Voigt transformations in retrospect: missed opportunities?

Abstract

The teaching of modern physics often uses the history of physics as a didactic tool. However, as in this process the history of physics is not something studied but used, there is a danger that the history itself will be distorted in, as Butterfield calls it, a "Whiggish" way, when the present becomes the measure of the past.It is not surprising that reading today a paper written more than a hundred years ago, we can extract much more of it than was actually thought or dreamed by the author himself. We demonstrate this Whiggish approach on the example of Woldemar Voigt's 1887 paper. From the modern perspective, it may appear that this paper opens a way to both the special relativity and to its anisotropic Finslerian generalization which came into the focus only recently, in relation with the Cohen and Glashow's very special relativity proposal.With a little imagination, one can connect Voigt's paper to the notorious Einstein-Poincaré priority dispute, which we believe is a Whiggish late time artifact. We use the related historical circumstances to give a broader view on special relativity, than it is usually anticipated.

On Finslerian extension of special relativity

“…The definition of simultaneity, introduced in Einstein's seminal paper [39], was actually previously considered by Poincaré (see [40] and references therein. Essentially the same operational definition of distant simultaneity was advocated by St. Augustine in his Confessions, written in AD 397 [41]).…”

“…These transformations leave the Finslerian interval (1) invariant provided that the x axis along which the observer S moves is in the preferred direction n. Interestingly, Einstein and Poincaré obtained the λ-Lorentz transformations, but both claimed λ(β) = 1, essentially based on spatial isotropy [40]. Finsler space-time arises in a more general situation when spatial isotropy is not assumed, and in this case the transformations (26) can be obtained in a more traditional way too, requiring the group property of λ-Lorentz transformations [40]. When the observer S does not moves along the preferred direction n, the generalized Lorentz transformations that leave the Finslerian interval (1) invariant have more complicated form.…”

Geodesic motion in Bogoslovsky-Finsler Spacetimes

“…They then observed that this is precisely the symmetry of the Bogoslovsky's Finsler metric (III.1). For a review of these ideas and their relation to much earlier work of Voigt [31], the reader is directed to the recent review [32]. For a recent discussion of Bogoslovsky-Finsler deformations in the light of ideas of Segal see [33].…”

Finsler spacetime in light of Segal’s principle

“…The obtained λ-Lorentz transformations (6) correspond to the inertial reference frame S ′ which moves along the preferred direction n. If the inertial reference frame S ′ moves with the velocity V = c β in an arbitrary direction, then the generalized Lorentz transformations that leave the Finsler metric (11) invariant have the form [13,14]…”

“…The explicit form of these generalized Lorentz transformations was obtained in [13,14]. They have the following form…”