1. Systematic approach to the relativistic Doppler effect based on a test theory
- Author
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Choi, Yang-Ho
- Subjects
Doppler effect -- Research ,Special relativity (Physics) -- Research ,Physics - Abstract
Numerous experiments have been carried out to validate the Lorentz transformation or to find possible violations of Lorentz invariance, based on test theories to test special relativity. The test theory of Mansouri and Sexl (MS) provides a general framework for the transformation of inertial frames, presuming a preferred system of reference. Based on the MS framework, this paper systematically approaches the relativistic Doppler effect such that its dependency on transformation coefficients and parameters can be investigated. The Doppler effect is formulated in a complex Euclidean space where time is represented with imaginary numbers. Two formulae of the Doppler effect, which have been derived in an arbitrary transformation within the MS framework, are presented: one between an inertial frame and the preferred one and the other between arbitrary inertial frames. It is shown from the former formulation that the Doppler effect is independent of the synchronization of clocks, which implies that the Doppler-shifted frequency in the absolute synchronization is the same as that in the standard synchronization. The latter formula can allow us to find Doppler shifts without information on the velocities of inertial frames relative to the preferred frame. Exploiting these theoretical results, we examine the transverse and the longitudinal Doppler effects in detail. Key words: relativistic doppler effect, wave vectors, test theory, clock synchronization. Un grand nombre d'experiences ont ete faites pour valider la transformation de Lorentz ou pour trouver de possibles violations de l'invariance de Lorentz, sur la base de theories des tests visant a verifier la relativite restreinte. La theorie de Mansouri et Sexl (MS) fournit un cadre general pour la transformation de referentiels inertiels, en supposant l'existence d'un systeme de reference preferentiel. Sur la base du cadre de MS, nous etudions ici de facon systematique l'effet Doppler relativiste de facon a identifier sa dependance sur les coefficients et parametres de la transformation. L'effet Doppler est formule ici dans un espace euclidien complexe oU le temps est represente par des nombres complexes. Nous presentons deux formules de l'effet Doppler qui sont derivees dans une transformation arbitraire a l'interieur du cadre de MS : une premiere, entre un referentiel inertiel et un referentiel preferentiel et l'autre entre deux referentiels inertiels arbitraires. Nous montrons dans cette formulation que l'effet Doppler est independant de la synchronisation des horloges, ce qui implique que le deplacement en frequence de Doppler dans la synchronisation absolue est le meme que dans la synchronisation standard. Cette derniere formule peut nous permettre de trouver des deplacements de Doppler sans information sur la vitesse des referentiels inertiels relativement au referentiel preferentiel. Exploitant ces resultats theoriques, nous examinons les effets Doppler transverse et longitudinal en detail. [Traduit par la Redaction] Mots-cles : effet Doppler relativiste, vecteurs d'onde, theorie des tests, synchronisation des horloges., 1. Introduction Special relativity [1, 2] predicts time dilation. According to special relativity, Doppler shifts can occur because of the effect of time dilation as well as relative motion between [...] more...
- Published
- 2016
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