V.5 No 1

55

Classical transverse Doppler-effect

One more important property of classical transverse Doppler effect is, the rate of effect decrease (corresponding to the rate of tending v/c   to 1) grows with growing frequency of source signal, and this is clearly seen in Fig. 8. In relativistic formalism this relation also is not present, since from general expression (11) under condition (27) we have

As we see, relativistic formalism predicts constant transverse effect at any aimed distances and at all frequencies of source radiation.

But what is, in its essence, the transverse effect as such? As we revealed before, the concept of time arises in presence of events changing for the observer. The same with time intervals. To register the time interval, we have to have two different events which are provided by sequential pulses sent by the source. With it, if the observer moved as to the source, he registers events as light pulses at different points of space, one of which he takes as the basis to compare with the second event. Hence, for example, having registered first pulse before the normal from the source to the direction of his motion, the observer can register the second pulse both before this normal and after having it passed. This depends only on, with which frequency the source sends pulses. But this affects the relation of distances which beams pass until crossing with the observer's trajectory - this means, it affects the Doppler effect as the whole.

The same in case of transverse Doppler effect. Having registered the angle by condition (27), we fixed the instant at which the observer received first of two signals of the source. But second signal will cross the observer's trajectory already not perpendicularly, and this angle depends on pulse frequency sent by the source. Proceeding from this, we have to expect that with growing frequency of source signal, the transverse Doppler effect will fall, and frequency of signals received by observer will monotonously approach the frequency of source signal. Just this we see in Fig. 9, where the relative frequency of signals registered by observer is shown against the frequency of source signal.

Fig. 9. Relative frequency of signals '/ registered by observer, against the frequency of source signal at = / 2 and H = 1 km, for different ratios of observer's speed to the speed of light

In case of transverse effect we also see that the regularity of ratio of received frequency to the frequency of source signal depends on the frequency of signal of the source as such. To the point, just from this there follows the cause, why the transverse Doppler effect has finite value at zero aimed distance. Actually, having received the first signal in the coordinate origin, the observer has displaced proportionally to his speed along the axis x. At zero aimed distance, the second signal from source located in the coordinate origin has to 'catch up' the moving observer, stretching with it the time interval between pulses received by observer. This is just the transverse effect at zero aimed distance whose presence we described above.

Thus, it is even phenomenologically seen: dependence of transverse Doppler effect on the source frequency follows from the very pattern of change of events that determines the time interval registered by the observer. We see here no reduction of space-time. Moreover, should such transformation take place, it would add to this phenomenology of processes, making them more complicated. While in relativistic conception we see a simple substitution grounded on outer likeness of mathematical formulas and nothing else. Deeper analysis immediately shows basic differences which cannot be reduced at small speed of observer to negligibly small quadratic terms. And this analysis shows classical description of transverse Doppler effect fully consistent with the phenomenology of this effect - and full discrepancy of relativistic substantiation of this phenomenology. Unambiguous conclusion follows from this: it is incorrect to model transverse Doppler effect on the basis of relativistic premises of space-time reduction.