Four easy routes to the Lorentz transformations: addendum to ‘Lorentz transformations and the wave equation’

Abstract

In this paper I briefly discuss and compare four easy derivations of the Lorentz transformations. Two of these derivations assume the invariance of the Minkowski spacetime interval in inertial frames and the other two assume the invariance of the d'Alembert operator in these frames. These derivations are suitable for a first view of special relativity. Finally, I discuss the comment made by Di Rocco on my original paper, 'Lorentz transformations and the wave equation' (2016 Eur. J. Phys. 37 025603).

Einstein’s time dilation and the relativistic Doppler shift: avoiding the pitfalls

“…An observer from S will agree about the monochromatic aspect of the wave emitted by the source from S (see e.g. [26][27][28] in this context). But there is no reason to agree on the angle of emission θ or on its frequency ν 0 (and implicitly on its wavelength λ).…”

Classical and special relativity in four steps

“…2 1 There will be, therefore, a limit for the speed v of the S′ frame with respect to the S frame in order for x′ and t′ to remain real. Calling this unspecified limiting speed V, where = -V n , 2 1 transformation (1a) now becomes the Ignatowsky transformation:…”

“…Recent papers in this journal [1][2][3][4] and elsewhere [5] have shown that considerable interest remains in the various methods of deriving the Lorentz [6] transformation of special relativity. Of these, Heras' [1] more recent paper must surely win the prize for the most new derivations (four) in one paper, these being derived from established laws of physics which are known to be relativistic, as in his earlier paper [2]. Chao [3] used symmetry to improve Einstein's derivation.…”