V.5 No 1

53

Classical transverse Doppler-effect

To understand it, let us try to adjust mathematically an equal-leg Michelson interferometer, accounting only the beam aberration, in supposition that aether wind is directed in perpendicular to the beam entering the interferometer. To begin, we will not change the inclination of mirrors, retaining them ideal and corresponding to Lorentz model. In other words, all reflecting mirrors will be strongly perpendicular to the axes of interferometer, and the semi-opaque mirror will be inclined by 45^o. And the beam will enter the interferometer at the aberration angle to the interferometer axis.

Therefore, the beam path will take the shape as shown in Fig. 7.

a) stationary reference frame

b) accompanying reference frame

Fig. 7. The beam paths in the interferometer at the basic positions of mirrors and entering beam inclination equal to the aberration angle; v is the speed of interferometer as to the aether

We see from the diagram that, first, the beams at basic positions of mirrors basically do not converge to one point. Second, beam paths are fully irrelevant to those on whose basis first Michelson and Lorentz and then relativists have yielded calculation formulas (22) and (23). If in order to converge beams, we begin to vary the angles of mirrors inclination, the pattern will become even more complicated and the more will not correspond to these formulas.

The more, if we begin turning the interferometer as to the aether wind, the beam paths also will change their arrangement as to each other. Righy noted it; Hedrick represented his calculation in Pasadena. On the basis of this calculation Righy concluded that "device rotation by 90^o in an ideal experiment causes absolutely no effect, since, despite exchange of distances passed by two beams, their locations at the same time also exchange; in this way the beam having longer path has the same relative position as to the beam having shorter path after rotation, as before. From this, the pattern of fringes after rotation cannot be differentiated from that before rotation" [7, Hedrick report, p. 149].

Did Lorentz know of it? Undoubtedly knew. Such were his own words: "Till today I believed considerations grounded on Fermat principle to be quite satisfying. But after Mr Hedrick's information it appears that result expected in the Michelson- Morley experiment numerically differs from that which we used to expect on the basis of classical theory. The numerical value of the second-order effect will differ from that calculated by Michelson. My version seems to me easier and straighter. However, we need to find, where is the difference in two ways. In case we choose the method different from Fermat, we would have to carry out a considerable work… As there is the discrepancy in results yielded by two methods, I am about to make detailed calculations as soon as possible" [7, from Lorentz speech, p. 160]. But he never did so. Further, relativists simply claimed Miller's results erroneous.

But if speaking, whether Lorentz knew of positive results of Michelson experiment, we have to draw attention to the fact that in the same his speech in discussion, Lorentz reproached that Miller was not enough attentive to the effect of full turn in the interferometer: "Now I would like to make few remarks as to Miller's experiment. I believe, there is a serious problem related to effect being periodic for a full turn of the instrument, which Miller dismissed, emphasising the importance of half-period effect, i.e., effect repeating with a half-turn of instrument, which is related to the issue of ether wind. Anyway, the effect of full period is much more than a half-period effect" [ibidem]. And he said it despite "the effect of full period is not new, it always was present in all experiments. It is also present in Michelson's primary observations" [5, Miller's speech, p. 169]. While "in presence of ether wind influence, there necessarily is present the full-turn effect by Hicks, and its presence can be thought one more evidence of presence of ether wind" [ibidem].

Thus, we see, the basis on which Fitzgerald advanced his hypothesis was not only ungrounded but formulated on the too simplified, incorrect model of processes in the interferometer. Just so relativists so much dislike to recall those discussions and developments of that time, in the early 20th century, and confine themselves to inaccurate derivations by Lorentz that never remade his calculation on whose basis he developed his transformation with reduced coordinates and time in moving reference frames.

From this the above inaccuracy follows that come to light at every step of relativistic conception. Namely so Einstein's special relativity never was put into consistence with the quantum field theory that, after the authors' intention, just had to describe the peculiarities of light speed constancy in all frames. This conception is mismatched with general relativity, too, as for its substantiation it needs the material space. Now we see, in description of longitudinal Doppler effect the relativistic conception also gives absolutely wrong predictions that simply were smoothed, because deeper analysis of corollaries of these predictions was omitted. Let us see now, how much true are predictions of relativistic theory as to transverse Doppler effect.