Dear Eckard
You: The desperate search for any explanation to the unexpected result led to the hypothesis by FitzGerald, by Lorentz, and by others of a length contraction to the arm ACA with far reaching implications...
Length contraction followed naturally from the idea that the spherical field of an electron at rest, turns out to be an ellipse when the charge moves. This was calculated in 1887-8 by Oliver Heaviside who was collaborating with FitzGerald. FitzGerald realized that if matter is composed of charges and their fields contracts in the direction of motion then an ensemble of charges (a body) should contract. Larmor was also in contact with FitzGerald and arrived at the same conclusion in his work published in 1900. Lorentz, for the same reasons as FitzGerald, arrived at the same conclusion independently some years later 1902. Marmet, instead, argued that bodies should expand. This conclusion I found it totally flawed.
You: The decisive step... ...You made then the same mistake as did M&M and perhaps everybody else since then.
I didn't make a mistake. The calculations are correct but they are restricted to the illustration of the most relevant aspects of the experiment. The article clearly states that I'll be dealing with the physics surrounding the MMX, not detailed calculations. The complete calculations should include gravitational and temperature effects, two angles (theta and phi) defining the orientation of the planes of the interferometer relative to the motion of the earth (see H. Munera et al., Mazur et al.), the refraction of the light when they pass through the mirrors, the calculations of the times from the half-silvered mirror to the detector, etc. If one consider all of this, we would have at least three kinematical variables, namely: v, theta and phi and one equation. Therefore the equation becomes unsolvable (theta and phi basically represent the motions of the earth), thus ruling out the main aim of the experiment. Capria et al. carried out more comprehensive calculations considering the propagation of light even from the half-silvered mirror to the detector (1992MMCapria_FoundPhys_24_885).
You: Did you find an error in my hopefully compelling reasoning? I think so. See below.
Should I question my sanity for that reason? Perhaps.
You: If I am correct, and Michelson's expectation was wrong from the very beginning, at least with vacuum, then I agree with Marmet concerning the due consequences. I tend to agree with you and also with Cahill on that the absolute space was not refuted by any MMX.
I: As I argue in my essay, whether the result of the experiment were positive or negative, the outcome wouldn't be evidence of the existence or non existence of absolute space. According to the scientific beliefs of that time Michelson and Morley naively (as judged in retrospective) thought that the absolute space could have been detected.
I don't have much time to reproduce your calculations, so, I'm assuming that they are correct. For me, it suffices to follow your rationale which is the most important part. Now, I'll give you my comments on your "Mistake".
If I understood well, you found an additional correction to the transversal rays which disagrees with that one calculated by Michelson and Morley in 1886-7. According to you, the time require for the ray in the transversal direction to complete a journey from the half-silvered mirror A to the mirror B and back to A is given as: t_ABA = (2d/c)/(1+r^2). Whereas in the longitudinal direction the round trip time is: t_ACA = 2d/c(1-r^2). According to your words: "=is too small as to be measured. This explains the null result." Actually, I don't understand why you make such affirmation.
If we carry out the time difference between the two rays in those journeys, neglecting terms of 4 order, we'll find that: t_ABA-t_ACA =(2d/c)/(1+r^2)-2d/c(1-r^2)=(2d/c)2r^2 (twice the accepted value). If we considered a 90 deg rotation the maximum time difference would be the double of the previous result, that is: (8d/c)r^2. This is 4 times larger than the value find in most textbooks. So, I don't understand why you affirm that the result is too small.
Now, in the case of the MMX the arms of the interferometer are of the same length, however, for the Kennedy-Thorndike the length of the arms is different, and in this case your calculation would not account for the null result. Moreover, one has to consider the angular dependence. Recall that the apparatus of 1887 was able to rotate. This rotation will induce a phase shift (see mazur and capria et al.), whose contribution to the phase shift is of more relevance than the fringe shift caused by the variations of the speed of the earth.
You: In that sense a photon seems to be as fictitious as a phonon, correct?
No
You: You were certainly not aware of the three papers by Feist.
No, I was not aware of Feist's papers and not of many other authors, it's impossible to be aware of everybody. So, why do you make emphasis on that?
Israel