Special Relativity (Lorentz Transformation) Follows from the Definition of Inertial Frames

TL;DR

This paper argues that the Lorentz transformation and special relativity can be derived solely from the fundamental definition of inertial frames and their symmetries, without additional postulates.

Contribution

It demonstrates that the principle of relativity and finite speed limit are derivable from the basic properties of inertial frames, simplifying the foundations of special relativity.

Findings

Finite speed limit inferred from inertial frame properties

Principle of relativity derived from space-time symmetries

Lorentz transformation follows from inertial frame definitions

Abstract

Besides the defining space-time symmetries (homogeneity and isotropy) of inertial frames, the derivation of Lorentz transformation requires postulating the principle of relativity and the existence of a finite speed limit. In this article, we point out that the existence of a finite speed limit can be readily inferred from the nature of allowed inertial frames. We also show that the principle of relativity can be obtained from the defining space-time symmetries of every inertial frame. Therefore, if the conventional definition of inertial frames is augmented properly, the special theory of relativity (Lorentz transformation) would follow from the definition of inertial frames.