SELF

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S.B. Karavashkin and O.N. Karavashkina

The same with the Fizeau's experiment.

"In 1851 Fizeau corroborated the Fresnel's formula of the drag factor by way of experiments with the light propagation in moving water. Michelson and Morley (1878) found a full agreement with Fresnel's formula too. Not so long ago (Mandelschtam lectured this in 1933 - Authors) the drag factor was highly accurately measured by Zeeman. His device some differed from Michelson's, in accordance with it the theory has been refined. Here the result also completely corroborated the Fresnel's formula. I would mention, in the Relativity the Fresnel's 'drag factor' is simply a corollary of the relativistic law of adding the velocities" [Mandelschtam: 11, The first lecture, p. 96].

If noting that Mandelschtam was an unconcealed and insistent relativist, the positive result of Fizeau's experiment is doubtless.

Thus the experiments to which Einstein referred could not justify his renunciation of the aether, as well as it was inadmissible to use only partially the relativity principle introduced by Mach and to ignore the experimental corroboration of the law by experience. However Einstein used this trick not only in introducing his postulates but in developing the whole his theory. He not only used it but has set this tone to all the followers of relativism. This is corroborated by many facts. In particular, consider briefly the Fresnel's drag factor by way of relativistic addition of velocities. As Mandelschtam stated above, according to the relativistic conception, the 'drag factor' follows from the simple relativistic summing the velocities. But to make the velocities addition possible, it is necessary, the source and observer to belong to the mutually moving reference frames. In the Fizeau experiment both the reference frames of the source and observer do not move relatively each other. So, if the light was not dragged by the medium, the velocity of water in the tube cannot affect the velocity of light propagation. Do the relativists know it? Undoubtedly. Here is what Mandelschtam writes of it:

"What should we require of the correct theory? We know beforehand that it will not satisfy the relativity principle: already the Fizeau's experiment teaches us so. For the stationary observer, the light velocity in the water at rest is c₁ , and in moving water c₁ + w(1 - n^-2)  (where c₁ = c/n , w  is the water flow velocity, and  n  is the water refraction factor - Authors). The experience tells so. But the relativity principle requires, for the observer moving together with the water, the light velocity to be  c₁ . But if the Galilee's transform was true, if it gave the true transition from the stationary system to that moving, then for the observer moving together with the water the velocity will be

not c₁ , i.e. the relativity principle is not true… Proceeding from this fact, we have to conclude that either Galilee's transform is true, then we cannot remain the relativity principle in electrodynamics, or the relativity principle remains its power, then we have to reject the Galilee's transform" [11, The fifth lecture, p.133- 134].

We possibly could consider to reject the Galilee's transform, should we have more solid grounds than simple juggling in summing the relativistic velocities made by the relativists. To clear the issue, let us see the standard derivation of such 'summing' presented by V. Pauli in his book "The theory of Relativity". First Pauli, conventionally for SR, obtains the formulas for the velocities addition in free space for the reference frame K '  moving relatively the frame K  with the velocity v  along the axis x . With it he obtains the known expression

Further, "supposing u'_x= u ' = c/n ;  u_x = u = V   and using (2), we yield

[Pauli: 12, chapter 1, item 6, p. 33- 34].

We can see that even Mandelschtam took the light velocity in a medium equal to c₁ = c/n , while in this derivation only u'_x  but not c  in the denominator has been transformed in order to account the medium! This means, the substitution was made only partially. If we transform (2) correctly, and given the light velocity varying in the medium, we will yield

We see from (4) that with the correct operation, the light velocity in the stationary and moving reference frames remains constant, and not approximately but strong. This result is quite regular in the view of postulating that the light velocity is independent of the reference frame, and this fully coincides with the above Mandelschtam's computation that showed Einstein's (not Mach's!) relativity principle fully contradicting the Fizeau's experimental results. Thus, we have to reject not the Galilee's transform but relativity principle.