The Premise for Comparing Ether Theories to Relativity Theory
copyright 2010 D.M. Marett
There is plenty of literature available on how to calculate the predicted result of an experiment from a relativistic perspective. However, there is some confusion about what different ether theories would predict for the same experiment. Some researchers who believe that there must be a medium of space, reject ideas like the Fitzgerald-Lorentz contraction or Larmor time dilation as being unnecessary. Quite often, they also attempt to prove their point by suggesting that some experimental results must be false. Herein the approach is taken that by and large the experimental results of the myriad of interferometer tests and tests on relativity theory are true. Any ether theory that could possibly describe reality must then be able to predict these same results in all of these experiments. This is not such a far-fetched idea, since if we examine the history of the development of relativity theory, we realize that the theory borrowed many ideas from ether theory (i.e. the work of Maxwell, Lorentz and Larmor) but put them in a slightly different mathematical form. Because they are so closely related, ether theory usually predicts the same result as relativity theory for most experiments. To highlight this idea, I quote from relativist A.A. Tyapkin from his 1973 paper "On the Impossibility of the First-Order Relativity Test",
"One of the first theoretical explanations for the failure to discover the "ether wind" developed by LORENTZ in a sufficiently complete form in 1904 was in fact, only another way of describing the relativity theory differing from the later one only by the acceptation of the agreement on a single simultaneity of events for two reference systems being in a state of relative motion. As is known Lorentz's approach to the explanation of the negative result of Michelson's experiment retains the presentation of the difference of the velocities of light along an opposite reference system motion, while the impossibility to observe the absolute motion appears as a result of taking into account the effect of the second order of the relativistic contraction of space cuts. It is important to clear out that Lorentz's approach not only should be acceptable for explaining Michelson's experiment, but also should be a consistent system for describing relativity effects for any possible experiments. Many scientists have stated quite justifiably the absence of an "experimentum crusis" for Lorentz theory and special relativity." 
It is precisely because relativity theory retained the ideas of Lorentz contraction and Larmor time dilation from Lorentz Ether theory (although with a different meaning), that relativity theory arrives at the same prediction as ether theory for the same experiment. Likewise, any new or modified ether theory needs to retain these ideas to be consistent with the experimental results. An example is the Ives and Stillwell experiment  - the reduction in the frequency of the canal rays from the high speed protons was proclaimed as being evidence of relativistic time dilation, conversely Ives himself stated, rightly so, that this was instead evidence for Larmor (mechanical) time dilation and a physical Lorentz contraction based on Lorentz ether theory. The two theories agree with the results, but for different reasons. To be consistent with the results, the ether theory requires Lorentz contraction and mechanical time dilation to be true. An ether theory without these two effects would be proven to be false by the same experiment.
Tyapkin goes on to argue that Lorentz's approach could be proven to be groundless if an experimental comparison of the light velocities in opposite directions was possible. The opposite is also true - relativity theory could be proven wrong if such an experiment could be devised. For relativists, by definition, such an experiment is impossible due to issues involving the synchronization of clocks at each end of the path. Relativists then argue that relativity theory is the theory of choice because it is "more convenient" or more "self-consistent". It is also has been argued that something which is impossible to detect by definition, cannot possibly exist. To quote J.P. Leahy:
"Such is the origin of Einstein's statement ``God is slick, but He ain't mean'' It was made in response to a claim in 1927 that a tiny "ether drift" had finally been detected. Einstein rejected this out of hand: to have an ether which was almost undetectable (requiring special relativity to be almost correct), but yet present (undermining the foundation of relativity) seemed absurd to Einstein, and indeed his intuition proved right. But the comment can be taken more generally as an emotionally powerful justification for the central idea of relativity theory: that what cannot be measured, does not exist. God would not be malicious enough to hide an important part of reality in a way that we cannot reach; if no experiment can reveal the true rest frame of the ether, then there is no ether, and no frame of absolute rest. "
From these statements we can take that relativity theory has never proved that an absolute rest frame for light (the ether) does not exist - rather, it has declared that it is by definition impossible to detect, and as such, does not exist!
We do not agree - in the current world where a universal rest frame has been shown to exist (the Cosmic Microwave background (CMB) radiation) which is now used as an astronomical reference frame for the motion of all objects in the universe, and where clock synchronization has been shown to be possible (i.e. with GPS satellites), it is becoming more and more possible to distinguish between the two theories, and relativity theory, now over 100 years old, is becoming increasingly pressed in its own defence. Further, the idea that because something cannot be measured it does not exist, is an arbitrary scientific justification. Quantum Electrodynamics uses the opposite idea - that virtual particles can exist because their existence is too fleeting to detect due to Heisenberg's uncertainty principle (these virtual particles can also break the law of conservation of energy for the same reason), or the similar idea that particles are composed of quarks even though it is impossible to isolate a quark - this concept in physics is applied in a contradictory and inconsistent fashion as justification for whatever theory is in vogue, and is undermining the credibility of physics as a whole.
It is precisely because of this that we feel current theoretical physics is going in the wrong direction, it is approximating the truth mathematically but failing to describe physical reality in a deterministic form. We reject the notion that an experiment is impossible, but rather accept that it is difficult. With sufficient progress in technology, theories once believed to be outside the realm of practical testing will surely succumb to experimental rigor. Theories obeying the Lorentz transformations (ether theories, relativity theory) should be experimentally distinguishable and capable of being proven true or false.
But to begin this task, we must first understand how ether theory can be consistent with all the experimental evidence to date. We will start with an explanation of how there could be a medium of space (a preferred frame for light) and light would still appear to be C to all inertial observers. This explanation is largely based on effects that were well described immediately prior to the advent of relativity, such as the Fitzgerald-Lorentz contraction and the Larmor time dilation effects.
1) Explanation of why the speed of light is the velocity that it is:
We start with the idea that space is a medium of some kind. This was James Clerk Maxwell's basic assumption when he theorized that light and electromagnetic waves are the same thing, waves in a medium of space.
Let's look at a simple equation describing the velocity of sound in a medium capable of supporting transverse waves:
where Ctrans is the velocity of sound in the medium, and G is the shear modulus, and r is the density. This is identical to the equation referred to by Maxwell in describing space (Maxwell calls shear modulus the "coefficient of transverse elasticity" - See James Clerk Maxwell "On the Physical Lines of Force." P. 499. )
It follows then that the speed of light has a specific velocity because this is the velocity of transverse waves in the medium of space, and this velocity is a function of the elasticity and density of this medium. Conversely, if space was a true vacuum, there would be no specific velocity attributed to light, since the only property of emptiness is that it has no properties.
2) If light is a transverse wave in a medium, how do we calculate the speed of light with respect to a moving observer?
If we were to imagine that we the observer are immersed in this medium, and light waves are waves in this medium, and we start to move at some velocity, what would the speed of light be with respect to us?
We start with the simple addition of velocities:
If light is moving at velocity C with respect to the medium (the page) and I am moving at velocity A also with respect to the medium, then the velocity of light with respect to me is simply C- A ( the difference). Similarly, if I am moving in the opposite direction at velocity B, then the difference is now C+B.
This works well when all relative velocity vectors are parallel, however, when they are not, we must use a triangle diagram and the Law of Sines or the Law of Cosines to work out the final velocity. We place the vectors head to tail with the angle between them being q. By the law of cosines:
Now C, V and L correspond to the time taken to cover each path. Since V points against C by a small angle, the time to traverse L is less than the time to traverse C. From the perspective of the observer moving along V, since the time L is less, then the observed velocity of light is more than C.
To derive the resultant velocity of light then with respect to the observer, we use the equation:
Where C' is the resultant perceived velocity of light with respect to the observer moving through the medium at velocity V and angle q with respect to the light. The law of cosines is built into this equation. Lets calculate some examples:
The observer and a laser are on the Earth. The laser is pointing south. If the observer runs with the laser west at 3m/s, what is the velocity (C') of the beam of light with respect to the observer?
The angle q between the beam and the velocity of the runner is 90 degrees.
v=3 m/s, c = 3E8 m/s
Using Eq. 2 and plugging in the values: C' = 299999999.999999985 m/s.
One would imagine that if the measured velocity of light as seen by a moving transverse observer was less than C, then it should be possible to detect ones motion. However, as pointed out in "Time Dilation - and how it could be an Illusion." the clock of the runner (time') will mechanically slow by exactly the same amount, so the forward and return time of the light will be measured to be exactly C. This is shown in example 2:
Example 2: time' = time x (1-v2/c2)1/2 = 1 x [1- 32/(3E8)2 ]1/2 = 0.99999999999999995 seconds.
c' / time' = 299999999.999999985/ 0.99999999999999995 = 300000000 m/s
After accounting for the slowing of the clock, the velocity is now seen as exactly C. This mechanical slowing of the clock is a conspiracy of light - it is a self-correcting process of light where the obvious change in the apparent velocity of light due to the transverse velocity of the observer is perfectly cancelled by a change in the speed of light in the clock of the observer, due to it moving at the same velocity. This was recognized early on by Joseph Lamor (1897).
The observer and a laser are on a plane. The laser is pointing west. If the observer flies with the laser in a plane west at 300m/s, what is the expected velocity (C') of the beam of light over the path from the back of the plane to a mirror at the front?
v= -300 m/s, (since he is flying in the same direction as the beam)
c = 3E8 m/s
angle q = 0 degrees
Using Eq. 2 and plugging in the values: C' = 299999700.0000000 m/s
The time is longer since the mirror is receding from the beam, so the velocity appears to be slower.
If the beam is sent from the mirror to the back of the plane, then C' = 300000300.0000000 m/s
since less time has elapsed due to the observer approaching the oncoming beam.
Thus the one way velocity of light appears to be C+/- v, depending on which was he flies.
However, our observer can't actually measure the time it takes for light to cover the distance from start to finish, since he is at the back. The only way he can do that is to reflect the light from the mirror at the front end of the plane and measure the two way trip. In this case, the velocity is:
(299999700.000 + 300000300.000)/2 = 300000000.000 m/s
The average velocity is C. This is a conspiracy of light (first order) in that although the one way speed of light is not C, the two way speed of light averages to C since the observer cannot be at the front and back at the same time.
However, if we look at the time in detail for the round trip, (with L = 1 m) it is actually:
t = L/(c-v) + L/(c+v) = 0.000000006666666666673330 seconds ( plane is moving at 300m/s)
which differs from 2L/c = 0.000000006666666666666670 seconds (plane is not moving)
The time is a little longer so the speed of light measured is slower by:
C' = 0.9999999999990 x C = 299999999.99970 m/s (A)
This small difference should be detectable, just like in example 2. However, two effects come in to play to obscure this small difference:
1) mechanical time dilation . Since the observer is flying at 300m/s his clock runs mechanically slower by:
time x (1-v2/c2)1/2 = 0.99999999999999995 seconds
So he should measure the 2 way speed of light as actually
C' = 299999999.999700 m/s / 0.9999999999995 s = 299999999.99985 m/s (B)
2) The Lorentz contraction. With the Lorentz contraction, the length of the path is also contracted by:
L x (1-v2/c2)1/2 = 0.9999999999995 x L
Thus the measured speed of light is further corrected from (B) by:
299999999.99985 m/s / 0.9999999999995 = 300000000.00000 m/s
Thus the two way measured speed of light is C, the difference being obscured by two conspiracies of light: 1) the mechanical time dilation and 2) the Lorentz length contraction, both second order effects.
The Equations of H.E. Wilhelm:
H.E. Wilhelm  wrote a paper in 1992 (Aiperon) that attempted to explain the results of two famous historical experiments on the propagation of light: The Fizeau experiment (1851) and the Hoek experiment (1868). The thing that was important about these two experiments is that they attempted to use dielectric media with a refractive index > 1 to affect the propagation velocity of light and thereby make ether drift visible in the experiment. The set of equations used by H.E. Wilhelm are derivable from Lorentz's theorem of corresponding states. In 1892 Lorentz wrote an extensive treatise on the electrodynamics of moving bodies, and was able to show that for a wave propagating along the direction of motion of a frame moving with velocity v, must have a velocity c/n - v/ n2 in that frame (to order v/c). Hence, the wave velocity with respect to the ether would be c/n - v/ n2 + v = c/n + v (1-1/ n2) in accordance with the Fresnel coefficient. This new view of Lorentz suggested that it
is the waves that are partially dragged and not the ether. The electric field of the wave displaces the electrons in the refractive medium creating a common motion. The moving electrons are then subjected to an additional Lorentz force from the magnetic field of the wave. Both of these effects reduce the velocity of the wave by v/ n2 from the value of c/n when the medium is at rest in the ether (5). Wilhelm devised the following equation to explain both the experiments of Fizeau and Hoek by calculating
the Doppler shifted phase velocity in a moving (v) dielectric (i.e. Fizeau) with ether velocity (w) (i.e. Hoek):
Generalized Wilhelm Equation:
The important thing about this equation is that it provides a method of calculating the final velocity of the light in a media with a refractive index >1 including the velocity of the ether drift. These velocities do not simply add and subtract in a Galilean fashion when R.I .> 1. In glass for example, the measured speed of light C' with an ether wind v would be:
C' = c/n +/- v/n2, where n = 1.47 rather than C' =( c +/- v) / n
If the dielectric media is moving rather than the ether frame, the equation becomes:
C' = c/n + ( 1-1/ n2 )v ,
where v is the velocity of the dielectric. This is latter expression is essentially the equation that Fizeau had worked out.
Wilhelm combined these two equations together into an equation to calculate the velocity of light in any path of an interferometer (Eq. 3) or the propagation time of light in any path of an interferometer (Eq. 4). However, the Wilhelm equation uses simply the cos of the angle between the velocities as a factor, which is inaccurate at second order. To explain, if we return to example 1 above, Wilhelm's equation would give us V = c + wcosf/n2. Since the angle is 90 degrees, and the refractive index n = 1, and the velocity
w = 3m/s, the equation reduces to V = c + 3*(0)/1 = c. As can be seen, the effect of the transverse velocity of the observer (i.e. when the observer is moving perpendicular to the light beam direction) does not figure in the Wilhelm equation, which would be C - 1.5 E -8 m/s, a very small second order difference, but very relevant in sensitive optical experiments such as the Michelson and Morley experiment. Nor is the counteracting effect of mechanical time dilation taken into account. Further, when the velocity of the observer and the beam of light are parallel, wcosf = w (since cosf =1) and if we were to simply average the velocities forward and back along the path L, we would get an average velocity of C and would not see the small second order time difference shown in example 3 that leads to the round trip velocity of light being 299999999.99970 m/s rather than C.
We therefore modify the equation as follows by adding in the law of cosines equation developed in Eq. 2. Further, we must calculate the result in terms of propagation time along the path rather than by calculating the velocity along the path, since we cannot simply average the velocities without taking into account that the effective path L is different from the perspective of the light beam fixed to the medium.
Our generalized propagation time equation for a light beam as measured by an observer is:
The sign of the velocity (v) depends on whether the velocity is that of the observer, or that of the apparent ether wind and the observer is taken to be stationary.
The effect of mechanical time dilation is not part of this equation, and is applied later as required. For interferometer experiments where we are looking only at the phase difference between different beams of light, mechanical time dilation cancels in the result since both beams are observed in the same velocity frame at the detector.
The equation simplifies to:
for most interferometer experiments excluding the Fizeau experiment.
The idea of using the relation C' = c/n +/- v/n2 is also consistent with Sagnac interferometers. The classic Sagnac equation:
Dt = 4Aw = 2(pi)r * 2v
can be re-expressed in the equation used by Ruyong Wang  to describe the Sagnac interferometer:
Dt = 2vDL/c2.
Wang points out that: "The travel time difference Dt = 2vDL/c2 in our experiment is independent of the refractive index n, as in the Sagnac type experiment."
This makes sense if c/n +/- v/n2 is added in as below:
This is because n2 cancels out in the numerator and denominator, making the Sagnac device independent of refractive index n.
We have developed a generalized equation (Eq. 5, Eq. 6) that can be used to calculate the propagation time and velocity for a beam of light in any arm of an interferometer, on the basis that there is at least one preferred frame of reference for the light (i.e. an ether). The equation takes into account:
1) refractive index of the arm,
2) the motion of the arm with respect to the ether at any angle
3) the motion of the dielectric of the arm with respect to the apparatus at any angle
4) any Lorentz contraction of the arm
This equation can now be applied to the various experimental results of interferometer test carried out in the last 150 years to see if theories that call for a preferred frame of reference, such as the Lorentz Ether Theory (LET), and Gravitational Frame Dragging Theories (GFD) yield the correct result. The results obtained can then be compared and contrasted to the predictions of relativity theory for the same experiments. This is performed in the next series of papers on this website.
Tyapkin, A.A., (1973) "On the Impossibility of the First-Order
Relativity Test." Lettere Al Nuovo Cimento Vo. 7, No. 15, 760-764.
1) Tyapkin, A.A., (1973) "On the Impossibility of the First-Order Relativity Test." Lettere Al Nuovo Cimento Vo. 7, No. 15, 760-764.
2) Herbert Ives and G.R. Stillwell (1938) An Experimental Study of the Rate of a Moving Atomic Clock. JOSA 28,No.7, 215-226.
E. Wilhelm, (1992)
Galilei Covarient Electrodynamics of Moving Media with Applications to
the Experiments of Fizeau and Hoek. Aiperon 15,1-6.
3) H. E. Wilhelm, (1992) Galilei Covarient Electrodynamics of Moving Media with Applications to the Experiments of Fizeau and Hoek. Aiperon 15,1-6.
Wang, et.al, (2003) "Modified
Sagnac experiment for measuring travel-time difference between
counter-propagating light beams in a uniformly moving fiber",
Physics Letters A, 312 7.
4) Ruyong Wang, et.al, (2003) "Modified Sagnac experiment for measuring travel-time difference between counter-propagating light beams in a uniformly moving fiber", Physics Letters A, 312 7.
5) Janssen, Michel, Stachel, John, The Optics and Electrodynamics of Moving Bodies. 2004.