From Einstein's 1905 Postulates to the Geometry of Flat Space-Time

TL;DR

This paper provides a geometric derivation of Minkowski diagrams in flat space-time, using thought experiments based on the constancy of light speed and relativity principles, emphasizing the role of photon trajectories.

Contribution

It offers a novel geometric derivation of Minkowski diagrams directly from fundamental principles without relying on algebraic methods.

Findings

Rectangles of photon trajectories determine simultaneity.

The invariance of the interval is established geometrically.

The derivation clarifies the geometric structure of flat space-time.

Abstract

Minkowski diagrams in 1+1 dimensional flat space-time are given a strictly geometric derivation, directly from two gedanken experiments incorporating the principle of the constancy of the velocity of light and the principle of (special) relativity. Rectangles of photon trajectories play a central role in determining the simultaneity convention and in establishing the invariance of the interval.