Lorentz transformations and the wave equation

Abstract

In this note we explicitly show how the Lorentz transformations can be derived by demanding form invariance of the d'Alembert operator in inertial reference frames.

Commentary: How to teach me physics: Tradition is not always a virtue

“…I understood special relativity better when I derived the Lorentz transformations in a different form. 3 This task was much more exciting than the usual assignment of calculating the length contraction of a rod. I understood Maxwell's equations better when I reviewed the Helmholtz theorem 4 and this task was far more thrilling than calculating the electric field of a charged sphere.…”

“…3 The second insight was Braunbek and Laukien's 1952 calculation 4 exhibiting Newton's eel-like undulations by plotting the trajectories of the Poynting…”

The Solution of the Wave Equation in the Class of Complex Numbers by Introducing Hyperbolic Coordinates

“…Maxwell one with Lorentz calibration can be led to it [2]. These equations are Lorentz invariant and give the theoretical argument for the creation of the Relativity [2,13] that stresses there importance.…”

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

“…There are so many derivations of the Lorentz transformations reported in the literature that an interesting task for an instructor is to investigate which of them are appropriate to be presented in an undergraduate physics course. In a recent note [1], I have suggested a simple derivation of these transformations, which uses the standard configuration 1 ) , which expresses the two postulates of special relativity. This derivation of the Lorentz transformation is suitable for a first view of the theory of relativity.…”

“…In order to put the derivation of the Lorentz transformations from the invariance of the d'Alambert operator in a pedagogical context, it is worthwhile to compare it with the usual derivation of these transformations, which uses the standard configuration and assumes the invariance of the Minkowski space-time interval: ¢ -¢ = x c t x c t 1 In the standard configuration two inertial frames S and ¢ S are in relative motion with the speed v along their common ¢…”