Time Perspective Distortion, Illusion of Accelerated Expansion

Arthur E. Pletcher1

1International Society for Philosophical Enquiry, Winona, Minnesota, USA

July 12, 2015email: artpletcher@ultrahighiq.org

Abstract

This alternative model to Accelerated Expansion, is supported by correlated studies of multiplegalaxy surveys with increased velocities across their minor axis. Thus, velocity within the samebody appears to increase per distance.Time Perspective Distortion (TPD) postulates the novel idea of a linear point perspective in thetime dimension. Just as subtended arcs in linear spacial perspective create the appearance ofdecreasing (and converging) geometry over distance, TPD proposes that time perspective createsthe appearance of decreasing (and converging) time intervals over distance.The result is an illusion of accelerated velocity, as the appearance of decreasing time intervals isequivalent to increasing velocity.TPD rewrites accelerating expansion, alternatively, as constant expansion viewed (obliquely) intime perspective. Photons travelling to an observer, from remote past events, will appear toarrive with successively decreased time intervals.Please note: TPD is distinct from time dilation and does not contradict or violateeither time dilation, GR, nor expansion. In TPD, corrections of skewed time intervals arefirst converted to true orthogonal length (t⊥) subsequently, all classical and relative physics arethen calculated using t⊥ instead of t.In the last chapter, I provide a vector calculation to distinguish accelerated expansion fromconstant expansion with TPD

Key words: cosmology: dark energy-infrared: galaxies

1. INTRODUCTION

TPD can be thought of as a perspective in the timedimension, analogous to linear perspective in architec-ture. Time intervals appear to decrease and converge.

2. SPACIAL VS TIME PERSPECTIVE (ILLUSIONS)

TPD offers the following alternate explanation for ac-celerated expansion:

Velocity with decreasing time intervals is equiv-alent to acceleration

Linear spatial interval perspective:

Imagine an observer, with a reference scale, measuringthe ties of a railroad track in perspective. See figure 1.The scale will measure each successive tie (n) with de-creasing spatial intervals, according to the inverse linear

perspective equation: ((Burton, 1945))

np =n⊥d

(1)

Where n ⊥ is true orthogonal length and np is theskewed length, as a result of perspective.

FIG. 1 2D linear perspective

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TPD time interval perspective:Now, imagine the observer with a reference clock, mea-

suring some motion with velocity (v) across (x). See fig-ure 2. In TPD, The clock will measure each successive(d/v) with apparent decreasing time intervals, accordingto the equation:

tp =t⊥

1 + (d1/2 ∗K)(2)

Where (K) is a minute constant ∼ 1/10−11

t ⊥ = d/v1 at the observer′s clock

d = distance from observer t0 event d/v2

tp = the resulting converged time interval

of event d/v2

FIG. 2 Time perspective

A. Decreasing Time Intervals Appear Equivalent toAcceleration

FIG. 3 Constant velocity with decreasing time intervals ap-pear as acceleration

Figure 3 illustrates Constant velocity with decreasingtime intervals, per equation 2. Remote galaxies appear

to be expanding with acceleration. However, the accel-eration is only an illusion of perspective.

Note: TPD does not attempt to contradict constantexpansion, time dilation nor GR.

B. Decreasing time intervals and pulsars

TPD suggests that the further away a pulsar is froman observer, the more frequent it’s flashes will appear tobe, as a result of decreasing time intervals per distance.

Calculating the true flash time intervals of pul-sars

Figure 4 shows three pulsars, at points: a, b and c,with the exact same time interval of t⊥, at respectivedistances: xa, xb and xc

FIG. 4 (3) pulsars, at points: a, b and c, with the exact sametime interval of t⊥, at respective distances: xa, xb and xc

Since TPD proposes that perceived time intervals tpappear to decrease with distance, per TPD equation 2,then the flashes will appear to decrease in time, givingthe illusion of increased rotational velocity.

Thus, pulsar at distance xc will appear to be flashingmore frequently than the pulsar at distance xb, and xbwill appear to be flashing faster than xa

However, the perceived difference is due to effect ofTPD.

Note the following:

true time interval =t⊥ = 1 second period

tp = perceived time interval

distance xa =100, 000 LY = 9.461 ∗ 1020m

distance xb =150, 000 LY = 1.892 ∗ 1020m

distance xc =200, 000 LY = 2.838 ∗ 1020m

TPD =factor from equation 2

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From equation 2, tp at distance x =

tpa =1

1 + (9.461 ∗ 1018)1/2 ∗ (10−11)

tpa =0.970s (perceived period)

tpb =1∗

1 + (1.892 ∗ 1019)1/2 ∗ (10−11)

tpb =0.958s (perceived period)

tpc =1

1 + (2.838 ∗ 1019)1/2 ∗ (10−11)

tpc =0.949s (perceived period)

Thus, TPD makes the bold assertion that pulsarflashes are actually slower than they are perceived here inEarth, due to time perspective distortion. ((Cook et al.,1994))

C. Superluminal expansion

Note that TPD effects all measurements involvingtime over magnitudes, including electromagnetic waveshifting.

To reiterate, TPD only contradicts the prime of expan-sion and not constant expansion. the true recession ve-locity (v⊥) can be obtained from high red-shifted galaxiesby calculating t⊥.

Solving for t⊥, (3)

t⊥ = tp ∗ (1 + d1/2K) (4)

t⊥ = 1 ∗ (1 + (3.027 ∗ 1026)1/2 ∗ (10−11)) (5)

t⊥ = 175 (6)

v⊥ =295, 050

175= 1, 687km/s (7)

Table 5 lists the perceived and adjusted values (perTC) of galaxy GN-z11.

Note: Although GN-z11’s apparent red-shift indicatesa radial recession approaching c, TPD provides an ad-justment factor of ∼ 175.

FIG. 5 perceived and adjust values (per TPD) of galaxy GN-z11. Although GN-z11’s apparent red-shift indicates a radialrecession approaching c, TPD provides an adjustment factorof ∼ 175.

D. Rotational Velocities Appear to be greater overmagnitudes

Figure 6 shows a remote, inclined galaxy and observeron Earth. TPD time intervals appear to be decreasingfrom observer’s perspective.

FIG. 6 Remote, inclined galaxy and observer on Earth. TPDtime intervals appear to be decreasing from observer’s per-spective

TPD makes the bold assertion that the actual galaxyrotational velocities are much less than the convention-ally accepted values, which defy physics.

In order to calculate the true rotational velocity v⊥from the perceived velocity vp, we must solve for t⊥ fromequation 4

Note: TPD requires that if the distances of galaxiesare based solely on red-shifting, then distance must alsobe adjusted per equation 2

The following is based on Messier 31

d =2.54 ∗mly = 2.403 ∗ 1022m

tp =1s (Can be any time period)

t ⊥= > (adjusted, true time)

vp =250km/s (perceived, false rotational speed)

v ⊥= > (adjusted, true rotational speed)

per equation 4,

t⊥ = 1 ∗ (1 + (2.403 ∗ 1022)1/2 ∗ 10−11)

t⊥ = 2.550s

t⊥ is the true time period. To clarify, the observerperceives a remote event that occurred in 2.55 secondsto be only 1 second. (This would sound radical, howeverit explains the physics defying receding and rotationalvelocities (approaching c) of very remote galaxies)

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To find the corrected velocity, we simply divide thenumerator by t⊥. Thus,

v⊥ =250

2.550= 98.039km/s (8)

Note that In TPD, Physics are unaltered, andorbital paths do not deviate from Keplers laws.

The principle in my manuscript, TPD only predictsperspective distortions resulting in the appearance ofaltered velocity.

3. PREDICTIONS

A. Galaxy rotation will appear to increase on the far sidefrom the observer and decrease on the near side.

Figure 7 shows two points on a spiral galaxy, at equaldistance from the center, but on opposite sides with re-spect to the viewer.

FIG. 7 Two pints on a spiral galaxy, at equal distance fromthe center, but on opposite sides with respect to the viewer.

Per the rotational velocity formula ((david morin,2008)):

v =

√GM

r(9)

If points a and b measure different velocities perequation 2, that would be in support of my theory.

Calculating the perceived differences from points aand b:

vp =250km/s

d (at core) =2.54 ∗mly = 2.403 ∗ 1022m

r =1.229 ∗ 1020m

compensatingfor12.7R inclination,

∆d =r ∗ cos(12.7R) = 1.199 ∗ 1020

da =2.403 ∗ 1022m− 1.199 ∗ 1020m = 2.39104 ∗ 1022m

db =2.403 ∗ 1022m+ 1.199 ∗ 1020m = 2.41529 ∗ 1022m

From equation 8,

v⊥ =98.039km/s

Calculating vp, for point a, using equation 2:

tp at xa =1

1 + (2.39104 ∗ 1022)1/2 ∗ (1 ∗ 10−11))

=0.393

vp at xa =98.039/0.393

=249.463km/s

Calculating vp, for point b, using equation 2,

tp at xb =1

1 + (2.41529 ∗ 1022)1/2 ∗ (1 ∗ 10−11))

=0.392

vp at xb =98.039/3.915

=250.419km/s

Thus, the difference in rotational velocity betweenpoints a and b = 0.956km/s

B. TPD Predicts that Supernovae Remnant Velocity willAppear to increase with the Distance From the Observer

Supernovae particles are expelled without bias toan observer. However, If the expelled electron x-rays(observed from x-ray space telescopes) of supernovaehave measured velocities with a bias of greater velocityaway from the Earth and less velocity toward the earth,that would be in support of my theory.

Figure 8 shows a hypothetical remnant cloud of r ra-dius, and x distance from the Earth.

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FIG. 8 Hypothetical supernova remnant cloud at r radius andx distance from the Earth. Time intervals appear to decreaseper TPD

Figure 9 Calculates the effect of TPD (apparent ve-locity decrease) using θ degrees at point A (which is onthe cloud outer boundary) by first deriving ∆x (the xcomponent displacement from the epicenter) then d =(x−∆x).

FIG. 9 deriving ∆x from point A on θ, then calculating TPD

The following parameters are similar, in magnitude, toCassiopeia A,

r =2500 ly = 2.365 x 1019m

θ =π

4radians

x =10000 ly = 9.461 x 1019m

∆x =rcosθ = 1.672 x 1019m

d =x−∆x = 7.789 x 1019m

t⊥ =1s

v⊥ =5000km

s(true expansion velocity)

Note:

• t⊥ can be any time period measured, using d̄, as dvaries with any non-perpendicular trajectory.

from equation 2,

tp =1

1 + (7.789 ∗ 1019)1/2 ∗ (1 ∗ 10−11)

tp =0.919

Between the scale of the observer and 10k ly, the ob-server measures velocity with a time perspective distor-tion factor of 0.919. That is to say that he measures ve-locity with a t at 0.919 of it’s actual value.

To arrive at the observer’s perceived velocity vp, wesimply divide the correct velocity by tp

thus,

vp =5000km

0.919s(10)

vp = 5441km/s (11)

Super nova multiple point studyFigure 10 shows multiple points of θ degrees, in orien-

tation to the direction of observation:

FIG. 10 Points a thru d of θ degrees, in orientation to thedirection of observation

The table in figure 11 lists the perceived (false) veloci-ties observed at points a thru d . Notice that the furtheraway a point is, the faster the velocity appears to be.

Note for θ,

velocity is radial (from epicenter)

v⊥ = true velocity

vp = perceived false velocity (with TC distortion)

Assume ideal, case, where, debris, scattering rate

is equal in all directions

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FIG. 11 Points a through d, of θ degrees correspond to variousdistances from the observer, and resulting perceived velocities

4. SUPPORTIVE DATA

I submit the follow correlation study, specifically onthe subject of increased velocity on the far sides of mul-tiple galaxies. It directly and explicitly adds support tomy prediction. Although not conclusive, it does justifyconsideration to my supposition

All academic credentials, laboratory, sources of data,correlation values and publisher are included.

Title: ”On Possible Systematic Redshifts Across theDisks of Galaxies”

Staff: T. Jaakkola1, P. Teerikorpi2 and K.J. Donner3

Academic credentials:1Professor of Astronomy at Helsinki2Department of Physics and Astronomy, University of

Turku, Vaisalantie 20, 21500 Piikkio, Finland3University of Helsinki

Laboratory:Observatory and Astrophysics Laboratory, University

of HelsinkiSources of data: Listed in figure 12.

Publisher: Astronomy and Astrophysics 40, 257-266(1975)

Note, in the Summary:”Velocity observations in 25 galaxies have been

examined for possible systematic redshifts across theirdisks: a possible origin for the redshifts could be theradiation fields. Velocities increase towards the farsides in most cases. This is so for the ionized gas,for neutral hydrogen, and in some cases for thestars.”

Correlation coefficients:Figure 12 shows ’table 1’, on page 258 which lists

25 galaxies, correlation coefficients and relevant columns(including sources of data):

FIG. 12 two vectors, observed at d = 1mpc, with different radial velocities

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5. MATHEMATICAL TEST TO DISTINGUISH TPDFROM ACCELERATED EXPANSION

Note: Not to be confused with total expansion,This section is only limited to the derivative ofconstant expansion.

Vector calculation in TPD (with constant expansion)

differs from the accelerated expansion, as demonstratedin Figure 5 which shows two vectors observed at d =1mpc, with different radial velocities

For simplicity, assume two SNLA. One at 1mpc and theother at 2mpc, allows for the following measurements ofdistance and velocity:

FIG. 13 two vectors, observed at d = 1mpc, with different radial velocities

initial velocity (vi) of ~A =50km/s

initial velocity (vi) of ~B =100km/s

distance (d) of ~A =1mpc

distance (d) of ~B =1mpc

Both objects travel from d = 1mpc to d =2mpc

resulting velocity, at mpc = 2, of ~A = ~A2

resulting velocity, at mpc = 2, of ~B = ~B2

Calculating ~A2 and ~B2, using Ho:Using Ho, both ~A2 and ~B2 will be determined by sum-

ming two vectors, since they are both at the same dis-tance of accelerated expanding space. Thus,

~A2 (usingHo) =50 + 68 = 118km/s

~B2 (usingHo) =100 + 68 = 168km/s

Calculating ~A2 and ~B2, using TPDTC calculates the illusion of acceleration as velocity

proportional to distance. Thus, the distinction is in the

difference between ~A2 and ~B2. Because ~B2 is 2x the valueof ~A2, ~B2 will appear to increase by a factor of 2

Using equation: 2,

~A2 (usingTC) =tp =t⊥

1 + (da ∗K)

~B2 (usingTC) =tp =t⊥

1 + (2da ∗K)

Thus, between 1mpc and 2mpc ~B2 will increase by 2x~A2, because it’s initial velocity (vi) was twice the rate.

Again, keep in mind that this distinction is only limitedto the prime of constant expansion.

REFERENCES

H. E Burton. The optics of euclid. Journal of the OpticalSociety of America, 1945.

G. B.; Cook, S. L.; Shapiro, and S. A Teukolsky. Recyclingpulsars to millisecond periods in general relativity. Astro-physical Journal Letters, 1994.

david morin. Introduction to Classical Mechanics. CambridgeUniversity Press, 2008.