SELF

46

S.B. Karavashkin and O.N. Karavashkina

On transverse Doppler effect in classical formalism

S. B. Karavashkin and O.N. Karavashkina

Special Laboratory for Fundamental Elaboration SELF

187 apt., 38 bldg., Prospect Gagarina, Kharkov, 61140, Ukraine

phone +38 (057) 7370624; e-mail: selftrans@yandex.ru , selflab@mail.ru

On the basis of complete solution of Doppler shift of frequency received by moving receiver, noting non-central motion of receiver as to the source, we compare the properties of longitudinal and transverse Doppler effect predicted by classical and relativistic formalism. We show that complete statement of problem predicts the transverse Doppler effect in frames of classical formalism, but its properties considerably differ from relativistic predictions. In particular, the sign of effect predicted by classical conception is opposite to that relativistic. While just the classical approach is most fully consistent with the phenomenology of effect, while the relativistic approach is essentially problematic both in description of phenomenon and in consistency of functional regularity with the properties of transverse Doppler effect. We show that the main difficulty being the underpinning of relativistic interpretation is Fitzgerald hypothesis on whose basis have been built both Lorentz theory and Einstein's conception of constant speed of light in all inertial reference frames.

Keywords: special Relativity, Doppler effect, longitudinal Doppler effect, transverse Doppler effect, Michelson- Morley experiment, Fitzgerald hypothesis, phenomenology of time as physical phenomenon

Classnames by MSC 2000: 83A05, 83B05

Classnames by PASC 2001: 03.30.+p, 11.30.Cp, 43.28.Py

1. Introduction

At present in physics the mind has struck root that "for large velocities, the relativistic formula

(where ' is the frequency of signal received by the moving observer, is the frequency of signal radiated by stationary source, and v is the speed of observer - Authors) differs from the classical

This difference becomes even more clear when directions of light wave velocity and relative velocity v of two reference frames do not coincide; in particular, when they are perpendicular to each other. In accordance with classical theory, in this case Doppler effect does not take place at all, whilst in the relativistic theory it exists. So we can speak of new relativistic effect that often is called transverse Doppler effect" [1, p. 292].

In such kind of statements, it raises a mistrust that to find the relativistic transverse Doppler effect, the scientists use the model of non-central mutual motion of source and receiver, while the results are compared with the solution of classical problem of central motion of source and receiver, in which by the very statement of problem whatever transverse effect is impossible.

For example, Pauli [2] at all combines the finding of Doppler effect with the problem of light aberration and states it so. "Consider a very distant source of light L that is at rest in the reference frame K. The observer is in the frame K moving as to K with the speed v in direction of positive values of coordinate x. Let the line connecting the source of light and the observer form the angle with axis x in the frame K and, besides, let the axis  z be perpendicular to the plane that is determined by these two directions" [2, p. 36].

While the classical model has the shape [1, p. 122, Fig. 70], see Fig. 1.

Fig. 1. Calculation graph of classical Doppler effect

The models are clearly irrelevant. This makes necessary to consider, how much correct are the conclusions of such comparison. In this paper we will account the difference in models and compare the solutions yielded on a par. In this way we will answer some basic questions, and first of all - whether the transverse Doppler effect is possible in the view of classical formalism.