Slowing time by stretching the waves in special relativity

Denis Michel (1)

1 UR - Université de Rennes

The correction of the classical Doppler formula by the time dilation factor gives the currently admitted relativistic Doppler equation. When the source path is not collinear to that of the receiver, this correction gives a transverse wave dilation whose possible detection was considered by Einstein as an ideal mean to prove the time dilation of special relativity. It is suggested here that this elusive effect whose measurement remains controversial, could in fact be absent from relativistic as well as classical contexts, but that this absence paradoxically proves the time-dilation of special relativity. An intuitive reasoning using parallel Doppler effects is first proposed to conceive why the absence of a wave carrier medium imposes time dilation for electomagnetic waves. A rational reconstruction of the non-collinear Doppler effect is then presented using only reciprocal quantities such as the source-receiver distance. This rigorous analysis reveals a virtual equation whose transverse contraction effect is exactly cancelled by the relativistic time dilation. The candidate Doppler equation emerging from this treatment is remarkably elegant, geometrically symmetrical and centered on the closest point between the source and the receiver.

Un nouveau calcul de l'effet Doppler électromagnétique

Mots clés: special relativity; relativistic Doppler equation; Time dilation

Domaines: Optique [physics.optics]

Denis Michel. Slowing time by stretching the waves in special relativity: The elusive transverse Doppler effect. 2014. ⟨hal-01097004v9⟩