Relativity: A matter of causality

TL;DR

This paper derives the structure of relativistic causality and inertial frames from fundamental assumptions about causality and event observation, leading to the Lorentz group without relying on physical laws.

Contribution

It provides a foundational derivation of relativistic structures solely from causality and observation principles, independent of physical laws.

Findings

Causality and event observation define inertial frames.

Maximal transfer-information velocity arises from observer communication constraints.

Causal group is the orthochronous inhomogeneous Lorentz group times dilatations.

Abstract

We take causality and uniqueness of events observation as our driving forces. They are built in in the way we define distinct observers, which then require a finite time to communicate between each other. This unavoidably leads to the existence of maximal transfer-information velocity between arbitrary (not necessarily inertial) reference frames. Inertial reference frames are defined by fixing the geometrical properties of (spatial) distance without any reference to relativity, electromagnetism, or laws of physics in general. For these inertial reference frames, the causality condition fixes the causal group to be the orthochronous inhomogeneous Lorentz group times dilatations. The mathematics we will use are quite basic.