part 5.

Two e+ and µD(s) make three u quarks


The "distributed charge" model is in perfect accordance with the asymptotic freedom

theory and experimentation.

6.5 Proton synthesis When experimentation produces a proton, this particle is not directly created. The collision of the incoming particle(s) with the target produces spacetime movements, which split into electrons and positrons or, in other words, into electrons and quarks. This scenario is exactly the same as the gamma production from an e+e- pair. Conversely, a gamma ray may produce a new e+e- pair and so on… Thus, the proton synthesis or meson/baryon interactions are not "special interactions" since particles and waves are made of spacetime. We must keep in mind that “all is spacetime”.

6.6 Asymptotic freedom The "asymptotic freedom" discovered by David Gross, Frank Wilczek and David Politzer (Nobel Prize 2004) states that, contrary to the other forces whose intensity decreases with the distance from interaction, the strong nuclear force increases with it. Thus, the quarks are practically free at short distance, but are prone to a very strong force, which ties them together when they move away from each other. Very often, physicists use the image of a rubber band to explain this asymptotic freedom: the more we move away from the center of the rubber band, the more intense is the recall force. That is exactly what the electron does in the Spacetime Model. Like a rubber band, it surrounds the three u quarks and prevents them from moving away from each other.

Note: This model of nucleons was not built of all parts to satisfy the asymptotic freedom theory. It results from the polymorphism concept of the wave-particle duality enigma described in Part 2, chapter 1. The initial problem, for the author, was to logically explain the "probability density of the Schrödinger Equation. The concept is mathematically perfect, but no one can rationally explain the probability. The "distributed charge" concept is a more rational solution.

The author extended this model to all particles, quarks, baryons, mesons. In this way, he noticed that, finally, all components of Nature are based on the same concept, the "distributed charge" model. One of the major successes of this model is to explain perfectly the enigma of antimatter in the universe (see chapter 5). It also means that the strong nuclear force doesn't exist per se. Instead, the electron acts as a rubber band and produces a Hooke Force, which is an elastic force. This conclusion is nothing but the logical connection between the Authors "distributed charge" model and the asymptotic freedom theory.

So:


6.7 Hydrogen atom (proposal) As curious as it seems, there is no difference between a neutron and a hydrogen atom (fig. 6-6). In both cases, an electron surrounds a proton, in accordance with the distributed charge model. The ∆° could probably be inserted into this scheme, as the ∆+ in a similar proton scheme. The only difference is the mass. In the neutron and ∆°, the electron creates a closed volume, with mass, while in the hydrogen atom, it creates an open volume, or is massless, since its orbital is much larger and is "porous" to spacetime. Nature’s favoring of the neutron or the hydrogen atom may be a simple fact of proximity and energy. When the proton is met, if the electron-wave is large, a hydrogen atom may be created. Conversely, if the electron-wave is small, as in a proximity phenomenon, a neutron may be created. This suggestion must be studied thoroughly. Note: Information in this paragraph needs verification and must be considered with great care.

6.8 Equality of charge of the proton One of the greater mysteries of physics is the charge of the proton: why is it strictly equivalent to that of the electron, with a theoretical accuracy of 10-21? With the "distributed charges" model, the explanation of this enigma becomes very simple:

• The proton is made up of three quarks (u u d) • But the quarks (u u d) are made up of (u u u) and one electron • The quarks (u u u) require 2 positrons, and thus have an overall charge of +2.

Fig. 6-6

p

Neutron

Electron

Proton

p

Hydrogen atom

p

∆°

Closed volume

Open volume


• Since the "d" quark is a "u" quark surrounded by an electron, the resulting charge is +2 - 1 = +1

• In this way, it seems logical that the proton charge, +1, would be equal to the electron charge since it comes from the excess positron.

To summarize, the charge of the proton is:

2 positrons – 1 electron = 1 positron. So, as in the resolution of antimatter of the universe,

6.9 Antineutron Experimenters try to detect spontaneous transformation from neutrons to antineutrons. It is theoretically possible if energy allows it (fig. 6-7, on the following page).

• The neutron decays in (u u u) quarks and two electrons. • The (u u u) quarks are recomposed into two positrons. • In addition, the two electrons are linked with µDomain(s) in order to make up three

antiup quarks. • The two positrons surround these three antiup quarks to make an antineutron.

The neutron and the antineutron are both made up of two positrons and two electrons.

The charge of the proton, which is exactly +1, comes from only one basic particle: the positron. This explanation shows that:

• The three quarks (u u u) of the proton come from two positrons

• The "d" quark is a "u" quark surrounded by an electron


Fig. 6-7

u uu

Electrons

u u

u

Neutron

u u

u

Antineutron

e+e+

e- e-

Positrons

u uu

The Spacetime Model - Part 3 - 33 - 7 - Interactions

7 Interactions

In Part 2, we have already studied two interactions, the e+e- pair production by a gamma, and the opposite effect, the e+e- annihilation. Since all components are made up of spacetime, it is possible that various interactions follow the same rule as the e+e- production or annihilation. This chapter covers basic interactions to establish a guideline.

7.1 Guiding principles According to the first principle of duality pointed out in chapter 1 of Part 2, any EM wave may be transformed into a particle and the converse. We must always keep in mind that For example, figure 7-1 on next page, shows the creation of six quarks, three u and three u bar, an e+e- pair, and a residual gamma. All these components are created at practically the same time from the spacetime movements, or gammas. In this example, the most probable scheme is the creation of a proton-antiproton pair. However, any other particles may be created. Of course, we must have the same quantity of electrons-positrons before and after the interaction, including the gammas1. Finally, the incoming gamma provides many possible combinations.

The same principle may be applied in high-energy interactions. The particles' jets come from spacetime movements produced by the particle collision. In our example, the creation of three u/u bar quarks requires the presence of two positrons/electrons very close to each other. The particles are created mainly due to energy, but the proximity should probably also be taken into account.

1 This new way to consider that, in the universe, we have only three components, the electrons, the positrons and the µDomains, doesn't change the current formulas in quantum mechanics.

Particles do not come from a vacuum

but from spacetime movements


It should be noted that these schemes are in perfect agreement with Feynman's diagrams.

This means that any heavy particles (SUSY…) may exist and will probably be discovered in the future since all particles are made of spacetime1.

7.2 Formulation (proposal) This document contains many schematics for teaching purposes. However, sooner or later, it will be necessary to classify particles according to the Spacetime Model.

1 Since the real nature of the spin is unknown, it is not impossible to find some heavy particles having a spin = 1 or 2 or, why not, 3 or 4…. Such cases do not mean that these heavy particles would explain gravity or other phenomena. A good knowledge of the spin mechanism is necessary before making any assertion.

Spacetime (waves) is converted into spacetime (particles) and the converse.

All interactions become virtually possible

Fig. 7-1

d

e+

u

u

u

e-

e-

e-

e+

u

u

u

e+

++ + - -

Various combinations of particles, like proton-antiproton

Gammas


In this way, it would be useful to have a simple method of representing the internal structure of the basic components, electrons, positrons, quarks….

The following scheme can be used. A parenthesis means an electron or a positron is surrounding the other basic particles. Of course, parenthesis must go in pairs. For example:

d quark e-(u) Proton e-(u, u, u) Neutron e-(e-(u, u, u)) Antiproton e+(u bar, u bar, u bar) etc…

The particles that surround the others are the electron and positron. They act as the "strong nuclear force". Since this force is necessary in any composite particle, meson, baryons…, we can state the following rule1: Or, as an alternative, 1 However, there are two exceptions, the Li3 isotope, which may not exist, and the ∆++, which is not stable.

All composite particles must have at least one parenthesis pair

All composite particles must have at least one electron or positron

The Spacetime Model - Part 3 - 37 - 8 - The Standard Model

8 The Standard Model

The Standard Model does not take into account the origin of the quarks, i.e. the positrons. Moreover, the presence of neutrinos among the leptons is very debatable. This chapter is a complement to the Standard Model.

8.1 Basic particles The scheme of the construction of quarks is indicated in the table 8-1 on the following page. The s, c, b and t quarks may be built with electrons and positrons, like the u and d quarks, with particular schemes and energy levels. This is also the case with the two other leptons, the muon and the tau, which are built with an electron. For that reason, these particles have not been represented in this table.

8.2 Neutrinos Within the Spacetime Model, the properties of neutrinos are not in accordance with the Standard Model. Here are their properties: ! Neutrinos seem to be backward movements in spacetime (see Part 2, chapter 5).

Sometimes, a simple annihilation can produce this backward movement; sometimes, various interactions are responsible. This means that neutrinos may depend on the interaction. However, this assumption requires verification.

! So, neutrinos are not "basic particles" but rather a kind of "secondary effect".

! The volume (mass) of the neutrino should be equal to the very slight difference in the volume of particles involved in the interaction.

! If the neutrino comes from an e+e- annihilation, its mass is equal to the difference of mass between the electron and the positron. As stated in Part 2, the neutrino seems to be a "residual particle", more exactly a "residual wave".

! The Spacetime Model predicts that neutrinos would have a very small charge, lower than a few parts in a million. Usually, physicists consider that the charge has an integer value of –1, 0 or +1, except for quarks and some particles like the delta++.


This point of view explains why the neutrino's charge has always been considered equal to zero. The fact that much experimentation has been conducted near a neutron reactor has not been taken into consideration so this very slight charge has never been highlighted1. On the other hand, "we find only that we are looking for".

! In an e+e- annihilation, a possible charge would be equal to:

With: q = charge of the neutrino, in Coulombs Ma, Mb = mass, or volume (see Part 1), of the electron and positron. The greatest mass of both is Ma.

! The charge should have the polarity of the particle having the greatest mass.

! Since the neutrino comes from an electron or a positron, its spin must be 1/2. Experimentation confirms this point of view.

! In the Spacetime Model, the only basic neutral particle that could exist is the µDomain. A neutral particle like the neutrino should not exist.

8.3 Other particles Among the seven particles of level 3 on figure 8-1, two are the basic particles of all the stable matter in the universe: the electron and the u quark. The d quark is not a "basic" particle since it is made up of a u quark and an electron.

1 However, it is possible that a quantum of charge may exist. In such a case, the charge of the neutrino may be equal to zero. Please note that this quantum of charge, if it exists, must not be confused with the Planck Quantum of charge, which is not a real quantum like "h" but a unit (the word "quantum" often leads to a confusion).

Ma 1.602 x 10-19 C q = Ma - Mb


e-

-1

e+

+1

uµD

0

u

Level 2

e-

-1

e+

+1

µD

0

Level 1

de-

-1

d µD

0

u

+2/3

e+

+1

u

Level 3

Note: As indicated in paragraph 8.1, this figure does not include neutrinos and particles of groups 2 and 3, such as heavy quarks, which are various combinations of electrons and/or positrons.

+ +

+ +

Spacetime (µDomains)

+1/3 -2/3 -1/3

-2/3 +2/3

Standard Model

Fig. 8-1

See Part 5


I

Complements

Predictions ! The u quark is made up of two positrons and µDomain(s) (Chapter 4). ! The d quark is a u quark surrounded by an electron (Chapter 4). ! Antimatter is located inside nuclei, more exactly, inside quarks (Chapter 5) ! An elastic diffusion or electrons on the d quark would highlight its distributed

charge model. The graphic must be close to that of figure 6-3. ! The configuration of the proton is e-(u u u) instead of (u u d) (Chapter 6) ! The neutron is a proton surrounded by an electron (Chapter 6). ! The strong nuclear force doesnt exist if the particle or nucleus has not at least one

electron or one positron (paragraph 6.6). ! The neutrino could have a very slight charge (Paragraph 8.2)

Partitioning the theory The five parts of the Spacetime Model can be downloaded at the following URL address:





/



II

Before understanding the constitution of matter, the author had to solve three enigmas:

1. How to explain the wave-particle duality from a scientific point of view. 2. Why electromagnetic waves have a constant speed of 300 000 km/s. 3. How an e+e- pair can be transformed into two gammas of 511 KeV, i.e. how matter is transformed into waves and the converse.

The solving of these three enigmas conducts to the knowledge of the constitution of matter and EM waves. This new theory is confirmed by much experimentation.

Part 2 - Constitution of Matter



/


Each atom has a particular proportion of open and closed volume. This is why mass and volume seem to be two different quantities but this is an illusion. At the particle level, more exactly at the electron and positron level, mass equals volume. Composite particles, like mesons, are combinations of other classes of volumes. Gravity Contrary to a preconceived idea, spacetime is not curved by mass but by closed volume. This phenomenon is the same as when a ball is immersed into water: It is the volume of the ball, and not its mass, which produces the displacement of water.


III

Contact

You can contact the author1 by email at:

[email protected]

or writing to:





The Universe A suggestion regarding the creation of the universe is proposed. In reality, the Big-Bang Theory does not explain the electron mystery" and this enigma is discussed. This Part offers two suggestions, much more credible than the Big-Bang, regarding the creation of the universe.



IV



V

Table of content

Introduction.........................................................................................I IV

1. MicroDomains

1.1 The basic particles............................................................................1 1.2 µDomains.........................................................................................2 1.3 Existence of µDomains ....................................................................3 1.4 Properties of µDomains ...................................................................4 1.5 Basic components of the universe....................................................4 1.6 Example of verification....................................................................5

2. The "Distributed Charge" Model

2.1 Electron in the atom .........................................................................7 2.2 The "distributed charge" model........................................................8 2.3 The Schrödinger Model ..................................................................8 2.4 The vacuum enigma ........................................................................9 2.5 The PE effect ...................................................................................10 2.6 U and d quarks .................................................................................10

3. Atom 3.1 Energy levels of orbitals...................................................................11 3.2 The E0 energy level ..........................................................................13 3.3 Schrödinger Equation.......................................................................14 3.4 The Pauli Principle (proposal) ........................................................14

4. U and d Quarks 4.1 Starting points .................................................................................15 4.2 U and d quarks construction (proposal) ...........................................15 4.3 Conclusions......................................................................................17

5. Antimatter 5.1 Starting points ..................................................................................19 5.2 Homogeneity of the atom.................................................................20 5.3 Example ...........................................................................................22 5.4 Antimatter in the universe................................................................23 5.5 Validation of the Spacetime Model .................................................24


VI

6. Nucleons

6.1 Proton...............................................................................................25 6.2 Neutron.............................................................................................26 6.3 Confirmation by experimentation ....................................................26 6.4 Direct proton creation ......................................................................27 6.5 Proton synthesis ...............................................................................29 6.6 Asymptotic freedom.........................................................................29 6.7 Hydrogen atom (proposal) ...............................................................30 6.8 Equality of charge of the proton.......................................................30 6.9 Antineutron ......................................................................................31

7. Interactions 7.1 Guiding principles............................................................................33 7.2 Formulation (proposal) ....................................................................35

8. The Standard Model 8.1 Basic particles ..................................................................................37 8.2 Neutrinos..........................................................................................37 8.3 Other particles ..................................................................................39 Complements......................................................................................I - IV









Part 4

Electromagnetism


II

Patent Rights


238268, 238633, 244221, 05 13355-2 895 559, 248427, 258796, 261255, 268327, 297706, 297751, 297811, 297928, 298079, 298080, 329638, 332647, 335152, 335153, 339797.







III

Before reading… To fully understand this part, the reader must be familiar with the deductions and results developed in Parts 1, 2 and 3. These results are summarized below:


The same phenomenon applies to spacetime. Contrary to generally accepted ideas, it is not mass which deforms spacetime, but volume.

Mass (Part 1) In our world, mass and volume seem to be two different quantities because in atoms, the mass is not proportional to the volume. So, we have a large range of atoms with different masses and volumes. However, at the particle level, mass = volume.

In reality, we have two classes of volumes:

! Closed volumes (A): These volumes make a displacement of spacetime. It is this spacetime curvature, which produces the mass effect. Nucleons and electrons are examples of closed volumes.



Gravity (Part 1) Two volumes inserted into spacetime curve it. Since spacetime is elastic, its curvature produces pressures on these two volumes. This tends to bring them closer to each other.

So, contrary to what we think:

Gravity is not an attractive force between masses but a pressure force exerted by spacetime on volumes.

A B


IV

Wave-Particle duality (Part 2) Since 1905, the wave-particle duality has been one of the greatest enigmas of physics. Indeed, nobody can explain this phenomenon, but there is one particular case where wave-particle duality becomes logical and rational. That is when waves and particles are of identical constitution. For example, a drop of water (corpuscle) and a water wave are of identical matter. Water has either a corpuscle behavior or a wave behavior. This explanation of wave-particle duality leads to an important deduction: when the particle is motionless, it remains in a corpuscular state, and when it is moving, it becomes a wave.



The "µDomains" (Part 3) It would seem that global spacetime of the universe is divided into quanta called "microdomains” which are nothing but electrons or positrons without charge. Therefore, µDomains could have a mass of 511 KeV but, like neutrinos, they can't be detected. The existence of µDomains is proven in several ways developed in Part 3. In particular, they fully explain, with consistency, the constitution of quarks and the location of antimatter in the Universe.

The "Distributed Charge" Model (Part 3) The explanation of wave-particle duality leads to an important deduction: electrons are not moving around the nucleus as a punctual particle but as a sort of "cloud of charge". Indeed, the charge of the electron is distributed into the µDomains surrounding the nucleus. Schrödinger's probability concept must be replaced by a more realistic concept called "Distributed Charge Model". The quantum mechanics formulas as Schrödinger Equation are not modified by this new approach, which is verified by experimentation.

The Spacetime Model - Part 4 - 1 - 1 - EM Radiations

1. EM Radiations

Paragraphs 1.1 to 1.7 of this chapter are identical to those of chapter 2 of Part 2 “Constitution of Matter”. These paragraphs have been duplicated only for teaching purposes. EM radiations are mathematically described with a high degree of accuracy, but no one is able to explain the constitution of photons and EM waves. To solve the mystery of EM waves, we will proceed by an indirect method. Initially, we will try to understand why "c", the velocity of light, is invariant. There is a good probability that the solution to this enigma will lead us to the constitution of EM waves.

1.1 History The nature of EM radiations has always been the "pet peeve" of physicists. To this day, this problem has not been solved. • Newton, during his time, thought that light was made of particles. • In the nineteenth century, physicists favoured the wave concept. EM waves were

propagated in aether, an unknown propagation medium. • In 1905, continuing the works of Max Planck (Nobel Prize - 1918), Albert Einstein (Nobel

Prize - 1921) built a particle theory of EM radiations. The concept of aether became obsolete since photons do not need any aether to be propagated. However, some problems, like Young's experimentations for example, were still not solved with the photon concept.

• Later, in 1922, Einstein returned to aether. He was confronted with the problem of duality since the photon is incompatible with the wave, and therefore with aether.

• In 1959, 39 years later, Louis de Broglie (Nobel Prize - 1929) proposed the idea that aether was made of neutrinos.

• Around 1980, physicists verified once more the constant speed of light with quasars, using embedded systems and telescopes in satellites.

These recent experiments show that the propagation of EM waves and the enigma of the constant speed of light are still not solved. The aether concept would help but no one is able to give an exact definition of it. Finally, since 1905, the enigma of the constitution of light has been so persistent it prompted Louis De Broglie to say: “Science will make a great step ahead the day that it can explain a simple ray of light”.


1.2 Nature of EM radiations One of the peculiarities of the EM wave is that it can be propagated in a vacuum. But in a vacuum there is nothing and the EM wave cannot exist in the absence of a propagation medium. The introduction of the photon partially solves this problem. Indeed, like any particle, the photon can move in a vacuum. However, if an EM radiation behaves like a particle in 90% of the cases, it also behaves like a wave in the remaining 10% of cases, as in Young's slits experimentation. The enigma thus remains unsolved for these cases. When a hard drive periodically makes one, two, three or more errors, it must be formatted. Of course, this leads to a waste of time, but there is no other solution. In quantum mechanics, errors or inconsistencies don't occur in ones, twos or threes, but in tens. In such a case, the only thing to do is to "format" quantum mechanics. The best approach is to start from scratch, ignoring the few laws of quantum mechanics that are inconsistent, but keeping experimentations in mind. Therefore, to understand the nature of EM radiations, we will not begin from 1905, when Einstein discovered the photon, but from 1916, after his discovery of general relativity. Indeed, if the key to the problem is spacetime, we must restart from general relativity. In this chapter, we will study the wave aspect of EM radiations. Important note: The particle aspect of EM radiations, namely photons, will be discussed in the following chapters.

1.3 Separation of media The problem of velocity additions suggests that we are in the presence of two distinct media:

1- “Apparent medium” This is the visible medium that carries out the experimentations, and from where the EM wave is emitted.

For example, in Fizeau Experimentation, this medium is water, and in Michelsons, it is the Earth's atmosphere moved by the Earth itself.

2- “Real medium” EM waves are propagated in a real medium. For example, this "Real Medium" could be De Broglie's "Neutrinos Sea". The "apparent medium" and the "real medium" are overlaid (fig. 1-1).


1.4 Properties of the "Real medium" The "real medium”, if it exists, must have at least the following two properties:

1- To be present everywhere Since EM waves are propagated everywhere, the "real medium” must also be present everywhere, in air, in water and even in a vacuum. Spacetime is an excellent candidate to be this "real medium” since it is present everywhere, even in a vacuum1. 2- To have propagation properties We know that any wave needs a propagation medium to move. Since spacetime is elastic and can be deformed, it is an excellent propagation medium.

Therefore, spacetime could be used without any problem as a support for EM waves. This being said, gravity and EM waves do not curve spacetime in the same manner. Please see Part 1 Mass and Gravity concerning these subjects.

1.5 Constant speed of light Let's imagine the emission of a beam, L, from a laser diode (fig. 1-2). The diode, A, is fixed on an "apparent medium" moving with the velocity "V". In fact, the laser beam L is not emitted from the apparent medium as this figure shows, but from the point 'A' located in this "real medium" which is spacetime of the universe. 1 Spacetime is not this unknown aether for which we are looking. Spacetime is spacetime. There is no other correct definition and spacetime cant be identified with aether. In order to avoid any confusion, we will use the term real medium instead of "aether.

"Apparent medium": Air, water, vacuum in which the experimentations are carried out

"Real medium" of propagation of the light Fig. 1-1

In this figure, points A and A', as well as the apparent and real media, are separated for teaching purposes but, obviously, they share the same place. Any apparent medium has, necessarily, a subjacent real medium that is associated with it. A’

A


Since light is propagated in the real medium, its speed depends only on the nature of this medium, and nothing else. In reality, the permittivity of free space ε0 is not a "vacuum permittivity" but rather a "spacetime permittivity", a physical constant that defines the spacetime propagation characteristics, as the "spacetime permeability" µ0. Fizeau, Michelson and other physicists thought that light is propagated in this apparent medium which is moving, water, air, vacuum etc, whereas, in fact, it is propagated in this real medium which is the "motionless" spacetime of the universe. Note 1 We should not have any confusion between the word “motionless” used in the context of the universe, which is correct, and the same word used in Special Relativity, which is not relevant. Note 2 The spacetime of the universe, sometimes called "global spacetime structure", is the one that was created about 13.9 billion years ago, and not the local spacetime of special relativity. So, in this document, the word "spacetime" will always refer to "global spacetime structure of the universe", as in Friedman-Robertson-Walker Definition. Note 3 There should not be any confusion between the apparent medium, from where the EM wave is emitted, and its propagation medium, the real medium, which is spacetime of the universe.

1.6 Case of two reference spaces Figures 1-3 and 1-4 show that the presence of a "real medium" does not affect the principles of Special Relativity.

"Apparent medium":Moving support holding the laser diode.

"Real medium": Motionless spacetime. Fig. 1-2

A

A'

L

L'


Fig. 1-3

A

B

Current Theory

A photon is emitted from A to B, or the converse, to synchronize the two reference spaces which are both moving. The points A and B belong to the apparent media. In this case, no one can explain why the speed of light is constant. Logically, the velocities should be added. Since this is not the case, this diagram must be revised (but not the experimentations!!!), despite the fact it has been used since 1905.

Photon

Light is not propagated in the apparent medium, which supports the sources of light A and B, but in the real medium, which is global spacetime of the universe. EM radiations do not consist of photons but of EM waves. As a result, the constant speed of light is easily explainable. The velocity of light is a function of the real medium characteristics, i.e. spacetime permittivity ε0, and spacetime permeability µ0. Thus, the speed of light is always 300 000 km/s, whatever the velocity of the reference space, or the apparent medium, from where the light is emitted.

Real medium: spacetime of the universe

B

B'

A

A'

Fig. 1-4

Proposed Theory

EM wave


Fig 1-5

Spacetime

Charged particle

1.7 Conclusions Therefore, although it amounts to the same thing, it would be more accurate to write:

“The speed of light is 300 000 km/s in spacetime”

rather than:

“The speed of light is 300 000 km/s in a vacuum”

Note: Under certain conditions, EM waves may move at a speed different than 300 000 km/s. For example, using Bose Einstein condensates made up with sodium atoms at -273.15°, Lene Vestergaard Hau, from Harvard University, USA, slowed down EM waves to 17 m/s. In the same way, EPR (paragraph 3.12) also is an exception to the theory. The Spacetime Model partially covers these exceptions, particularly in Part 1 "Mass and Gravity".

1.8 Application 1: Displacement of charged particles By no means, can a moving, charged particle emit other particles called "photons". In the same way, a stone falling into water cannot emit tiny stones in all directions. The photon concept (chapter 3), from this point of view, is nonsense. Reality is much simpler. With the image of a stone falling into the water, the displacement of a particle produces movements in spacetime (fig. 1-5). From a mathematical point of view, these spacetime perturbations are "EM waves" but have all the characteristics of photons.

• EM waves are emitted from an apparent medium but are propagated by the real medium, which is global spacetime of the universe.

• In this real medium, the speed of light is 300 000 km/s. Its invariant velocity is only a function of the permittivity of spacetime ε0 and of the permeability of spacetime µ0

• EM waves are a succession of spacetime vibrations.


1.9 Application 2: The ∆∆∆∆q/∆∆∆∆t As we know, a motionless stone in water doesn't produce water movements. A stone begins to make eddies only when it moves. We have the same phenomenon in spacetime; a motionless electron doesn't create any perturbation, or wave. Therefore, we have a perfect match between this common phenomenon on Earth and electromagnetism (∆∆∆∆q/∆∆∆∆t). This simple example clearly shows that the photon concept, despite the fact it has been used since 1905, is inconsistent. Moreover, this phenomenon is in perfect accordance with the third principle of duality (see chapter 1 of the document Constitution of Matter).

1.10 Application 3: Changes in orbitals In the same way, there is no emission of photons when an electron moves from a higher to a lower orbital (fig. 1-6). This point of view is also scientific nonsense. The explanation of the EM radiation emitted during a change of orbital follows the same principle as the precedent. The passage of the electron from one orbital to another of less energy creates movements in spacetime, like whirpools or eddies in water. These movements are EM waves or, to be more precise, "quantified EM waves" (see the following chapters). Note: In reality, contrary to a preconceived idea, the electron does not move continuously on the orbital. Therefore, this diagram is not exact. Part 3, “Quarks and Antimatter”, covers this subject.

e-EM wave

Fig. 1-6

The Spacetime Model - Part 4 - 9 - 2 - Electromagnetism

2 Electromagnetism

Everyone acknowledges the EM force but no one can clearly explain how it works. This chapter examines the electromagnetism force in detail and solves this enigma.

2.1 The electron The volume of the electron is measured with remarkable accuracy: 510.998918 KeV. Therefore, its borders are very precise and clearly defined. Indeed, the electron and positron are not those particles that were described in Part 2 Constitution of Matter, as figure 2-1A shows. They are, rather, particles illustrated in figure 2-1B. Part 3 Quarks and Antimatter demonstrates that electrons and positrons are charged µDomains whose borders make a volume, or mass effect, of 510.998918 KeV (see the introduction in page 3 of this part). Since these borders are very "clean", the propagation of the charge of the electron, i.e. spacetime density (see Part 2 Constitution of Matter), over its boundary is an enigma. How can the EM field exceed the electron's borders? The solution is very simple. µDomains, defined in Part 3, have a homogenous spacetime density that makes their charge neutral. Under an external influence, like near a charge, this homogeneity is disturbed.

Fig. 2-1

A B

e+ e- e+ e-


The electric field creates a pressure of spacetime on one side of the µDomain, and a depression on its opposite side. Thus, the electric field can be gradually propagated, step-by-step, inside the µDomain (fig. 2-2). Each µDomain acts like an electric dipole.

2.2 1D polarization of µDomains Let's use polar co-ordinates. The electric polarization seen in the preceding paragraph is a function of the radius, r, which has only one dimension (1D). At a distance r from the center, all µDomains are electrically polarized with the same intensity, regardless of the ϕ and θ angles. This situation is normal since we are in a spherical symmetry. Figure 2-3 represents, on the left, a 3D view of a static electron and six µDomains. On the right is a cross-section of the left view. If the electron is fully static it produces only an electric field, which is this one-dimensional polarization. As we know, the magnetic field does not exist.

The electric field is a one-dimensional polarization of µDomains, which is only a function of the "r" radius

Fig. 2-2

+ + + + + + - - - - - -

+ + + + + +

+ + + + + +

- - - - - -

- - - - - -

Electron

The representation of this figure is only for teaching purposes. The µDomains and the electron have the same volume: 511 KeV., and not the different volumes represented in this figure.

µDomains


2.3 3D polarization of µDomains We know that:

! Electromagnetism appears only if the charged particle is moving, ! The electric field and the magnetic field are two different effects of a common

phenomenon. James Clerk Maxwell demonstrated this in 1872.

These two remarks lead to the following deduction. The radial co-ordinate is already used by the electric field. We can, therefore, deduce that the magnetic field uses one or both of the remaining co-ordinates, angles θ or/and ϕ. This point of view is exactly what the experimentation proves. Indeed, to describe magnetism, we need vectors perpendicular to each other, whereas only one vector is necessary to define the electric field. We don't know exactly the shape of the magnetic polarization of the µDomains. We may suppose that it is in 3D, but a 2D polarization must not be excluded. The only thing of which we are sure is that the magnetic field is propagated inside µDomains, like with the electric field, but with different directions of polarization.

2.4 Principle of magnetism Why does this polarization appear only in this situation, when the electron is moving? The response to this question is found in the third principle of wave-particle duality: “When the particle is moving, it becomes a wave” (see Part 2 Chapter 1).

Fig. 2-3

- - -- - -

r

r

- - -+++

- - -+++

- - -+++

- - -+++

- - -+++

- - -+++

r

µDomains

Electron


Indeed, when the electron is moving, its shape changes from a corpuscular state to a wave. We know that the magnetic field doesn't exist when the electron is motionless. In this case, the field is only a function of the radius "r", as seen in the preceding paragraph. When the electron is moving, it becomes a wave. Its spherical symmetry disappears. Therefore, the field can't be expressed with only one variable, the "r" radius. Additional variables, angles θ or/and ϕ, are necessary to describe the field. Figures 2-4 A and B show the difference between a static and dynamic electron. We must only keep in mind that when a charged particle is moving, the corpuscular shape disappears and the particle becomes a wave. ! Static electron (on the left, fig. 2-4 A)

When the electron is motionless it is a particle with a spherical symmetry. The electric field is propagated in µDomains, which are polarized in only one direction: the "r" radius (1D). In other words, at a distance "r" from the particle, each µDomain is polarized in the same manner. The magnetic field doesn't exist

! Dynamic electron (on the right, fig. 2-4 B) When the electron is moving it is no longer that particle with a spherical symmetry, but becomes a wave. Each µDomain is subject to many polarizations produced by the different parts of the wave. For example, point "x" receives three different fields, each having different intensities. An additional 2D polarization is thus added to the previous 1D one. The result is that all µDomains are polarized in 2D or 3D (r, ϕ and θ) instead of 1D (r only).

In other words, magnetism does not exist as a fundamental force. It is the Coulomb Force, nothing more. The magnetic field is a sort of "lateral" Coulomb Field. The orientation of the µDomains polarization produces a new phenomenon called "magnetism", but we must keep in mind that magnetism is nothing but a Coulomb force in a different direction.

r

Fig. 2-4

r r

A B

Dynamic electron (wave)

Static electron (motionless particle)

x


We must also note that the particle, when it is motionless, has an electric field (1D), which acts like a monopole since it is a punctual object. On the other hand, the magnetic field (2D/3D) requires dipoles (the wave) to create it. So, the magnetic monopole can't exist. This is exactly what is proven by experimentation. Lastly, it is also possible to have a magnetic component without an electric field. This is the case, for example, of permanent magnets. It is only a matter of the polarization of µDomains1.

2.5 The spin (proposal) Since its discovery by Pauli in 1924, the spin remains a true mystery. No one knows exactly what the spin is. The Spacetime Model doesnt share the complexity of quantum mechanics. The universe is very simple by necessity and needs only 4 dimensions, no more. From this point of view, we can deduce that the spin is related either to the charge, like electromagnetism, or to the mass (volume). It seems that the spin is related to electromagnetism rather than to the mass. Since the spin is not proportional to the charge, it could be a simple ratio, like h/l on figure 2-5, in relation to the wave or, more precisely, to the magnetic component of the wave. The following example (fig. 2-5), which is only a suggestion, shows the idea proposed. The two particles, an electron and a neutrino, go towards the reader. On the left (A), the two particles are motionless, i.e. in their corpuscular form. The spin doesnt exist. On the right (B), these two particles are moving as waves producing the spin effect.

1 The current document cant cover, completely, so vast a subject.

Fig. 2-5

A

Electron

Dynamic particle (wave)

Neutrino

h

h

l

l

Static particle (corpuscle) B

Spin of electron = h/l

Spin of neutrino = h/l


If this point of view is correct, the spin would not be a value attached to any particle but rather a value attached to the mode of propagation of the waves. More precisely, the spin would be 0 with an EM wave, and a multiple of 1/2 with matter waves. This point of view means also that any motionless particle can't have a spin. In other words, the theory described in this document predicts that the spin exists only when the particle is moving, i.e. only when the particle is in its waveform. However, if the particle is moving at low speed, its form is between a corpuscle and a wave. In such a case, the spin could have a different value, for example 1/4 instead of 1/2 (this suggestion must be considered with great care). This approach may be illustrated by the following examples (fig. 2-6):

Cases A and B: Matter waves. The spin is a multiple of 1/2 in absolute value.

Case C: EM waves. The spin of a half-period cancels each other.

Case D: In some cases, we can have a set of half-periods. This is the case when an atom is moving. The atom is moving as a complex set of waves (quarks, electrons) and their individual spins can or cant be mutually cancelled. This depends on the overlap of the individual waves.

Fig. 2-6

A

t

S

Spin = |1/2|t

S (Spacetime density)

Spin = |1/2|

t

S

Spin = 0 t

S

Spin = ?

B

C D


2.6 Rule of addition of spins The rule of addition of spins has been devised taking into account the experimentations conducted in 1930's. This theory is applied with success in the majority of cases (molecules, atoms), but its application to all components of physics without any reservation is highly debatable for the following reasons:

1/ It is not possible to create a reliable theory concerning the spin since the real nature of this parameter is unknown1.

2/ The rule of addition of spins applies in most cases, but this does not mean that it applies in all cases. Any extrapolation toward the quarks or other particles may produce debatable results since our knowledge of the nature of these components, as our knowledge of the spin, is very poor. More precisely, we have an excellent knowledge of the particles behavior from a mathematical point of view but we are still not able to answer the fundamental questions concerning the basic phenomena: What is the charge? mass? gravity? spin?....

3/ Moreover, the spin seems to be a function of the overlap of waves. As we know, molecules and atoms are much larger than protons or quarks. When these elements are moving, the overlap of their waves is different. Therefore, we may get erroneous results when extrapolating the rule of addition of spin toward elementary particles since we don't know exactly the wave shape of each particle, which is concerned.

To summarize, molecules and atoms are well known, but

1/ the real nature of the spin is unknown, 2/ the overlap of waves is unknown, 3/ the wave of an atom is much larger than the wave of a quark 4/ the basic phenomenon of electrostatic is unknown, 5/ the basic phenomenon of magnetism is unknown, 6/ charge is unknown, 7/ mass is unknown, 8/ gravity is unknown, 9/ the nature of electrons, quarks and other particles is unknown 10/ the mass of quarks is measured with poor precision etc

Under these conditions, is it reasonable to assume that the rule of addition of spins, which is 100% correct with molecules, atoms, and some particles, can be extrapolated to all particles of physics without reservation? Of course, not. This extrapolation is hazardous.

For all these reasons, the violation of the rule of addition of spins can't be retained as a valid objection to the proposed theory, the “Spacetime Model”.

1 Saying "the spin is a quantum value" doesn't mean anything. Indeed, this definition the spin is a quantum value doesn't explain the real nature of the spin.

The Spacetime Model - Part 4 - 17 - 3 - The Photon

3 The Photon

In chapter 1, we have considered the wave-like behavior of EM radiations. Here, we study its particle-like behavior, i.e. the photon.

3.1 Justification of the photon The following experimentations seem to confirm the existence of the photon:

• The Planck Quantum is a physical reality and not just a mathematical concept. This unit absolutely must be preserved.

• Experimentations (photoelectric effect) also tend to prove that the photon exists. The interpretation of these experimentations is, however, debatable1.

• The EM wave decrease. This decrease in 1/r² makes it impossible for a wave to exist far from its origin. Only the photon concept would resolve this paradox. This chapter contains a new explanation of this phenomenon.

• Vacuum propagation. This enigma is not relevant since EM waves can be propagated in spacetime, and spacetime is present in a vacuum. This problem was solved in chapter 1.

1 In 1905, when Einstein explained the PE effect using the Planck Quantum, the atom's internal configuration was unknown. Rutherford thought that the atom was like an "English pudding". In 1905, physicists didn't know that the atom had a nucleus. Einstein thought that the poor efficiency of the PE effect was in relation to the probability that the photon had to meet an electron (in 1905, electron distribution was described as being like raisins in a pudding). Later on, physicists demonstrated that the electron was: 1/ infinitely smaller than the nucleus and, 2/ a huge distance from it, proportionately. This means that the collision probability between a photon, if it exists, and an electron is practically null. However, and paradoxically, the yield was increased to attain about 98% today. This paradox remains a mystery. The cross section calculations and other theories about the photon are highly debatable, not from their mathematical point of view, but, in their interpretation, if we regard the photon as a particle. On the other hand, as every physicist knows, several different mathematical theories may be devised to explain a given phenomenon. For example, we know three different theories which are mathematically verified, to explain mass and gravity: the Higgs boson, Superstrings (E. Wirren) and the Spacetime Model (Part 1). At least two of these three theories are wrong, despite the fact that they are all mathematrically verified. It means that any theory, which is not fully explained with logic and good sense, must be considered with great care. This is the case of theories concerning the photon and the PE yield, because their explanation is not consistent and remains a true mystery. See paragraphe 3.2.


3.2 Inconsistencies of the photon • Its velocity: The photons velocity is 300 000 km/s, no more, no less. This is illogical

because if the photon is a particle, it may travel at any speed. What would we think of a vehicle moving at only one speed, 100 km/h, no more, no less?

• Its impossibility to stop: Why cant the photon stop? In the preceding example, what would we think of a vehicle (a particle), that can't stop?

• It’s massless: If the photon is a particle, how does one explain its lack of mass?

• Its acceleration: If the photon is emitted from an electron moving at 280.000 km/s, how can it immediately accelerate to 300 000 km/s 1? What is this unknown force that gives the photon an additional speed of 20 000 km/s?

• The causal principle: The photon concept continuously violates this principle. Some experimentation needs a particle-like behavior, and other a wave-like behavior. It is obvious that the photon, once emitted, has not the ability to predict its future. It does not know its own destiny. More precisely, it does not know if the experimenter needs a particle-like behavior for his experimentation, or a wave-like behavior. Since the two behaviors do not simultaneously exist, this prediction causes a real scientific problem.

• Its constitution: What is the constitution of the photon? No one knows

• Displacement of a charged particle (paragraph 1.7): How can a charged particle that is moving emit other particles called "photons"? It is like a stone falling into water emitting tiny stones This concept is disconcerting.

• Orbital change of an electron (paragraph 1.9): In the same way, no one can explain how an electron, moving from one orbital to another, can emit tiny particles called "photons".

• EPR: In this experimentation, it would be necessary for the photon to have a kind of thought transference with another photon at a distance of several meters

• Young Slits: Here too, the photon poses a serious problem of logic.

These 10 inconsistencies - and probably more - mean that the photon concept, despite the fact it has been used since 1905, must be seriously revised.

3.3 Decrease in 1/r ² We pointed out that EM waves are propagated gradually in µDomains. At a distance "r" from the emission source, it arrives at a moment when the charge contained in a µDomain becomes too weak to be propagated in the next adjacent µDomain. This limit is, in fact, a quantum. But this is not exceptional since all objects are quantified, in one way or another. In accordance with Max Plank, the quantum is a necessity.

1 We could say that the speed may increase in order to preserve the momentum but the interaction remains a true mystery, not from a mathematical point of view but if we try to understand the phenomenon using logic and good sense. The main problem comes from the mass of the photon, which is null.


The charge, which passes from one µDomain to another, must be higher than this quantum. Under this condition, how will an EM wave react when the charge transmitted in the µDomains approaches this quantum? There are only two possibilities:

• The charge disappears completely. The EM wave dies. • The charge remains grouped. In this case, the EM wave ceases to decrease.

The first possibility is not credible because, in Nature, nothing totally disappears. Therefore, the second possibility is more reasonable.

3.4 The "quantified wave" The various steps of the wave during its travel, from its creation to a distance away, are represented on figure 3-1.

• Step 1: The wave is created in a 360° space (grey circle). Note that the angle is not

necessarily 360° and may have any other value. • Step 2: At some distance from its source, the decrease in 1/r² of the EM wave reaches

its quantum. The spacetime density of the wave is too weak to continue to decrease while propagating from µDomains to µDomains. The wave has only one solution: to break at an unspecified place to remain grouped 1.

• Step 3: The distance increases, and the arc of the circle decreases proportionally. • Step 4: The wave is now very far away from its source and its curvature becomes

practically a segment or, in quantum mechanics terms, a "wave pack". The EM wave always keeps its wave behavior while remaining grouped. It can thus travel billions of light-years as a photon would, but as a small "piece of wave".

This is what we call a quantified wave.

1 This phenomenon may be better understood by replacing the EM wave with a water wave. The quantum of water is the H2O molecule. It is obvious that a water wave can't be smaller than a H2O molecule. When the H2O quantum is reached, the wave doesn't continue decreasing but breaks. However, please note that this simple comparison is done for teaching purpose only. A quantified wave cant be identified to a H2O molecule.

1 3 4

Fig. 3-1

2


During its travel, the EM radiation keeps its waveform.

It can, nevertheless, be quantified if the distance requires it.

So, when we see galaxies, our eyes do not perceive a photon but a "quantified wave". During all its travel, this wave remains grouped1. Let's now consider the different phases of a quantified wave.

3.5 The emission EM radiations are always spacetime movements, or EM waves. The photon, as a particle, doesn't exist.

3.6 The travel Once emitted, an EM radiation keeps its waveform. Beyond a certain distance, since the charge can't go under the quantum level, there is a possibility that an "ordinary wave" become a "quantified wave". Figure 3-2 shows an EM wave that is propagated gradually in µDomains. The charge is q at the source level, and is divided by 3, then by 5. In figure 3-2, the quantum q/5 is reached at Time t + ∆t2. The EM wave doesn't continue decreasing over time t + ∆t2.

1 On earth, we have a similar phenomenon: capillarity.

Fig. 3-2

x, t

Time t

t + ∆t1

t + ∆t2 t + ∆t3 t + ∆t4

q

q/3

q/5 q/5 q/5

Quantum = q/5


The interaction takes place with a kind of "virtual photon", which is, in reality, an EM wave. ! This wave may be quantified if the distance requires it. ! This wave is absorbed at the place of measurement.

3.7 The reception When a part of the wave inside a µDomain meets an element, atom or something else, an interaction may take place. The µDomain is emptied of its charge. Gradually, it empties all other adjacent µDomains forming the wave (fig. 3-3).

• Phase 1: The EM wave propagates normally.

• Phase 2: It meets an element that absorbs its energy. The µDomain in contact is emptied. This element is not necessarily in the center and can be anywhere at the front of the wave.

• Phases 3 and 4: The EM wave continues to be absorbed by the element. The µDomains are gradually emptied, step-by-step, µDomain-by-µDomain.

• Phase 5: The EM wave is almost completely absorbed by the element of interaction. An identical process exists on Earth (fig. 3-4). The EM wave is replaced by a trickle of water. The particle, which absorbs the wave energy, is replaced by a blotting paper. The trickle of water is absorbed by the blotting paper at the place of interaction, or measurement. To summarize:

1

Fig. 3-3

2 34

5

Note: This figure is for teaching purposes only. µDomains are represented in a line, but they are grouped in "wave packets".


3.8 Validation of the proposed theory How can we prove that photons must be replaced by "quantified waves"?

We already have multiple proofs.

• The constant speed of light, 300 000 km/s, proves that we are in front of a wave and not of a corpuscle. If an object moves at one and only one speed, this object can't be a particle but a wave, and the speed of this wave is function of medium characteristics.

• Any particle has the ability to stop. Why doesnt the photon? It means that the so-called "photon" is not a corpuscle but a wave. Indeed, a wave never stops.

• Saying that the "mass" of the photon must be null is scientific nonsense. Only a wave has a null mass, not a particle.

• The displacement of a charged particle (∆q/∆t) can't emit tiny particles called "photons". This is nonsense. If this displacement produces waves, this enigma becomes consistent. Etc

3.9 The Experimenter Let's return to the example in chapter 1 of a small sailing boat in the middle of a swimming pool. The experimenter is assumed to be inside it. If the boat starts to pitch, the experimenter wouldn't know if his boat was hit by a stone (a particle) or by a wave of water (EM wave). Likewise, in quantum mechanics, the experimenter is unable to say if he measured a photon or an EM wave.

Trickle of water

Blotting paper

Fig. 3-4

Interaction

If we replace the word "photon" by "quantified wave", we solve all of these inconsistencies, and many more.


The simple fact of measuring the EM wave produces the disappearance of it, giving the illusion of having

measured a virtual "photon-like particle"

This phenomenon is quite simple to understand by returning to our blotting paper of fig. 3-4. The simple fact of putting this blotting paper anywhere on the trickle of water produces the disappearance of the water. The experimenter believes that, at the point "c" on the figure, he measures a photon but in reality, he measures a wave.

3.10 Young Slits Let's imagine a group of five EM waves (fig. 3-5). These waves pass by two slits. Two detectors, right (R) and left (L), count the number of "photons" passing by each slit. When a wave reaches an atom of a detector, the energy included in µDomains is emptied by a PE effect (or Compton Effect, or anything else). The µDomains are immediately emptied at the speed of 300 000 km/s. This speed is so high and the vacuum between atoms and particles is so huge that a wave can't activate two detectors at exactly the same time. In other words, a wave may reach the two detectors at approximately the same time but activates one, and only one at a time. A very short ∆t or fraction of pS is sufficient to make the difference. However, there is a very slight probability, nearly zero, that the two detectors are activated at the same time. In this case, it is logical to think that the energy of the incoming wave is split. For example, a 1 MeV wave may be detected as two waves of 500 KeV each, or 520 KeV -480 KeV. Examining the distribution of the measured waves with a coincidence system must highlight this phenomenon, which could be additional proof that we measure waves and not photons. However, please note that this prediction is not 100% certain. It is only a suggestion.

L RFig. 3-5


To better understand this principle, lets replace the five waves of fig. 3-5 by five trickles of water and the two detectors by two blotting papers (fig. 3-6). A trickle would be absorbed by the first blotting paper reached. It is obvious that when a trickle has been absorbed by one blotting paper there is no water left for the second blotting paper to absorb. The experimenter therefore thinks he is counting the number of photons. In reality, he is counting the number of waves randomly absorbed by each detector.

3.11 The Heisenberg Uncertainly Relation Everyone knows the formulation of the Heisenberg (Nobel Prize 1932) Relation but no one is able to explain it. In the framework of the proposed theory, its explanation becomes very simple and gives additional proof in favour of this new theory. Lets consider, for example, an electron. Quantum Mechanics: If the electron moves as a particle, it must pass through point A (fig. 3-7) and not points B or C. This would seem to be nonsense. However, this nonsense is a reality. Why? No one can explain with consistency this strange phenomenon. Proposed theory: The third principle of wave-particle duality (see Part 2 Constitution of Matter) states: “When the particle is moving, it becomes a wave”. Therefore, points A, B and C are all crossed by the electron-wave. We are facing the same phenomena as the Young Slits1 explained in the preceding paragraph. As in our example of blotting paper, the wave may be absorbed at point A or, with a less high probability, by points B or C.

1 Althought it amounts to the same thing, it would be wise to compare the Uncertainly Principle to the Davisson-Germer rather than to the Young Slits Experimentation.

Blotting papers (the two slits with two detectors)

Fig. 3-6

L R

Five trickles of water (five EM waves)

The L or R blotting paper absorbs waves randomly at these points


Note: With regard to the Uncertainly Relation, we may suppose that the shape of the wave packet depends on its speed. Taking into account experimentations and the Heisenberg Theory, the immediate deduction is that the wave becomes more conical as its energy increases (Gauss Curve for example).

3.12 EPR1 (proposal) A simplified diagram of the EPR is given in figure 3-8. In the EPR experiment, it is necessary to replace the photon concept with waves. Two waves, "A" and "B", are emitted with a perpendicular polarization of the one compared to the other. These waves are propagated in µDomains and are "catalysed" in x and y. If it has been decided to take the vertical wave "A" in point x, it will remain the horizontal wave "B" for point y, and the converse. Whatever the wave taken in x, it will always remain the complementary wave in y. If the two measuring instruments, x and y, are isolated by something to avoid interference such as a concrete or a metal wall, the wave still exists, even if it is not seen. The reason is quite simple: the EM wave is propagated in spacetime, and spacetime is present EVERYWHERE even inside a concrete or a metal wall However, it must be pointed out that, as a consequence of the curvature of spacetime (see Parts 1 and 2), the EM wave may be slowed down or absorbed by molecules of the wall.

1 The author is a physics hobbyist and has no access to reliable data concerning many EPR experimentations. Therefore, explanations given in this paragraph must be taken with great care.

Fig. 3-7

Quantum Mechanics

Electron

B A C ∆x ∆x

Proposed theory

Electron

B A C ∆x ∆x

? ?


From this point of view, the Spacetime Model predicts that the mystery of EPR disappears if the two points of measurement, at 180°, are located far from the point of emission. The reason is quite simple. In such a case, traditional EM waves become quantified EM waves. In other words, the mystery of EPR exists only if the EM waves are not quantified. This enigma no longer exists with quantified waves.

3.13 Conclusions The table on the following page draws a comparison between the photon and the quantified wave concepts. To summarize this chapter: 1 Most physicists agree this point of view

Wave A

Wave B

xy

Concrete wall

Fig. 3-8

What is the photon?

A mathematical object, like a vector1........ YES A reality, like a particle...............................NO


Problem Explanation

Replacing the photon by a quantified wave doesn't modify the Planck Quantum. This unit is perfectly logical and must continue to exist. This problem is solved by the "quantified wave" This question becomes meaningless since this problem has been solved in chapter 1. The fact that the photon can move at only one speed, c, is nonsense if it is considered as a particle. Indeed, a particle can move at any velocity. Since the photon doesn't exist as a physical reality, even though it may exist as a mathematical object like a vector, the question about its speed becomes meaningless. When an EM radiation is emitted from a particle moving at a speed of 280 000 km/s, it is a (quantified) EM wave which is emitted, not a photon. Knowing the origin of this additional 20 000 Km/S speed becomes meaningless. EM radiations are nothing but waves. Since a wave has no alternative about duality, i.e. a wave is a wave and not a photon, the choice between wave and particle is meaningless. The fact that the photon is interpreted as a mathematical object doesn't conflict with this principle. Since the photon doesn't exist, this question is meaningless. It is impossible to explain how an orbital change by an electron can emit photons. On the other hand, if this orbital change produces spacetime movements, EM waves, all becomes clear. It is impossible to explain how a charged particle, which is moving, can emit photons. On the other hand, a moving particle, which produces spacetime movements, is easy to understand. If the EM radiation is made of photons, the e+e- pair creation, as the e+e- annihilation, is a true mystery (Part 2 Constitution of Matter). Only an EM wave, quantified or not, can explain this enigma. This enigma is explained. See § 3-10 This enigma is explained. See § 3-11 This enigma is explained. See § 3-12

Planck Quantum Decreased in 1/r2

Propagation in a vacuum

Only one velocity, "c"

The photon acceleration

Causal principle Matter of photon Orbital change Displacement of a particle e+e- pairs creation and e+e- annihilation Young Slits Uncertainly Relation EPR

The Spacetime Model - Part 4 - 29 - 4 - Waves and Complements

4 Waves and Complements

This chapter gives additional explanations concerning waves, in the framework of the Spacetime Model, taking into account the equality Mass = Closed Volume developed in Part 1. This chapter is not fundamental and is included, primarily, for the benefit of non-physicists.

4.1 EM waves: Simplified explanation Here is a simple experiment explaining the EM wave emission produced by an orbital change in atoms. You can do it yourself in your bathtub. This example highlights that a change of orbital produces waves, not photons.

Open your hand beside your lengthened legs and wait until the water is still. Then, suddenly, close your hand. You will immediately feel a wave being propagated on your entire body.

Closing your hand produces a wave of water, which carries some energy. We have exactly the same phenomenon in spacetime. An orbital change of electron produces a movement in spacetime, which is an EM wave, not a photon.

4.2 EM waves: Detailed explanation A second example is given in figure 4-1. A perforated balloon is immersed into a container filled with water. The holes allow water to infiltrate the balloon. If its volume varies from V1 to V2, or the converse, a wave of water is produced. However, since the balloon is perforated, the quantity of water remains unchanged. The volume of water doesn't increase or decrease since these movements in water are bipolar (pressure + depression).


4.3 Matter waves: simplified explanation A balloon is immersed into a container filled with water (fig. 4-2 A). Using a pump “P”, a vacuum is made, instantaneously, inside the balloon (fig. 4-2 B).

The difference ∆V of the balloon volume produces a wave.

When the wave reaches the surface, it is transformed back into a volume of water ∆V identical to the decrease of the balloon's volume ∆V.

This experiment describes exactly how a mass, or a volume, can be transformed into a wave, also a volume, and may be transformed back into a mass, which is another volume, and so on.

t

Spacetime density

Fig. 4-1

EM wave

Positive and negative volumes can be recovered separately. We have the same phenomenon during an e+e- production from a gamma (see Part 2).

V2

V1

µDomains

When the balloon passes from V1 to V2, it yields its energy; it deflates. However, some energy is necessary to make it pass from V2 to V1. In both cases, the whole volume of water remains unchanged since the perforated balloon, like orbitals in atoms, is an open volume.

Mass ↔ waves Volume (particle) ↔ volume (wave) Illogical explanation Easy to understand, consistent


4.4 Matter waves: detailed explanation The figures 4-3 and 4-4 show negative and positive matter waves. That which is called a matter-wave is a moving particle having its charge, or spacetime density, distributed in several µDomains. When a "matter-wave" is moving, each µDomain transfers to the other ones some quantity of additional spacetime, in positive or negative charges. These µDomains become charged during the period of the wave and act like a "partial" electron or positron.

t

S (Spacetime density)

Fig. 4-3

Particle

Negative matter wave

µDomains

Fig. 4-2

P P

∆V

∆VA B

Note: Remember that ∆V = ∆m (see Part 1)


4.5 Differences The difference between "EM waves" and "matter waves" is only a question of charge. Let's examine the following figure 4-5. ! EM waves: The charge is bipolar, alternatively positive and negative. The charge

moves gradually inside the µDomains. As a result, EM waves produce some variations of the internal polarization of the µDomains. The charge of a µDomain, which is neutral, remains neutral for the full period. In this case, the µDomain doesn't

Fig. 4-4

t

S (Spacetime

Particle

µDomains

Positive matter wave

Fig. 4-5

EM waves Matter waves

Neutral µDomains

+ + + + + + + + + + + + + + + + + +

- - - - - -

+ + + + + + + + + + + + + + + + + +

- - - - - -

+ + + + + + + + + + + + + + + + + +

- - - - - -


get mass since it has no additional charge (+ or -). The velocity of the propagation is a function only of the permittivity ε0 and permeability µ0 of spacetime.

! Matter waves: Each µDomain receives, during a short period of time, an additional

charge. Since the charge is transmitted from one µDomain to another, each involved µDomain becomes charged and gets mass. The example of figure 4-5 shows a positive charge like a "positron wave".

4.6 E = hv To understand this formula with µDomains, according to the equality Mass = Volume, let us consider again the first experiment, which you can carry out yourself.

While having your legs lengthened in your bathtub, quickly close your hand. You will note that the wave is more or less pronounced according to the velocity of the movement of your hand.

This reaction is exactly the same as the quantum phenomenon described by: E=hv or E=h/T. The shorter the period of time, or the more quickly your hand is closed, the greater the energy produced.

4.7 e+e- annihilation This phenomenon is an enigma with regard to its comprehension: “how can a mass (e+e-) be transformed into two gammas?”. We have already explained the e+e- annihilation in Part 2 Constitution of Matter. We give below another explanation (fig. 4-6), taking into account the equality Mass = Volume. Let's consider that the electron and positron are both motionless, that is to say, the magnetic component of the EM field does not exist.

• When an electron meets a positron, the excess spacetime in one particle moves inside

the other. • The annihilation of the two charges is assimilated to a double ∆q/∆t. Indeed, the

charge of the positron passes from +1 to 0, and that of the electron from - 1 to 0. • The annihilated electron and positron become two ordinary µDomains. • This annihilation produces two movements in spacetime, or EM waves. • These movements, resulting from the double ∆q/∆t, are propagated gradually through

adjacent µDomains. • The EM radiation will not be propagated like a photon, but like an EM wave,

quantified, if necessary, and called a "gamma". • And finally, as seen in chapter 6 of Part 2, if this gamma passes near a nucleus, it may

be split into a negative and a positive part, if its energy allows.


4.8 Mass and energy Before explaining the E=mc² enigma, it is useful to reconsider the mass - energy equivalence. It is often stated that Mass = Energy. This is not exact and there is a subtlety to this equation. The dimensional quantity of the mass is [M] while that of energy is [ML²/T²]. These two quantities are different. The E=mc² formula is homogeneous because it has a dimensional quantity, c². This constant has the dimension [L²/T²]. In other words, a mass, or a volume, can produce energy, certainly, but never "Matter = Energy". Saying "Matter = Energy" is scientific nonsense since mass and energy are two different dimensional quantities.

4.9 E = mc² This formula is fully verified using mathematics and experimentation. However, no one is able to explain it using logic and good sense. The solution is quite simple within the Spacetime Model. Let us take again the figure 4-2 which, slightly modified, becomes the figure 4-9.

The overall process is as follows. In parenthesis and italics, the equivalent in quantum mechanics is given: ! The balloon (the particle) is filled with air. It doesn't have any energy.

! The balloon deflates during a ∆t time ("Matter" disappears, like in the e+e- annihilation). This decrease in volume produces waves, which are ∆V variations.

e-

e+

Neutral µDomains

Fig. 4-6

−∆q/2 −∆q/2

+∆q/2+∆q/2

Propagation is gradually done in µDomains (EM wave)

Charged µDomains (electron and positron)

Note: For teaching purposes, only 2 µDomains have been represented on each side. In reality, we have a wave packet.

Gamma 511 keV

Gamma 511 keV


These waves are moving in water (in spacetime) and carry some energy, which is a function of ∆t, at the time of the balloons deflation (in the same way, the wave energy is E=h/T).

! When the waves reach the surface, they are converted back to a volume (a gamma may produce e+e- pairs).

It is important to note that energy appears ONLY in phase 2, when the volume is in its wave state. When the volume is in a particle state, as in phases 1 and 3, energy doesn't exist or, more exactly, we have a sort of "potential energy".

This energy comes from the speed "c" of gammas, which are the result of decays. Only a movement can produce energy. A motionless particle only has a "potential energy". In other words, the E=mc² formula simply means that energy appears only when the volume of the particle becomes waves, or gammas (fig. 4-9, phase 2).

Finally, the E=mc² formula is very simple to understand (fig. 4-10) if we keep in mind these three points:

! There is a relationship between mass and volume (see Part 1). ! The particle may become a wave and the converse (see Part 2). Both, particles and

waves, are made up of spacetime. ! Energy is not embedded inside the particle as we think. A particle is an area of

spacetime, nothing more. Energy appears when the particle is destroyed and when this area of spacetime becomes a wave, as in the e+e- annihilation. Energy is carried out by these EM waves, which move at the speed c.

Thus, although it amounts to the same thing, it would be more accurate to write:

"The volume (mass) of the particle is converted into another volume, the EM wave, which moves at the speed c, and gets energy due to its speed"

rather than: "The mass is converted into energy".

Fig. 4-9

∆V

Pump Pump Pump

−∆V

1 2 3

Waves


NOTE: When the particle disappears, as in the e+e- annihilation, it becomes an EM wave (gamma). This is why the term c² is present in E=mc². In this formula, c is not related to the particle itself but comes from the speed of the light. This speed, c, which appears after annihilation, must not be confused with the speed of the particle, v, if the latter is moving. Please also note that this explanation doesnt modify calculations already in place.

Since we have only volumes, the proposed explanation is perfectly homogenous.

How can a mass be converted into energy ???No one is able to explain this formula.

E = mc²

Fig. 4-10

When a particle (a spacetime volume) disappears, it becomes an EM wave (another spacetime volume). Whatever the interaction is, a volume remains a volume. Since the speed of gammas is "c", the original volume (the particle) gets some energy as it attains speed “c” (E=mc²), becoming an EM wave. We must note also that replacing E=mc² by E=kvc² (when m=kv) gives a homogenous formula since ALL is volume.

Current theory (Special relativity)

Suggested explanation (Special relativity and Spacetime Model)

k = Mass per volume unit v = volume of the particle E = kvc²

Wave (volume)

Particle (volume)

The gamma carries out energy: E = hv

A motionless particle has a “potential” energy


I

Complements

Predictions ! The spin disappears when the particle is motionless. The spin is not a "quantum value"

attached to a particle but a value attached to the mode of propagation of waves: 0 = no spin, 1/2 = matter wave, 1 = EM wave (Chapter 2). However, it is possible that the spin of a particle may have a different value when it is moving at very low speed.

! The magnetic monopole doesn't exist (Paragraph 2.4). ! In the Young Slits experiment, we have a very slight probability that the energy of the

incoming wave (the "photon") might be split, depending on the amount of energy. In such a case, each detector measures a part of the wave, close to 50-50%, for example 51% and 49%. This experiment must be done with a coincidence system (paragraph 3.10).

! The EPR enigma disappears at huge distances (Paragraph 3.12) Partitioning the theory The five parts of the Spacetime Model can be downloaded at the following URL address:





…/…



II





Quarks This part demonstrates that we need two positrons to make three u quarks. A u quark with an electron becomes a d quark (please note that the rule of addition of fermions is covered in Part 4). This deduction, from the wave-particle duality and spacetime, has been extended to all particles. Finally, u quarks, d quarks, antiquarks, muons, antimuons, taus, mesons, baryons etc... can be made with only two basic particles: electrons and positrons. .../...


…/…


Each atom has a particular proportion of open and closed volume. This is why mass and volume seem to be two different quantities but this is an illusion. At the particle level, more exactly at the electron and positron level, mass equals volume. Composite particles, like mesons, are combinations of other classes of volumes. Gravity Contrary to a preconceived idea, spacetime is not curved by mass but by closed volume. This phenomenon is the same as when a ball is immersed into water: It is the volume of the ball, and not its mass, which produces the displacement of water.


III

.../...




The Universe A suggestion regarding the creation of the universe is proposed. In reality, the Big-Bang Theory does not explain the “electron mystery" and this enigma is discussed. This Part offers two suggestions, much more credible than the “Big-Bang”, regarding the creation of the universe.



IV


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or writing to:




V

Table of content

Introduction.........................................................................................I – IV

1. EM Radiations 1.1 History..............................................................................................1 1.2 Nature of EM radiations...................................................................2 1.3 Separation of media ........................................................................2 1.4 Property of the “Real Medium” ......................................................3 1.5 Constant speed of light ....................................................................4 1.6 Case of two reference spaces ...........................................................5 1.7 Conclusions......................................................................................6 1.8 Application: Displacement of charged particles ..............................6 1.9 Application: ∆q/∆t ...........................................................................7 1.10 Application: Changes in orbitals......................................................7

2. Electromagnetism 2.1 The electron......................................................................................9 2.2 1D polarization of µDomains...........................................................10 2.3 3D polarization of µDomains...........................................................11 2.4 Principle of magnetism ...................................................................11 2.5 The spin (proposal) .........................................................................13 2.6 Rule of addition of spins ..................................................................15

3. The Photon 3.1 Justification of the photon ...............................................................17 3.2 Inconsistencies of the photon ...........................................................18 3.3 Deacrease in 1/r²...............................................................................18 3.4 The “quantified wave” ....................................................................19 3.5 The emission ....................................................................................20 3.6 The travel .........................................................................................20 3.7 The reception....................................................................................21 3.8 Validation of the proposed theory....................................................22 3.9 The Experimenter.............................................................................22 3.10 Young Slits.......................................................................................23 3.11 The Heisenberg Uncertainly Relation ..............................................24 3.12 EPR (proposal).................................................................................25 3.13 Conclusions......................................................................................26


VI

4. Waves and Complements

4.1 EM waves: Simplified explanation..................................................29 4.2 EM waves: Detailed explanation .....................................................29 4.3 Matter waves: Simplified explanation .............................................30 4.4 Matter waves: Detailed explanation.................................................31 4.5 Differences .......................................................................................32 4.6 E = hv ...............................................................................................33 4.7 e+e- annihilation ..............................................................................33 4.8 Mass and energy...............................................................................34 4.9 E = mc².............................................................................................34 Complements.....................................................................................I - IV









Part 5

Forces, the Universe


II

Patent Rights


238268, 238633, 244221, 05 13355-2 895 559, 248427, 258796, 261255, 268327, 297706, 297751, 297811, 297928, 298079, 298080, 329638, 332647, 335152, 335153, 339797.







III

Before reading… To fully understand this part, the reader must be familiar with the deductions and results developed in Parts 1 to 4. These results are summarized below:


The same phenomenon applies to spacetime. Contrary to generally accepted ideas, it is not mass which deforms spacetime, but volume.

Mass = Volume? (Part 1) In our world, mass and volume seem to be two different quantities because in atoms, the mass is not proportional to the volume. So, we have a large range of atoms with different masses and volumes. However, at the particle level, mass = volume (with some reservations explained in Part 1).

In reality, we have two classes of volumes:

! Closed volumes (A): These volumes make a displacement of spacetime. It is this spacetime curvature, which produces the mass effect. Nucleons and electrons are examples of closed volumes.



What is Gravity? (Part 1) Two volumes inserted into spacetime curve it. Since spacetime is elastic, its curvature produces pressures on these two volumes. This tends to bring them closer to each other.

So, contrary to what we think:

Gravity is not an attractive force between masses but a pressure force exerted by spacetime on volumes.

A B


IV

Wave-Particle duality (Part 2) Since 1905, the wave-particle duality has been one of the greatest enigmas of physics. Indeed, nobody can explain this phenomenon, but there is one particular case where wave-particle duality becomes logical and rational. That is when waves and particles are of identical constitution. For example, a drop of water (corpuscle) and a water wave are of identical matter. Water has either a corpuscle behavior or a wave behavior. This explanation of wave-particle duality leads to an important deduction: when the particle is motionless, it remains in a corpuscular state, and when it is moving, it becomes a wave.



The "µDomains" (Part 3) It would seem that global spacetime of the universe is divided into quanta called "microdomains” which are nothing but electrons or positrons without charge. Therefore, µDomains could have a mass of 511 KeV but, like neutrinos, they can't be detected. The existence of µDomains is proven in several ways developed in Part 3. In particular, they fully explain, with consistency, the constitution of quarks and the location of antimatter in the Universe.

The "Distributed Charge" Model (Part 3) The explanation of wave-particle duality leads to an important deduction: electrons are not moving around the nucleus as a punctual particle but as a sort of "cloud of charge". Indeed, the charge of the electron is distributed into the µDomains surrounding the nucleus. Schrödinger's probability concept must be replaced by a more realistic concept called "Distributed Charge Model". The quantum mechanics formulas as Schrödinger Equation are not modified by this new approach, which is verified by experimentation.

The Spacetime Model - Part 5 - 1 - 1 - The Binary Structure of Nuclei

1 The Binary Structure of Nuclei

We could think that the nucleus is built on the same principle as that of the quarks, leptons, mesons, baryons and atoms: the "distributed charge" model.

This chapter does not undertake a complete study of the nucleus, this subject being so huge, but proposes suggestions according to the "distributed charge" model.

1.1 Isobars Usually, nucleus graphs are plotted from the atomic number "A", the neutron number "N" or the proton number "Z". The figure 1-1 was drawn on a u quark basis. The u quarks inside the d quarks were taken into account. That is to say, each proton is made up of three u quarks and one electron, and each neutron is made up of one proton surrounded with one electron, or ((u u u)e-)e-.

Fig. 1-1

9-4

11-6

15-7

18-9

21-1

1

24-1

2

27-1

4

30-1

5

33-1

7

36-1

8

39-2

0

41-2

1

45-2

3

48-2

4

12

10

8

6

4

2

0

1st number : u quarks - 2nd number : electrons

∆ mass


This graph covers the first nuclei, those for which the mass number goes from 3 to 16. The X-coordinates thus go from 9 to 48 since each nucleon, proton or neutron, has three up quarks each. The mass of each nucleus was initially divided by the mass number A. An offset of 930,9 MeV was subtracted from each element in order to make the graph more readable1. Figure 1-1 shows a simplified graph. A more precise graph emphasizes that the lowest point of each isobar’s group is always reached when the number of electrons is equal to half the number of u quarks, including the d quark electrons.

1.2 Isotopes The lowest point noted with the isobars is repeated with the isotopes. However, examination of the curves shows that the mass of each isotope oscillates with a period of two elements. In order to better emphasize this oscillation, the difference between two adjacent isotopes, the derivative, has been plotted. Thus, every other time, we have a negative derivative (fig. 1-2 and 1-3). The object of these graphs is to know what the electron of the d quarks becomes inside the neutron. For that, it is necessary that the number of protons doesn't vary. 1 There have been many studies of atoms. However, it is the interpretation that is particularly interesting because this study has a new basis, namely that the d quark is made up of a u quark surrounded by an electron. This appears to highlight a binary structure, in figures 1-2 and 1-3, which seems to be a new idea.

C Na

Zn La 126

Fig. 1-2

This conclusion is very important since it gives additional proof that the d quark is

made up of a u quark and an electron


On these graphs, the mass increases and decreases alternately in steps of two neutrons.

1.3 The deuteron structure The only possible explanation of this binary structure is to consider that the nucleus has a deuteron (deuterium nucleus) structure (fig. 1-4). There is no alternative. It is highly probable that when a neutron meets a proton inside the nucleus, the outer-shell electron of the neutron “phagocytoses” the proton to make a deuteron. Deuterons would not, therefore, be composed entirely of a proton and a neutron, but of two protons and an outer-shell electron, which act as a strong nuclear force, keeping the two protons locked inside the deuteron. Moreover, the structure in two protons and one electron of the deuteron is more homogeneous and logical than the structure of one proton and one neutron. It should be noted that other structures, like e-(e-(e-(u u u u u u))) or e-(e-(u u u (e-(u u u)))) are also possible but improbable.

Au Pb

Rn Th 126

Fig. 1-3

126

126

These graphs, which extend to all the elements, don't leave any doubt about

the binary structure of nuclei


1.4 The He nucleus Physicists suspect the He structure to be one of the basic structures of the nucleus. Within the "distributed charge" model, many configurations are possible for the He structure. However, taking into account the great stability of this nucleus, it is judicious to think that the following scheme (fig. 1-5) is the most probable. This configuration is very close to the deuteron scheme (fig. 1-4).

Fig. 1-5

6 electrons

u uu

4He

u uu

u uu

u uu

4 protons

12 u quarks, made up with 8 positrons

6 electrons + 8 positrons = charge of 4He (= +2).

Fig. 1-4

Electrons

Proton

u uu

u uu

Neutron

Deuteron

u u

u

u uu

The outer-shell electron goes into deuteron periphery to make, what we call, the "strong nuclear force".


This diagram is homogeneous because the two outer-shell electrons of the He nucleus make it particularly strong. Alpha particles are also very strong.

1.5 H isotopes Figures 1-7 and 1-8 cover the possible configurations of H isotopes where electrons replace the strong nuclear force. These diagrams are only for teaching purposes. The 4H isotope (fig. 1-8 on the following page) is divided into three groups: with one, two and three outer-shell electrons.

1H

u u u

u u u

u u u

u uu

u uu

u uu

u uu

u uu

u uu

u uu

2H u uu

u u u

3H

(proton)

Fig. 1-7

Most probable

Most probable

u uu

u uu See note

Note: This scheme can be repeated for 3H, 4H …


These schemes are only suggestions. Intuitively, the most probable configurations are when electrons surround protons. The correct configuration would require some investment of time, and must be in accordance with many parameters: decay modes, binding energy, volume differences from one isotope to another, the mass derivative, quadripolar moment etc… It should be pointed out, once more, that if a decay or radioactivity produces protons and neutrons, it does not mean that these particles were parts of the nucleus before the interaction. Since waves and particles are both created from spacetime, it is necessary to keep in mind that what we see is not necessarily what really exists. The only thing we can be sure of is that all these particles and waves come from spacetime.

4H

u u u

u u u

u u u

u u u

u u u

u u u

u u u

u uu

u uu

u uu

u uu

u uu

u uu

u uu

u u u

u uu

u uu

u uu

u uu

u uu

u u u

u u u

u u u

u u u

u u u

u u u

u u u u u

u

u uu

u uu

u uu

u uu

u uu

u uu

u u u

u uu

Fig. 1-8

Most probable


1.6 Possible explanation of binary steps (a proposal) The binary oscillations of figures 1-2 and 1-3 suggest that, when a group of isotopes is examined, the nucleus is created in two phases (fig. 1-9).

Phase 1: The first neutron takes its place in the nucleus as a proton. It is stripped from its electron. The latter joins the other electrons on the nucleus’s periphery Phase 2: The second neutron takes its place in the nucleus as a proton. Its electron also surrounds the preceding proton, making a deuteron, instead of going on the periphery of the nucleus.

In both cases, the volume of the nucleus increases since it contains one more proton. When the electron goes on the nucleus’s periphery, it produces an increase in volume. When it is used to make a deuteron, the increase in volume is different. This could explain the binary steps1.

1 We can suppose that the electron decreases the Coulomb Field inside the nucleus and the repulsion force between protons is decreased too. However, this is only an assumption.

Fig. 1-9

Phase 1

u u

u

u u

u

Neutron

Nucleus

Phase 2

u u u

Deuteron

u uu

u uu

Proton

Proton


These two phases are repeated in a loop. Thus, we have a succession of increasing and decreasing volumes in a same isotope group. Figures 1-2 and 1-3 confirm this deduction. It is also possible that the electrons go on the periphery, two per outer layer, such as in the orbitals of the atom, as the Pauli Principle states. This process could also explain the periodicity of two.

1.7 The Bethe – Weizsäcker Formula This formula determines the binding energy of a nucleus of mass m (A, Z):

• The first term is the volume energy (av = 15,56 MeV). • The second term is the surface energy (as = 17,23 MeV). • The third term comes from the Coulomb Force (ac = 0,7 MeV). • The fourth term is an asymmetry energy (aa = 23,6 MeV) • C is an adjustment constant.

The traditional explanation of the "strong nuclear force" is not in accordance with this formula. The problem lies in the two following terms:

1/ Surface energy1: The strong nuclear force supposes linking protons and neutrons inside the nucleus. Under no circumstances is this force a "surface force". In this way, the Bethe-Weizsäcker Formula should not have a surface term.

On the contrary, within this Spacetime Model, the surface component term is perfectly logical. Indeed, it matches exactly the model of outer-shell electrons, which act like a rubber band and may explain the "strong nuclear force".

2/ The Coulomb Force: A similar problem is met with the Coulomb term. Since the Coulomb Force is far less important than the strong nuclear force, this term is unexplainable in the present theory.

Within this Spacetime Model, the nucleus volume comes from the repulsion force between protons. Since the nuclear force does not exist as a basic force, the magnitude of the Coulomb Force does not cause any problem. The presence of a Coulomb term in this formula is, therefore, perfectly logical. It is even a necessity.

Another point must also be considered. The nuclear volume, i.e. the mass, and the binding energy increase both as A, the atomic number. Currently, physicists think that the nuclear forces are saturated since each nucleon interacts only with its neighbours. Reality is different …and much more simple!

1 The explanation of this surface energy usually uses the Van Der Walls Model. The author is not fully convinced by this model, which is a good comparison, but not a reliable explanation of the phenomenon.

B = avA - asA2/3 - acZ2/A1/3 - aa (N - Z)2/A + C


If we consider that the neutrons are transformed into protons inside the nucleus, the atomic number A relates the overall number of protons, that is to say, the original protons + the protons coming from neutrons. In other words, it is highly probable that All these protons make a repulsive Coulomb Force between them, which creates the volume (see Part 2). It is, therefore, normal that the volume increases as the atomic number does. It is only a simple Coulomb problem …and not a complex and unexplained phenomenon of saturated forces. To summarize,

The Bethe-Weizsäcker Formula isn't in accordance with experimentation concerning

the strong nuclear force of the nucleus… but

…it is in perfect accordance with the Spacetime Model

The nucleus doesn't have Z protons and N neutrons, but rather A protons and N electrons.

The Spacetime Model - Part 5 - 11 - 2 - Quarks and Mesons (a proposal)

2 Quarks and Mesons (a proposal)

This chapter covers the other quarks and mesons in accordance with the "distributed charge" model. However, this chapter contains only suggestions and this information must be taken with care.

2.1 C and s quarks In the "distributed charge" model, it would seem that the charmed quark would rise from the strange quark (fig. 2-1). A positron may surround the s quark. µDomains are enclosed between the positron and the s quark.

2.2 T and b quarks As we know, the t quark mass is huge, 178 000 MeV. This does not mean, however, that it contains a great number of components. Since it is a closed volume, few electrons and positrons are sufficient to make a t quark having a huge volume of … 178 000 MeV! Inside this quark, we would probably find that 99,99999% is made up of µDomains. The t quark has a volume hermetic to spacetime. Therefore, it has mass.

Fig. 2-1

S quark -1/3

C quark +2/3

Positron

Closed volume (= mass, see Part 1)


2.3 The π°π°π°π° meson The π° meson would be made up of four quarks: u + dbar + d + ubar. It must be noted that all physicists do not agree on this configuration; some papers indicate different schemes. Since d and dbar quarks are built from u and ubar quarks, the electron and the positron are peripheral (fig. 2-4). These two particles maintain the four quarks locked inside the meson. Other configurations are also possible. We must keep in mind that the electron or positron has to be peripheral to the other particles.

Fig. 2-2

B quark

T quark

Positron

u u

uu

Fig. 2-4

Electron (*)

Positron (*)

(*) The electron or positron, comes from the d or d bar quark. Their position may be interchanged.

ππππ° meson


The π meson is probably not spherical as the figure 2-4 shows, because the four quarks introduce attractive and repulsive forces (fig. 2-5). In the proton and the neutron, the three u quarks produce exclusively repulsive forces (fig. 2-6). This is why the volume, or the mass, of the proton (938 MeV) or neutron (939 MeV) is greater than that of the π° meson (135 MeV), although this last contains an additional quark.

2.4 Decay of the π π π π meson Assuming figure 2-5 is correct, the stability of the quarks is broken during an interaction. The two pairs of quarks are destroyed, as in the case of the electron and the positron of the π° meson. There remains only the electron or the positron from the external layer (fig. 2-7). This internal annihilation is possible because the u-u bar pairs are very close to each other. The interaction is immediate and internal and, therefore, invisible to the experimenter. It is possible that such invisible interactions are more frequent than we would think. This scheme (fig. 2-7) is in perfect accordance with experimentation that gives: Neutral pion: 134,9766 MeV Charged pion: 139,57018 MeV The remaining electron or positron has a volume close to that of the π meson. This scheme suggests a muon (105 MeV) as a result. This is exactly what the experimentation indicates, with a Γ/Γtotal of 99,9877%. Note: The figure 2-7 is generic and may be adapted to other particles.

u u

u u

ππππ° meson

Fig. 2-5 Fig. 2-6

u

u

u

Proton or neutron

Repulsive force

Répulsive force

Attractive force


u u

uu

u u

uu

Fig. 2-7

The electronand positron have

annihilated each other

The u and u bar quarks are mutually annihilated

Future muon or antimuon

The electron or positron becomes a muon or

antimuon.

Decay of the charged pion

This electron or positron comesfrom the d or d bar quarks

This electron or positron converts the neutral pion into a charged pion

The Spacetime Model - Part 5 - 15 - 3 - Radioactivity (a proposal)

3 Radioactivity (a proposal)

The study of α radioactivity allows us to foresee the origin of the phenomenon. On the other hand, other types of radioactivity remain unexplained. In the standard model, it is difficult to understand from where the electron comes in β- radioactivity, since we suppose that the neutron (u d d) doesn't have an electron. The Spacetime Model provides an answer to some questions about radioactivity. However, this chapter can't completely cover so vast a subject and this information must be taken with care.

3.1 Origin of the radioactivity Radioactivity always takes its source in spacetime movements inside the nucleus. If the internal configuration of the nucleus is a little unstable, these spacetime movements break the deuteron, alpha or other structures.

3.2 Mathematical point of view We know that any wave, in a closed space, produces reflective secondary waves. Inside the nucleus, a multitude of waves are permanently reflected on electrons, protons, deuterons etc…. These waves are mathematically represented by vectors, such as gluons, bosons etc…. They are by no means particles but spacetime waves.

Thus, what we call “bosons exchanges” are nothing but EM waves and their own multiple reflections from any part.

We know that quarks, leptons, bosons, waves… are made of spacetime. It is not exceptional to see a W- boson being transformed into an electron or anything else since W bosons and electrons are both made of spacetime.


3.3 ββββ−−−− radioactivity Some suggestions of possible schemes are represented in figure 3-1.

The mass of a β- isotope is higher than the mass of the chemical element. Neutrons are in excess. This tends to prove that the electron comes from an internal structure made up of neutrons and confirms that the neutron structure has at least one electron. Please refer to the preceding chapters to understand this deduction.

Note: The neutrino has not been represented in figures 3-1 and 3-2. See Part 3 concerning this subject.

3.4 ββββ++++ radioactivity 1 The mass of a β+ isotope is lower than the mass of the chemical element of reference. There is a lack of neutrons. Since a neutron is nothing but a proton with an electron, there is a lack of electrons too.

One of the possibilities of the β+ radiation is a spacetime movement produced inside the nucleus (fig. 3-2). We know that a gamma ray moving near a nucleus splits into electron(s) and positron(s) if its energy is sufficient. This subject was discussed previously. However, it is not possible to be nearer to a nucleus that inside the nucleus itself. This means that any high energy EM wave inside the nucleus may be split into electron(s) and positron(s).

1 It is probable that the positron doesn't come from a quark. Thus, the paragraph 5.1 in Part 3 is not verified. However, the reasoning is correct.

Fig. 3-1

Excessive electrons ββββ-

ββββ-

Deuteron or other element, surrounded by one or several electrons, possibly in various combinations.

Outer electron of nucleus

The electron, or W- boson, comes from a deuteron or other internal element.

W-


The electron issued from the gamma is immediately used to link protons into binomials, like deuterons, or into other configurations. The positron is ejected by way of a W+ boson and tunnel effect. Other schemes are also possible but this one (fig. 3-2) gives an explanation of β+ radioactivity in perfect accordance with experimentation.

Since a gamma, a positron and a W+ boson are all made of spacetime, waves are converted into particles and the converse. All these interactions are very simple to understand, but require complex mathematics to describe them (QCD).

It should be pointed out that all these phenomena are well known: e+e- annihilation, e+e- creation…. Inside the nucleus, we probably have the same phenomena.

3.5 Alpha radioactivity Alpha radioactivity lets us suppose that the He configuration is already present inside the heavy nucleus. However, we don't have proof of this. Taking into account the "binary steps" of the nucleus, the Spacetime Model considers that the alpha is built by two deuterons when these particles take off the nucleus (fig. 3-3). Since the "binary steps" are a reality (see graphs 1-2 and 1-3), alpha radioactivity must be in accordance with this configuration. We consider that alpha particles are directly emitted from the nucleus. This point of view doesn't explain the binary steps; however, the proposed scheme (fig. 3-3) does.

Fig. 3-2

ββββ+

e-

γγγγ

Note: Neutrinos are not represented


3.6 Electronic capture In accordance with the "distributed charge" model, the incoming electron has two possibilities: it either surrounds the nucleus, or it links two protons to make a deuteron or another nucleus.

3.7 W and Z Bosons (a proposal) It must be noted that the nucleus is a closed volume, as explained in Part 2. This means that the nucleus behavior could be the same as that of a black hole. Therefore, we have a Schwarzschild Singularity inside the nucleus which may produce an invertion between time and space. This may explain the mass of the W and Z bosons (???). On the other hand, it must be pointed out that, inside the nucleus, the µDomains are compressed and spacetime properties may be modified. Who knows if, inside the nucleus (inside the Schwarzschild radius), "c" is still 300 000 km/s? Part 4 covers this subject. If c, inside the nucleus, is modified, there may be consequences. These could affect the W and Z bosons’ mass for example.

Deuteron

Fig. 3-3

u uu

4He

u u u

u u u

u uuu u

u

u u u

+

u u u

u u u

The Spacetime Model - Part 5 - 19 - 4 - Forces

4 Forces

Physicists consider that all forces come from ONE generic force. Why one force rather two or three? No one knows, but one thing is sure: to understand the GUT or ToE, it is necessary to drop all preconceived ideas that have no consistent base. In accordance with experimentations, the Spacetime Model considers that there would be only two fundamental forces. These two forces cannot be unified into a generic force, but include, nevertheless, a common element: spacetime.

4.1 Gravity Gravity is a pressure force produced by volumes and not an attractive force produced by masses. Its origin is spacetime curvature made by volumes (see Part 1).

4.2 The weak nuclear force Weinberg and Salam (Nobel Prize 1979) proved that the weak nuclear force is the EM force. The Spacetime Model is in accordance with this theory. Whatever the words used, EM wave, W or Z bosons, protons, neutrons, electrons, gluons… the basic elements are always made of spacetime. So, it is logical to consider that the weak nuclear force is nothing but the EM force.

4.3 The EM force The origin of the EM force is the variations of spacetime density inside the µDomains. The magnetic force is a particular case of the Coulomb Force. The only difference is the µDomain polarization: 1D, 2D or 3D.

4.4 The strong nuclear force The strong nuclear force does not exist per se. Electrons and positrons surround some particles like a rubber band. This force is an "elastic force of constraint" which comes from the Hooke Law. It is identical to gravity, which also conforms to an elastic force.

The Spacetime Model - Part 5 - 20 - 4 - Forces

In gravity, the pressure comes from µDomains. In the strong nuclear force, the pressure comes from electrons or positrons. Since µDomains, electrons and positrons are made of spacetime, gravity and the strong nuclear force are finally identical.

4.5 Unification of the two fundamental forces The only existing relation between the Hooke Force and the Coulomb Force is spacetime. These two forces cannot be unified since the first is a pressure force on any particles, while the second is an attractive - repulsive force, which relates only to the charged particles.

Fig. 4-1

Forces in the universe

Spacetime

Exerts only on charged particles Exerts on all particles

Application : Electroweak force

2D polarization of µDomains

Magnetism

Application :

Gravity

1D polarization of µDomains

Electrostatic

Application :

Strong nuclear force

Coulomb's Force attractive and repulsive force

Hooke's Force Constraint and pressure force

2D/3D polarization of µDomains Electromagnetism

The Spacetime Model - Part 5 - 21 - 5 - The Universe (a proposal)

5 The Universe (a proposal)

Apparently, physicists have never posed a fundamental question concerning the origin of the universe: the "enigma of the electron" (see below). This question is of great importance because it allows for only two solutions. The creation of the universe necessarily resides in one of these two solutions. Since the Big-Bang Theory doesn't solve this enigma, this theory is not credible.

Important note Information given below is only an assumption since no one can prove anything about the birth of the universe

5.1 The "enigma of the electron" Electrons and positrons have extremely precise volumes (masses): 510,998918 KeV. How can it be that all electrons and positrons of the universe have strictly the same volume? Indeed, electrons in Europe, in the USA, in Asia… always have the same volume: 510,998918 KeV, a volume measured with an extraordinary precision of +/- 0,000044, or

< 0,0000086% !!! To fully understand where the problem lies, let's imagine the following scenario:

A chairman says to a production engineer: "In my factory, we make packets of sugar of 500 g. With the packaging, the total weight is exactly 510,998918 g. The precision is 0,0000086%."

And he adds: "We obtain the same precision in all our production. We can manufacture billions and billions of packets of sugar always having the same weight of 510,998918 g. each. And we are sure that this accuracy is reached with each packet without carrying out any control…"

The production engineer can only be challenged by such a remark. Indeed, he knows that, in any production in the world, it is very difficult to obtain 0,001% tolerance without any control. To reach a tolerance of 0,0000086% with repeatability of billions and billions of pieces without any control is simply … impossible. He will suspect that there is a trick or a gimmick. Obviously, this assertion needs a rational explanation.


The "enigma of the electron" is exactly like this scenario. This enigma needs a rational explanation, other that "Matter came from a Planck Length" or the "big-bang theory", which doesn't mean anything. In reality, the universe is a kind of machine that manufactures electrons and positrons in astronomical quantity. These electrons are produced precisely with the same volume, namely mass. So, undoubtedly, there is a "trick" somewhere. It cannot be otherwise. The fundamental challenge is …to find this trick. This is the GREAT QUESTION and, by far, the most important mystery regarding the creation of the universe.

5.2 Two possibilities This question may have many solutions, but two seem obvious:

- Division - Multiplication

These two solutions are very similar and are studied in the following section. The multiplication solution seems to be the most probable.

By which process can this astronomical quantity of electrons and positrons be created with exactly the same volume of

510,998918 KeV …and always with the incredible precision of:

< 0,0000086% ?

The answer to this question solves 50% of the enigma of the

creation of the universe.


5.3 Division This scenario is explained in figures 5-1 and 5-2.

5.4 Multiplication The previous scenario explains the quantum of 511 KeV but does not solve the creation of spacetime that is explained below. This is why the following scenario is more credible than the preceding one. It supports an alternative:

! Simple multiplication: A cell multiplies with identical volume, or mass, in 2n steps: 2, 4, 8, 16, 32, 64, 128 etc…

! Increase with division: A cell is growing then is divided by two, and so on. The divider is therefore 2, 4, 8, 16, 32, 64, 128 etc…. This version is more interesting than the preceding one because the creation of spacetime is fully explained. In addition, this scenario is close to the behavior of Nature on Earth.

Fig. 5-1

Spacetime is initially created in three parts: neutral, negative and positive. The high spacetime densities are in dark grey. The charge symmetry is conserved.

Fig. 5-2

A binary division takes place: 2, 4, 8, 16, 32, 64 … 2n. It is repeated until reaching the quantum 511 KeV. With this limit, each element will have exactly 1/2n of the total volume of the universe. We thus obtain strictly identical volumes.

+ -


5.5 The Nature behavior on Earth Human beings, animals, plants etc… are "manufactured" according to a model of increasing cells followed by a division. This model varies from one species to another but the guidelines are always the same. For the human being, the cellular multiplication presents the following properties:

! Precision: The cell’s creation is extremely precise. A cell of a given type is exactly the replication of another cell of the same type.

! Reproducibility: The six billion human beings on Earth are created on the same model: two eyes, a nose, a mouth etc… Nature has an extraordinary capacity for replication in great quantities.

! Huge amount of replication: Two basic cells are sufficient to create a human being. Indeed, nine months after the initial conception, the number of cells reached is billions of billions.

! Common process: The replication process is sometimes very simple, as in bacteria, sometimes very complex, as in human beings. However, it is always the same principle.

This faculty of reproduction in nature and the simplicity of the process are …incredible. In other words, we must be conscious that Nature on Earth has an extraordinary capacity for self-reproducibility with the same accuracy. This capacity is found on Earth, but also on Mars, and on all components of the universe.

What we need to explain the creation of the universe

What exists on Earth

Precision Nature is able to make very precise replications.

Quantity Nature is able to make replications in astronomical quantities, as in human beings, with billions of identical cells.

We need a process able to create electrons of 510,998918 KeV with the incredible precision of <0,0000086%.

We need a replication process of electrons and positrons in astronomical quantities. The universe is "manufactured" through this unique process.

To explain the creation of the universe, we need the same reliable and accurate reproducibility but in greater quantity than that which we have on Earth


5.6 Scenario of replication The following scenario describes one of the possibilities of the creation of the universe. The conclusions are very interesting. The first part of this scenario must, necessarily, be very simple. It is a major condition. In addition, it must take account of the quantum concept, which is a reality. This quantum of volume is 511 KeV (see Part 2). Nothing has been invented. This process is well known on Earth, for example in the replication of bacteria. Since Nature tends to always repeat the same models, this scenario illustrated in figure 5-3, on the next page, is very relevant.

5.7 Spacetime In this process, a question arises: "What grows, only the 3D volume or 4D spacetime?”. When the universe was created, there were no masses. Out of the gravitational field, the Riemann Curvature is reduced to a Minkowski Space expressed as follows:

ds² = c²dt² -(dx² + dy² + dz²)

or:

ds² = c²dt² - dr² - r²(dθ² + sin²θ dϕ²) If we consider that: ! The universe was created from nothing, neither space nor time. ! There is a perfect symmetry. Nothing can be created without a counterpart.

… it is then necessary to take the Minkowski Equation and add ds² = 0.

It seems that the creation of the universe is nothing but a simple replication process


This ds is an infinitesimal spacetime. At the beginning of the universe, as there was nothing, all ds² were equal to zero. In polar co-ordinates, since we have a spherical symmetry, we can ignore dθ² and dϕ². We get c.dt = dr. Usually, in physics, length is expressed by x and not by r, so:

c.dt = dx

This well-known formula must be interpreted as follows:

“Time creates space” or the converse

In the begining, we have only one µDomain. Like cells in bacteria, it increases up to 1022 KeV according x=ct When it reaches this limit, there is a division by two. The volume is split into two parts of 511 KeV each since the quantum of volume is 511 KeV.

The same process is repeated to create 4 µDomains from two. The four µDomains grow and the volume of 4 x 1022 KeV is divided by two making volumes of 8 x 511 KeV …and so on. The same process is repeated indefinitely.

Fig. 5-3


From a mathematical point of view, the dimensional quantities "time" (T) and "space" (L) are different. The dimensional constant c, which keeps homogeneity in the equation, should not be removed. So, we should not take this sentence "time creates space" word for word since, from a mathematical point of view, this sentence is not exact. It has the same imprecision as the sentence "money creates employment". Of course, this sentence is correct, but not from a mathematical point of view since the words "money" and "employment" are of different dimensional quantities.

5.8 Before the creation of the universe From a philosophical point of view, this proposal renders obsolete the question “What was there before the creation of the universe?” The word “before” does not make any sense in this context since time was created simultaneously with dimensions xyz. The same phenomenon exists on Earth.

Let's consider a baby who has just been born and ask the mother: “what was the size of your baby two years ago?” This question does not make any sense since, for this baby, time was created nine months ago. Space, i.e. the size of the baby, was created 9 months ago too. Two years ago, this baby had neither time nor space.

As in this example, it is absurd to want to know what the universe was before its creation since there was no time and no space. The word "before" doesn't mean anything in this context. On the other hand, we may note that, in this example, the process is the same as in the universe: time creates spaces (or the converse).

5.9 The creation of objects Let's imagine a company that is created. There is also a relation between space (the factory, the office, the parking…) and time. For this company, before its creation, time and space did not exist. We may apply the same reasoning to common objects. For example, a stone on Earth has a maximum age of 4,5 billion years. Asking, “What was the size of this stone 10 billion years ago?” is a nonsensical question. …Many such examples can be given.

Since Nature tends to repeat itself, we may think that the creation of the universe follows the same principle as the creation of common objects we know on Earth. We have a creation date, and before this date, there was nothing: no time and no space.


5.10 Creation of the universe Everyone is able to describe spacetime with mathematics using special relativity formulas, but its comprehension is not so obvious. On the universe level, spacetime means "a ∆x space created by a ∆t time, or the converse". This is why space (3D) and time (1D) are inseparable. This relationship between time and space is emphasized in the proposal of new models of the creation of the universe described in figures 5-4 and 5-5. We have good reasons to consider that the universe has been created in two phases: ! Phase 1 (t0, t1, t2): During this phase, only µDomains were created. The universe

was empty. It had only space and time, nothing else. Billions of billions of billions of µDomains were created. This phase is common in figures 5-4 (scenario A) and 5-5 (scenario B).

! Phase 2 (t3...): During the second phase, due to chance, "islands of matter" are created. Several scenarios are possible, but we will study only two.

Scenario A (fig. 5-4) The matter is created randomly after the µDomains. The charge of µDomain(s) is shifted from one to another µDomain(s). Electrons and positrons may be "manufactured" in this way. The movements in spacetime produce gammas, which can make another electron-positron pair from µDomains and so on… Scenario B (fig. 5-5) Due to chance, the charge of a µDomain is shifted to another µDomain, thus creating an electron-positron pair. This pair, which is a sort of "malfunction of nature", is replicated, and so on, in accordance with the formula x = c.t.

Notes 1: It is possible that the creation of the universe was a combination of these two scenarios. Note 2: In phase 2, spacetime movements or e-e+ pairs have formed galactic clusters, which are separated only by (empty) µDomains. These µDomains can, however, transmit EM waves and gravitational field. It is also interesting to note that the expansion of the universe seems to be outside galactic clusters, not inside. This statement is in accordance with these two scenarios.


As time continues, µDomains are created, always following the same formula: ∆x = c.∆t. Therefore, the universe, which is made of µDomains, is continuously expanding, as the time does.

Due to chance or another effect, a quantum of space is created by a quantum of time, or the converse. Symmetry is preserved in accordance with ∆x = c.∆t

There was nothing, neither time, nor space

t1

t2

t0

Fig. 5-4

Due to chance, the charge of one or more µDomain(s) is shifted to another µDomain(s). Electron and positron pairs are, thus randomly created. They annihilate one another and the gammas produced disturb the other µDomains, and so on. We get a sort of "plasma" of gammas, electrons and positrons.

Electrons and positrons are transformed in quarks, protons, neutrons, H atoms etc…. This process has been described in Part 3. The continuation is well known: Bethe Cycle, Darwin Theory etc… Matter in galactic clusters may be created in this manner, dueonly to chance.

t3

t4

Scenario A


Electrons and positrons are combined in quarks, neutrons, H atoms etc.... This process has been described in Part 3. The continuation is well known: Bethe Cycle, Darwin Theory etc… Matter in galactic clusters may be created in this manner, due only to chance.

Billions of billions of µDomains are created. Due to chance, a µDomain presents a replication defect. Its charge is transferred to the adjacent µDomain. We get, therefore, an electron and a positron.

Electrons and positrons are replicated like cancerous cells.

t3

t4

t5

As time continues, µDomains are created, always following the same formula: ∆x = c.∆t. Therefore, the universe, which is made of µDomains, is continuously expanding, as the time does.

Due to chance or another effect, a quantum of space is created by a quantum of time, or the converse. Symmetry is preserved in accordance with ∆x = c.∆t

There was nothing, neither time, nor space

t1

t2

t0

Fig. 5-5

Scenario B


5.11 Solved enigmas The consequences of these scenarios are very interesting: ! Same phenomena on Earth

All these phenomena have their equivalent on Earth. Since we know that Nature always tends to repeat itself, this scenario is much more credible than the unexplained and irrational Big-Bang Theory.

! The electron enigma This scenario solves perfectly the electron enigma discussed at the beginning of this chapter. Its volume or the µDomain volume, 510,998918 KeV, is replicated in billions of billions of billions of copies. The Big Bang Theory doesn't explain this enigma.

! Starting from nothing This scenario starts from nothing: no time, no space. Time and space are created mutually according to the Minkowski Formula ∆x = c.∆t. This is probably due to chance.

! Density of matter "Manufacture accidents", which transform a µDomain in an e+e- pair, have a very low probability: 10-40, 10-60, 10-80? The e+e-/µDomain ratio is, thus, very small: 10-40, 10-60, 10-80.... This ratio is in accordance with experimental measurements, which state that the average density of matter in the universe is very low, only a few electrons per m3.

! Spacetime This scenario gives a physical explanation of spacetime: “A time ∆t creates a space ∆x or the converse".

! Charge of electron-positron pairs The charge is transferred from one µDomain to another. The +∆q of the one corresponds to -∆q of the other. This explains why electrons and positrons have precisely the same charge in absolute value and, consequently, solves the enigma of the proton charge and antimatter.

! Expansion of the universe This scenario also solves the enigma surrounding the expansion of the universe. Time, unfortunately, continues to run; we can't stop it. In accordance with the ∆x = c.∆t formula, each second of our life creates 300 000 km of space, or more precisely, of µDomains.

Time, which continuously runs, is the best proof of the perpetual creation of the universe, and thus of its expansion.


! Antimatter This subject has already been covered. These scenarios of the creation of the universe also explain the location of antimatter. Indeed, each electron created has its counterpart, the positron, which is, by necessity, close to it. In the universe, there are as many electrons as positrons. With these scenarios, it is IMPOSSIBLE to find even one electron or positron in excess. We have precisely the same number of each.

! The Horizon Enigma In any direction, the deep sky temperature is constant, about 2.7°K. This is why the "Inflate Model" has been added to the Big-Bang Theory. The Spacetime Model explains the constancy of the sky temperature very simply:

The e+e- pairs are created randomly Small "islands" of matter (fig. 5-6) are, thus, created in the universe, without any relation to each other. The perpetual creation of matter is probably due only to chance. Regarding the 2.7°K temperature, its origin probably comes from various interactions involving electrons, positrons, gammas, and combinations of these elements in these small islands of matter (fig. 5-6).. This new approach concerning the creation of the universe is not incompatible with the 2.7°K discovery. Moreover, the spatial distribution of the 2.7°K temperature seems to confirm the scenario suggested in this document.

Note A part of the charge is initially transferred from one µDomain to another. The amount of each part is probably due to chance as well. It may be, for example, 5%. In this case, the electron has 95% of the µDomain charge and the positron 105%. If this were the case, in others galactic clusters, we may have some electrons and positrons having the same volume, but with different charges. This could have many consequences. This subject is not covered by the present document.

Fig. 5-6


5.12 The assumption of the Big-Bang Theory The following table compares the current Big-Bang Theory to the one described in this chapter. The main enigma to be solved is obviously that of the electron (see paragraph 5-1). We can compare the Big-Bang Theory to a volcano. Is it credible to think that a volcano can emit millions of stones of 510,998918 gr. each, with a precision of 0,0000086%? Moreover, why would the amount of matter be exactly identical to that of antimatter under these conditions? Of course, not. From a scientific point of view, the Big-Bang Theory has too many inconsistencies to be credible. This theory is scientific nonsense. In the following table, the symbol (???) means that the question is unanswered within the Big-Bang Theory. On the other hand, all questions are logically and rationally answered within the proposed model. Each enigma below is fully explained in the preceding paragraph.

Enigma to solve Taking examples of already known phenomena on Earth Electron enigma Starting from nothing Charge of e-e+ pairs Spacetime explanation Density of matter Expanding universe Enigma of antimatter Enigma of horizon Overall explanation

Big-Bang

No

???

???

???

???

???

???

???

Inflate model (???) The universe came from a Planck Length that no one can explain (???).

Spacetime Model

Yes

Explained

Explained

Explained

Explained

Explained

Explained

Explained

Explained

Replication of µDomains from spacetime equation

∆x = c.∆t


I

Complements

Partitioning the theory The five parts of the Spacetime Model can be downloaded at the following URL address:




1. Closed volumes. These volumes produce a displacement of spacetime. As we know, the spacetime curvature produces gravity, but it also produces a "mass effect". Electrons are examples of closed volumes.

2. Open volumes. These volumes exist but do not produce any displacement of spacetime. If there is no curvature, there is no "mass effect" either. Orbitals in atoms are examples of open volumes. Orbitals are massless.

Each atom has a particular proportion of open and closed volume. This is why mass and volume seem to be two different quantities but this is an illusion. Gravity Contrary to a preconceived idea, spacetime is not curved by mass but by closed volume. This phenomenon is the same as when a ball is immersed into water: It is the volume of the ball, and not its mass, which produces the displacement of water.

A particle also produces a displacement of spacetime. Since spacetime is elastic (Einstein), the curvature of spacetime produces a pressure on volumes. This tends to bring them closer to each other. It means that gravity is not an attractive force between masses, but a pressure force on closed volumes.



II





Quarks This part demonstrates that we need two positrons to make three u quarks. A u quark with an electron becomes a d quark (please note that the rule of addition of fermions is covered in Part 4). This deduction, from the wave-particle duality and spacetime, has been extended to all particles. Finally, u quarks, d quarks, antiquarks, muons, antimuons, taus, mesons, baryons etc... can be made with only two basic particles: electrons and positrons.




III


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IV



V

Table of content

Introduction........................................................................................I IV

1. The Binary Structure of Nuclei

1.1 Isobars ..............................................................................................1 1.2 Isotopes ............................................................................................2 1.3 The deuteron structure .....................................................................3 1.4 The He nucleus ................................................................................4 1.5 H isotopes ........................................................................................5 1.6 Possible explanation of binary steps (a proposal) ............................7 1.7 The Bethe-Weizsäcker Formula.......................................................8

2. Quarks and Mesons (a proposal) 2.1 C and S quarks .................................................................................11 2.2 T and b quarks..................................................................................11 2.3 The π° meson ...................................................................................12 2.4 Decay of the π meson.......................................................................13

3. Radioactivity (a proposal) 3.1 Origin of the radioactivity................................................................15 3.2 Mathematical point of view .............................................................15 3.3 β- radioactivity.................................................................................16 3.4 β+ radioactivity................................................................................16 3.5 Alpha radioactivity...........................................................................17 3.6 Electronic capture ............................................................................18 3.7 W and Z Bosons (a proposal)...........................................................18

4. Forces 4.1 Gravity..............................................................................................19 4.2 The weak nuclear force ....................................................................19 4.3 The EM force ...................................................................................19 4.4 The strong nuclear force...................................................................19 4.5 Unification of the two fundamental forces.......................................20


VI

5. The Universe (a proposal) 5.1 The "enigma of the electron" ...........................................................21 5.2 Two possibilities ..............................................................................22 5.3 Division............................................................................................23 5.4 Multiplication...................................................................................23 5.5 The nature behavior on Earth...........................................................24 5.6 Scenario of replication .....................................................................25 5.7 Spacetime.........................................................................................25 5.8 Before the creation of the universe ..................................................27 5.9 The creation of objects .....................................................................27 5.10 Creation of the universe ...................................................................28 5.11 Solved enigmas ................................................................................31 5.12 The assumption of the Big-bang ......................................................33 Complements.......................................................................................I - IV

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