The path to Special Relativity

TL;DR

This paper derives the transformation rules between inertial frames solely from the existence of inertial systems, revealing a universal constant of nature and allowing for Lorentz, Galilean, or Euclidean transformations without assuming an absolute velocity.

Contribution

It provides a derivation of inertial transformation rules without assuming an absolute velocity, unifying Lorentz, Galilean, and Euclidean transformations based on a universal constant.

Findings

Transformation rules characterized by a universal constant of nature.

No need for an independent postulate of absolute velocity.

Allows for Euclidean transformation rules alongside Lorentz and Galilean.

Abstract

Following an early observation of Ignatowsky, we present a derivation of the transformation rules between inertial systems making no other assumptions than the existence of the latter, and show that generically these rules are characterized by a constant of nature with the dimensions of an inverse velocity squared having the same value in all inertial frames. No independent postulate of the existence of an absolute velocity for light waves or other carriers of physical information is necessary. Aside from the usual Lorentz- and galilean transformations, our analysis also allows for the existence of four-dimensional Euclidian transformation rules between inertial systems.