Relativistic reactions visualized through right triangles in space

TL;DR

This paper introduces a geometric visualization method using right triangles to understand relativistic particle reactions, simplifying complex kinematic relations and proofs.

Contribution

It presents a novel geometric approach to relativistic kinematics using right triangles, enabling easier derivation of particle reaction properties.

Findings

Simplified proofs of relativistic kinematic relations

Geometric visualization of energy-momentum relations

New insights into particle collision and decay processes

Abstract

In this article we exploit the fact that the special relativistic formula which relates the energy and the 3-momentum of an elementary particle with its rest mass, resembles the pythagorean theorem for right triangles. Using such triangles, suitably arranged, we can prove all kind of equalities or inequalities concerning the kinematical properties of elementary particles in a wide variety of cases regarding particles' collision, decay or production. Moreover, relations that are somehow hard to produce by the usual analytic methods arise much more naturally through geometric constructions based on right triangles.