SELF

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S.B. Karavashkin and O.N. Karavashkina

Having cleared this insignificant nuance, let us return to comparing the predictions of classical and relativistic conception. We should mark, the sign inversion is typical also for relativistic solutions, only in this case it is caused by the sign changed before cos   in general expression (11). Given this, the relativistic formula for longitudinal Doppler effect will be

Basically, mere mathematically we can continue (18), representing

With it (18) will take the form

We can compare the yielded expression (20) with classical (15).

In Fig. 5 we show typical regularities that describe the longitudinal Doppler effect from the view of relativistic conception (blue curve) and classical conception (lilac curve).

Fig. 5. Relative variation of frequency received by observer moving centrally as to the source, against the ratio of observer's speed to that of light. The blue curve shows the relativistic prediction, and lilac curve - classical

Let us draw our attention that at large speeds of observer, predictions of relativistic and classical formalism considerable differ only for the case when observer moved towards the source, in Fig. 5 it corresponds to the negative values of v/c. Should the divergence were the matter of principle, as relativists claim, it would concern to both branches of curves. But in this case, when the observer moved towards the source, the relativistic conception predicts an unlimited growth of frequency of received signal with growing speed of observer, while the classical conception predicts only doubling frequency. But with the source moving from the observer, the curves, though with large error, replicate each other. At the speed equal to that of light, the frequency in both cases vanishes.

Such unlimited growth of frequency in relativistic conception is caused by the time transformation claimed by this conception in accordance with Einsteinian formula

It follows from (21) that the frequency of received signal grows without limit because, when the observer's speed becomes equal to the speed of light, his clock must simply stop and all events which he observes have to merge into one event. "To the observer who approaches some source of light with the speed of light c the source will seem infinitely intensive" [4, item 7, p. 27].