Talk:Transverse Doppler effect: Difference between revisions

Content deleted Content added
Line 22:
 
The transverse Doppler effect is by definition the effect which is observed when an observer being in uniform rectilinear motion observes an optical point source from the lateral direction under an angle of 90° with respect to his line of motion. Contrary to what the present author of the Wikipedia article on the transverse Doppler effect asserts (and contrary to what is stated in almost any textbook on SRT), the optical transverse Doppler effect is known since the year of 1842, when Christian Doppler published his famous article (translation from German) "On the coloured light of the binary stars and of some other celestical bodies - Attempt of a general theory including Bradley's theorem as an integral part". The article is contained in Doppler's collected papers (edited by H. A. Lorentz).
Bradley's theorem, also known as his law of velocity aberration or as his theorem for the addition of the velocity of light, reads: '''c' ''' = '''c''' - '''v'''. It defines the direction under which the wave fronts of a distant light source arrive at normal incidence. During the astronomical observation of a fixed star for example the observer's telescope, therefore, is aligned in the direction antiparallel to light's relative phase velocity '''c' '''. The transverse Doppler effect is observed during the short moment when the vector '''c' ''' is aligned precisely perpendicularly with respect to the velocity vector '''v'''. Bradley's theorem then leads to a rectangular vector triangle the hypotenuse of which is '''c'''. From the proportionality relation f ' / f = c' / c (where f ' is the Doppler shifted frequency of oscillation) and the Pythagorean law follows then the well known formula for the transverse Doppler effect, which in the framework of classical optics of moving bodies is exactly the same as in SRT. Now, a second order type of effect which is very well known already since the year of 1842 can hardly be a consequence of the phenomenon of time dilatation, as currently asserted in textbooks on SRT. The proposal that the transverse Doppler effect should be regarded as a pure effect of time dilatation was put foreward by Albert Einstein in a short note published in 1907 in ''Annalen der Physik''. In that note Einstein had by no means asserted that the transverse Doppler effect should be regarded as a novel phenomenon. He rather suggested indirectly that from now on the well known aberration effect should be re-interpreted as an effect of time dilatation. That his proposal should merely be regarded as a bad joke can best be seen from the fact that the Lorentz contraction would have to be simultaneously zero when the transverse Doppler effect is observed, because solely if this were the case the transverse Doppler effect could be interpreted as a "pure" effect of time dilatation. This, however, is by no means the case: The Lorentz contraction is zero not if '''c' ''' is perpendicular on '''v''', but rather if '''c''' is perpendicular on '''v''' , i.e., not if the inclination angle of the observer's telescope amounts to 90° but rather when the ''emission angle'' of the light ray amounts to 90° (because only then the relative velocity between source and observer passes through zero). In the latter case, however, a second order blue shift is predicted (both by classical theory and by SRT; for the case of SRT compare Pauli's encyclopaedical article - Pauli presented a formula for "his" transverse Doppler effect, which predicts a second order blue shift), not the desired second order red shift. It should be noted, however, that Doppler's original optical Doppler theory indeed requires modification because from historical reasons it ignored the transverse character of light waves. (It is strictly valid solely for longitudinal waves, such as acoustic waves). In the case of transverse waves (not solely of light waves) an additional aberration phenomenon enters the scenery, which may qualitatively be described as "velocity aberration of angular velocity". It is responsible for effects which in the framework of SRT are wrongly attributed to "time dilatation". If the former (classical) phenomenon is taken into account, the classical formula for the Doppler effect of transverse waves resembles very much the formula predicted circumstantially by means of SRT. Readers interested in this discussion should first consult a review of the classical optics of moving bodies, such as the one presented in Miller's historical account of SRT. Another suitable review article, written by one of the pioneers of SRT, Max von Laue, is available in ''Handbuch der Experimentalphysik''. The content of the "Textbook quotes" (Mould, d'Inverno) has nothing to do with reality, but is what authors of textbooks on SRT like to "believe" (since now one century). Other textbook authors try to "prove" that for the case of lateral oberservation the relation f' = f is obtained in classical physics (among them is J. D. Jackson). The "proof" works in fact in the case of a plane wave, but a point source, such as a fixed star, does not emit plane waves, and if one resorts to plane waves then this is from the very beginning only an approximation. A "proof" based on approximately valid relations is inacceptable, however. The confusion in the literature, which concerns the transverse Doppler effect, can be traced back to the circumstance that so-called "authorities" of SRT, like Max von Laue and Max Born, had misinterpreted (in blind trust) Einstein's proposal of 1907 and had asserted in their textbooks indirectly (Max von Laue) or directly (Max Born) that the transverse Doppler effect is due to "time dilatation". Later textbook authors then relied on these "authorties". In the many editions since 1932 of the textbook on theoretical physics by Joos the erroneous interpretation of Einstein's proposal of 1907 leads to a direct contradiction. Thus, in the section on the acoustic Doppler effect Joos writes down correctly the aberration law valid in acoustics. Moreover, he also states explicitely the formula for the relative phase velocity valid for the special case of lateral observation. About ten pages further on, in the section on the relativistic Doppler effect, Joos then, however, states that in acoustics the relation f' = f is strictly valid for lateral observation from a moving platform. [[User:84.154.74.1|84.154.74.1]] 19:07, 13 April 2006 (UTC)[[User:KraMuc|KraMuc]] 09:51, 15 April 2006 (UTC)