On the Invariance of the Spacetime Interval

TL;DR

This paper provides a geometric proof of the invariance of the spacetime interval in special relativity, using light rectangles and the principles of constancy of light speed and spacetime symmetry, also deriving Lorentz transformations.

Contribution

It offers a novel geometric derivation of the spacetime interval invariance and Lorentz transformations based solely on fundamental spacetime symmetries and light rectangle constructions.

Findings

Proves invariance of spacetime interval using light rectangles.

Derives Lorentz transformations from geometric principles.

Highlights the role of spacetime symmetry in relativity.

Abstract

We present a geometric proof of the invariance of the relativistic spacetime interval based solely on the constancy of the speed of light, and the homogeneity and isotropy of spacetime. The derivation is based on a simple construction involving light rectangles, whose areas remain invariant across inertial frames. Based on this construction, we also derive the Lorentz transformations.