Page 1

1

Light Speed Invariance is a Remarkable Illusion

Stephan J. G. Gift

Department of Electrical and Computer Engineering

Faculty of Engineering

The University of the West Indies

St. Augustine, Trinidad, West Indies

“Einstein’s special theory of relativity requires that the one-way velocity of

light be a constant. If that turns out not to be so, special relativity falls.”

Paul A. LaViolette, Genesis of the Cosmos, 2004.

“Any clear sign of a variation in c, the speed of light, as the Earth [revolved]

would prove that the aether existed.”

George Smoot, Wrinkles in Time, 1993.

“Those physicists - and they are many - who now regard belief in the

possibility of an ether as a superstition have simply not learnt the lessons of

history, which teach us that discarded ideas have a way of returning to

favour.”

Herbert Dingle, Science at the Crossroads, 1972.

Abstract. Though many experiments appear to have confirmed the

light speed invariance postulate of special relativity theory, this postulate

is actually unverified. This paper resolves this issue by first showing the

manner in which an illusion of light speed invariance occurs in two-way

light speed measurement in the framework of a semi-classical absolute

space theory. It then demonstrates a measurable variation of the one-way

speed of light, which directly invalidates the invariance postulate and

confirms the existence of the preferred reference frame of the absolute

space theory.

Page 2

2

1. Introduction

A fundamental tenet of Einstein’s Special Theory of Relativity is the Light Speed

Invariance Postulate according to which the speed of light is constant in all inertial frames [1-4].

This postulate is used to derive the Lorentz Transformations relating the coordinates in different

inertial frames and these transformations are in turn used to derive the length contraction and

frequency reduction formulae of special relativity.

The light speed invariance postulate has been subjected to numerous tests over the past

century [5] as a result of which most scientists believe that it has been confirmed. Thus it is often

claimed that the postulate has been verified by the classic experiments of Michelson and Morley

[6] and Kennedy and Thorndike [7] and by the many later improved versions of these

experiments such as those by Brillet and Hall [8] and Hils and Hall [9]. However while the

results of this class of experiments suggest a constant light speed c, they do not directly test one-

way light speed. In experiments that do attempt a one-way light speed test such as those by

Gagnon et.al. [10] and Krisher et.al. [11], Zhang [5] has pointed out that these are not true one-

way tests because of the inability to independently synchronize the clocks involved. Thus 100

years after the introduction of the relativistic paradigm, light speed invariance on which the

paradigm is based remains an open issue, despite the strange declaration by the scientific

community that it is correct by definition! Ives has in fact described it as untenable [12].

One-way light speed testing is therefore necessary in order to determine the validity of

the light speed invariance postulate. This test can differentiate between Special Relativity

Theory, which involves light speed invariance, and the Maxwell-Lorentz Ether Theory, which

involves light speed variation relative to a moving observer. This latter theory in its modern form

is a semi-classical Absolute Space Theory in which light propagates isotropically at a speed c in

a preferred or absolute reference frame. In such an absolute frame and in keeping with classical

analysis, the one-way speed of light changes according to the observer’s motion relative to the

preferred frame. The theory incorporates the ether-induced Fitzgerald-Larmor-Lorentz (FLL)

contractions experimentally confirmed by Ives [13] according to which a rod of length lo in a

preferred frame, when moving with speed w relative to that preferred frame, is shortened to a

length l given by

(1.1)

2/ 1

)

22

/ 1 (

o

cwll

−=

Page 3

3

and a system of frequency fo when stationary in the preferred frame, has a reduced frequency f

given by

(1.2)

2 / 1

)

22

/ 1 (

o

cwff

−=

This incorporation is achieved by the adjustment of the classical Galilean transformations

resulting in

(1.3)

ooooo

ttzzyy wtxx

1

,, ),(

−

===−=γγ

Here the zero-subscript coordinates are the coordinates of space and time in the preferred frame,

the unsubscripted coordinates are coordinates in a reference frame moving at speed w relative to

the preferred frame andγ is the FLL contraction factor given by

(1.4)

2/ 1

−

22

)/1 (

−=

cw

γ

Many researchers [14-17] have observed that the Absolute Space Theory is in close agreement

with Special Relativity Theory over virtually its full range of predictions.

However the two theories make quite different light speed predictions. In the case of the

Absolute Space Theory, for measurements made by an observer at rest in the preferred frame, the

(real) speed u relative to the moving frame is given by

r′

wuur

−=

′

(1.5)

where

is the speed relative to the preferred frame. This is the Galilean law of velocity

composition. For measurements made by an observer moving relative to the preferred frame,

Levy [16 p42-43] has shown that because the FLL contractions result in contracted metre sticks

and retarded clocks, the (apparent) speed

u

a u′ relative to the moving frame is given by

)/1 /()(

22cwwuua

−−=

′

(1.6)

which can be written as

u

(1.7)

wucw

a

′

−=−

)/1 (

22

This is the Galilean law of velocity composition when contracted metre sticks and retarded

clocks are used to measure speed relative to the moving frame. From (1.5) and (1.7), the real

speed u and the apparent speed u are related by

r′

a′

(1.8)

r

′

a

′

ucwu

=−

)/1 (

22

The law of velocity composition in Special Relativity Theory corresponding to equation (1.6) of

the Absolute Space Theory is [1-4]

Page 4

4

u (1.9)

)/1/()(

2

c uwwu

−−=

′

where u is the speed relative to the moving frame. If

′

cu = in (1.9), then

(1.10)

cu =

′

i.e. the measured speed in Special Relativity Theory is c. This result is independent of the

direction of

and consistent with the light speed invariance postulate. If in (1.6) of the

Absolute Space Theory, then

wcu =

u

(1.11)

cwwccwwc

a

′

<<−≈−−=

,)/1/()(

22

i.e. for sufficiently low relative speed

, the measured speed in Absolute Space Theory is the

classical value

and not c. If the direction of is reversed, then (1.11) becomes

w

wc−

w

u

(1.12)

cwwccwwc

a

′

<<+≈−+=

,)/1 /()(

22

Thus for light speed measurements made by an observer in a frame moving at speed

relative to the preferred frame, Special Relativity Theory predicts light speed invariance

while the Absolute Space Theory predicts classical light speed variation c

. In this paper

therefore, we examine the possibility of light speed variation and its measurability in the

framework of the Absolute Space Theory. To this end, we summarise the careful results of Ives

relating to out-and-back optical tests which show how experiments such as the Michelson-

Morley and Kennedy-Thorndike involving light speed variation in a preferred frame yield a

measured constant light speed c. We then show that light speed variation can indeed be detected.

Specifically we demonstrate that the variation in the period of Jupiter’s satellite Io observed from

Earth as it orbits the Sun (“Roemer Effect”) is a direct manifestation of changes in the speed of

light relative to a moving observer.

w

c

w

±

2. Light Speed Measurement on a Moving Platform

Consider the Maxwell-Lorentz semi-classical Absolute Space Theory in which light

propagates isotropically at a speed c in a preferred frame. In such an absolute frame, the one-way

speed of light relative to an observer changes according to the observer’s motion relative to the

preferred frame. In addition, FLL contractions (1.1) and (1.2) occur as a result of movement

relative to the preferred frame. These contractions alter the normal Galilean transformations that

relate the coordinates of the preferred frame to coordinates in any other inertial frame, which

now become (1.3).

Page 5

5

2.1 Two-way Light Speed Test [18]

Since one-way light speed methods have failed because of clock synchronization

problems [5], we here focus on two-way light speed testing which appears to confirm light speed

c. We consider light speed measurement on a platform moving at a speed w relative to the

postulated preferred reference frame and examine the possibility of detecting and measuring the

speed

of similarly directed light relative to the platform [18]. In Figure 1, let ab be the

moving platform on which measurements are to be made with a clock at a and a mirror at b. Let

the speed of the platform relative to the preferred reference frame be w and let

wc−

Dbe the distance

from a to b as measured on the platform.

ba

w

Figure 1. Platform moving at speed w relative to the preferred reference frame

Because of the FLL contractions that arise as a result of movement with respect to the

preferred frame, the true length D is less than the measured length and is given by

2/ 1

)

22

/1 (

cwDD

−=

(2.1)

Let the time of transit of a light signal travelling from a to b and back to a as measured by the

clock at a be t. Because of the FLL contractions, the true time of transit t (measured by a clock

stationary in the preferred frame) from a to b and back is greater than tand given by

2/ 1

)

22

/1 (

cw

t

t

−

=

(2.2)

Now the true time of transit of a light signal from a to b is

)/(wcD

−

and the true time of transit

from b to a is. Therefore )/(wcD

+

22

2

wc

cD

−

wc

D

+

wc

D

−

t

=+=

(2.3)

Substituting from (2.1) and from (2.2) in (2.3) yields tD

2/ 1

)

22

2/ 1

)

22

22

/1 (

/ 1 (

2

cw

t

cw

wc

Dc

−−

=−

(2.4)

It follows from (2.4) that the speed of light cas measured on the moving platform is given by

Page 6

6

c

t

D

c

==2

(2.5)

Therefore even though the speed of light relative to the platform is

wc−

out and back, the

light speed measured on the platform is c.

wc+

To appreciate the full significance of this remarkable result, it should be noted that the

true average out and back speed

is, using (2.3), calculated to be

AV

c

ccwcwc

cD2

D

t

D

AV

≠−=−==

)/ 1 ()(

22

2222

c

(2.6)

The result in (2.6) indicates that with no FLL contractions, the average two-way light speed

varies with w to second order and is not equal to c: The FLL contractions compensate for the

second-order term

in (2.6) such that the measured average two-way speed

AV

c

22/cw

c is c as given

in (2.5). This result has been generalized for any direction of light travel by Levy [16] and

validates the standard out-and-back method of determining light speed c relative to the preferred

frame from a moving platform. It means however that this method gives c relative to the

preferred frame but does not yield the one-way light speed wc±

relative to the moving platform.

3.

Light Speed Measurement Using a One-way Signal Pulse Train

Neither one-way two-clock light speed experiments nor two-way one-clock light speed

experiments give the one-way light speed relative to the moving platform. We now describe a

one-way one-clock experiment that does. It is based on the following principle: Instead of timing

a one-way light signal pulse over a known distance using two clocks, we time successive pulses

of a one-way signal train using one clock. It is somewhat similar to timing a passenger train with

one clock by starting the clock as the front of the train passes and stopping the clock as the rear

of the train passes. If the length

of the train is known, then with the time

T

D

T T measured by the

single clock, the train speed

T S can be found from

TTT

TDS/

=

(3.1)

3.1

The Roemer Experiment

Consider the Earth-Sun-Jupiter planetary system. As the Earth revolves around the Sun at

speed w, the innermost satellite of Jupiter, Io, is observed to undergo regular variations in its

Page 7

7

period To [19]. Because Io, as observed from Earth, is periodically eclipsed by Jupiter, this

occulting source emits what may be described as “pulses of darkness” travelling at speed c to

Earth as Io revolves around Jupiter. This is shown in figure 2. The distance between successive

pulses is fixed at λo given by

oo

cT

=

λ

(3.2)

Jupiter

Earth

Pulses of Darkness

λ λo

c

Figure 2. Pulses of Darkness from Earth-Sun-Jupiter Planetary System

As the Earth moves away from Jupiter, the period

H

o

T

of Io, which is the time between successive

pulses, is observed on Earth and found to be greater than To. The light speed relative to the

receding Earth can now be determined using λ and

H

T in the fundamental speed-determining

equation “speed equals distance over time” which for this system is

H

o

R

T

c

λ

=

(3.3)

Of course, as in the case of the train, in order to determine the actual speed, the distance λo must

be known. This is easily obtained by measuring

H

T for

0

=

w

corresponding to (by for

example employing a space probe), measuring c using the independent out-and-back method,

and using these values in (3.2) to determine λ

o T

o. Establishing the value of λo using ) 0

=

H(wT and

an independently determined c may be viewed as calibration of the measurement apparatus; once

this is done, all light speed variations relative to the receding Earth can then be directly

determined by measuring

H

T and using (3.3).

In order to verify this method of determining variable light speed, we determine light

speed relative to the receding Earth by the direct substitution of measured values for

HoT ,T

and c

in the equation (3.3) for light speed. Thus using (3.2) in (3.3) yields

Page 8

8

H

o

H

o

R

T

cT

T

c

= =λ

(3.4)

Substituting in (3.4) the measured values Ts

o

944, 152

=

and s

H

2 .959, 152

=

=

c

T corresponding to

the increased period of Io [19] along with the independently determined

gives the relative light speed value

1

458, 792,299

−

ms

1

667,762,299

2 .959,152

944, 152458, 792, 299

−

=

×

=

mscR

(3.5)

Note that since

, second-order FLL contraction effects associated with the measurement of

cw<<

H

T are small and therefore do not significantly affect this result. We observe that the

experimentally determined light speed value in (3.5) is not c as the light speed invariance

postulate demands. The light speed in (3.5) is almost exactly equal to the classical value of

relative light speed value c

for the receding Earth, which using for the Earth

is

w

−

1

790, 29

−

=

msw

−wc (3.6)

11

668,762,299)790,29458, 792,299(

−−=−=

ms ms

Therefore for movement of the Earth directly away from Jupiter, the relative light speed

R c is

given by

wc

T

c

H

o

R

−==λ

(3.7)

For movement of the Earth directly towards Jupiter, the period

L

T of Io (which again is

the time between successive pulses) is observed on Earth and found to be less than To. The light

speed relative to the advancing Earth can be determined using

o λ and

L

T in the fundamental

speed equation for this system which is

L

o

R

T

c

λ

=

(3.8)

Substituting in (3.8) the measured values Ts

o

944,152

=

and s

L

8 .928,152

=

1

−

ms

T corresponding to

the shortened period of Io [19] along with c gives the relative light speed

value

458,792,299

=

1

255,822,299

8 .928,152

944,152458,792,299

−

=

×

=

mscR

(3.9)

Page 9

9

We again observe that the experimentally determined light speed value in (3.9) is not c as the

light speed invariance postulate requires. The light speed in (3.9) is almost exactly equal to the

classical value of relative light speed cw

+

for the advancing Earth, which

usingwfor the Earth is

1

790,29

−

=

ms

+ wc (3.10)

11

248,822,299)790,29 458,792,299(

−−=+=

ms ms

Therefore for movement of the Earth directly towards Jupiter, the relative light speed

R c is given

by

wc

T

c

L

o

R

+= =λ

(3.11)

On the basis of the experimentally demonstrated classical light speed variations in (3.7)

and (3.11) relative to the moving Earth, we conclude that the change in the period of the

planetary satellite Io measured by an observer on the Earth, is a direct indication of a change in

light speed relative to that moving observer. The results (3.7) and (3.11) directly confirm the

light speed predictions (1.11) and (1.12) of the Absolute Space Theory and falsify the light speed

invariance postulate of Special Relativity Theory. Additionally, these light speed variations

represent detection of movement of the Earth relative to the ether in the Earth’s approximately

uniform motion around the Sun, exactly the motion that Michelson and Morley failed to detect

also using light speed variation in their unsuccessful second-order experiment of 1887 [6].

4. Conclusion

The light speed invariance postulate that underpins Special Relativity Theory has not

been directly confirmed for one-way light transmission. For two-way light travel, the one-clock

out-and-back measurement of light speed on a moving platform always yields the value c and

this appears to confirm the postulate. This is reinforced by the failure to detect light speed

anisotropy in several one-way two-clock tests [10, 11]. However, these one-way two-clock tests

yielding c are flawed because of clock synchronization problems [5, 16]. Further, as shown in

this paper, the light speed invariance observed in the two-way one-clock measurement is an

illusion created by the compensating effect of the FLL contractions and consequent elimination

of platform speed

from the measured speed. By using a one-way one-clock measurement

procedure, we escaped the compensating effect of the FLL contractions as well as the clock

w

Page 10

10

synchronization problems and thereby succeeded in revealing variable light speed crelative

to a moving frame.

w

±

c

We demonstrated that in the Roemer experiment involving the moving Earth and an

occulting light source Io, changes in the speed of light relative to the moving Earth w

±

do

occur and are measurable and result in observable variations in the period of Io as seen on Earth.

The light speed variation established in the Roemer experiment directly contradicts Einstein’s

Light Speed Invariance Postulate. Therefore this postulate, which results from what Will

([20],p247) referred to as “Einstein’s revolutionary insight” and which Kaku ([21],p82)

described as “one of the greatest achievements of the human spirit”, is wrong. As a result Special

Relativity Theory, which is based on this postulate and which also predicts it, collapses [22]!

In addition to the falsification of the light speed invariance postulate, the measured light

speed anisotropy in the Roemer experiment represents detection of ether drift and confirms the

existence of the preferred frame of the Absolute Space Theory [16, 17] in which light propagates

at speed c. This detection of the movement of the Earth relative to this preferred frame or ether in

the Earth’s approximately uniform motion around the Sun was recently reported by Gift [23]

based on light speed variation in the Roemer and Doppler experiments. The existence of this

preferred frame is consistent with the absolute speed measurement of the Earth arising from

anisotropic measurement of the cosmic microwave background radiation [24] and the apparent

determination of absolute motion in experiments by Marinov [25] and Silvertooth [26].

In light of the incontrovertible revelation in this paper of light speed anisotropy occurring

in the physical world and the consequent invalidation of Special Relativity Theory, we urge the

scientific community to reject the century-old relativistic doctrine of Albert Einstein with its

many paradoxes and contradictions and return to the absolute frame of the causal ether embodied

in the space-time framework of the modern Maxwell-Lorentz Absolute Space Theory [16, 17].

The luminiferous ether, whose existence was accepted by all scientists up to the end of the 19th

century but later abandoned because of the failure of the 1887 experiment to detect it, is real and

should now be the focus of exhaustive scientific investigation.

Page 11

11

References

1. Einstein, A. On the Electrodynamics of Moving Bodies, in The Principle of Relativity by

H.A. Lorentz, A. Einstein, H. Minkowski and H. Weyl, Dover Publications, New York,

1952.

2. French, A.P., Special Relativity, Nelson, London, 1968.

3. Rindler, W., Introduction to Special Relativity, Clarendon Press, Oxford, 1991.

4. Williams, W.S.C., Introducing Special Relativity, Taylor and Francis, London, 2002.

5. Zhang, Y.Z., Special Relativity and its Experimental Foundations, World Scientific,

Singapore, 1997.

6. Michelson, A.A. and Morley, E.W., On the Relative Motion of the Earth and the Luminiferous

Ether, Am. J. Sci. (3rd Series) 34, 333-345, 1887.

7. Kennedy, R.J. and Thorndike, E.M., Experimental Establishment of the Relativity of Time,

Phys.Rev., 42, 400-418, 1932.

8. Brillet, A. and Hall, J.L., Improved Laser Test of the Isotropy of Space, Phys. Rev. Lett., 42,

549-552, 1979.

9. Hils, D. and and Hall, J.L., Improved Kennedy-Thorndike Experiment to Test Special

Relativity, Phys. Rev. Lett. 64, 1697, 1990.

10. Gagnon, D.R., Torr, D.G., Kolen, P.T. and Chang, T., Guided-wave Measurement of the

One-way Speed of Light, Phys. Rev. A 38, 1767, 1988.

11. Krisher, T.P., Maleki, L., Lutes, G.F., Primas, L.E., Logan, R.T., Anderson, J.D. and Will,

C.M., Test of the Isotropy of the One-way Speed of Light Using Hydrogen-Maser Frequency

Standards, Phys. Rev. D 42, 731, 1990.

12. Ives, H.E., Revisions of the Lorentz Transformations, Proceedings of the American

Philosophical Society, 95, 125, 1951.

13. Ives, H., The Fitzgerald Contraction, Scient. Proc. R.D.S., 26, 9, 1952.

14. Maciel, A.K.A. and Tiomno, J., Experiments to Detect Possible Weak Violations of Special

Relativity, Physical Review Letters, 55, 143, 1985.

15. Mansouri, R. and Sexl, R.U., A Test Theory of Special Relativity: I. Simultaneity and Clock

Synchronization, General Relativity and Gravitation, 8, 497, 1977.

16. Levy, J., From Galileo to Lorentz…and Beyond, Apeiron, Montreal, 2003.

Page 12

12

17. Selleri, F., Recovering the Lorentz Ether, Apeiron, 11, 246, 2004.

18. Ives, H.E., The Measurement of the Velocity of Light by Signals Sent in One Direction,

Journal of the Optical Society of America, 38, 879, 1948

19. Saito, Y., A Discussion of Roemer’s Discovery Concerning the Speed of Light, AAPPS

Bulletin, 9, 15, 2005.

20. Will, C.M., Was Einstein Right? Basic Books, New York, 1986.

21. Kaku, M., Hyperspace, Doubleday, New York, 1995.

22. Gift, S.J.G., The Invalidation of a Sacred Principle of Modern Physics, Physics Essays, 17, 3,

2004.

23. Gift, S.J.G., The Relative Motion of the Earth and the Ether Detected, Journal of Scientific

Exploration, Vol.20, No.2, 2006, pp.201-214.

24. Smoot, G.F., Gorenstein, M.V. and Muller, R.A., Detection of Anisotropy in the Cosmic

Blackbody Radiation, Phys. Rev. Lett. 39, 898, 1977.

25. Marinov, S., New Measurement of the Earth’s Absolute Velocity with the Help of the

“Coupled Shutters” Experiment, Progress in Physics, 1, 31, 2006.

26. Silvertooth, E.W., Experimental Detection of the Ether, Speculations in Science and

Technology, 10, 3, 1987.