Elementary derivation of the expressions of momentum and energy in special relativity

TL;DR

This paper presents an elementary derivation of the relativistic momentum and energy formulas, including E=mc^2, using only Lorentz transformations and conservation principles, avoiding complex concepts from electrodynamics or quantum theory.

Contribution

It offers a straightforward derivation of key relativistic expressions solely based on Lorentz transformations and conservation laws, simplifying understanding for students.

Findings

Derivation of relativistic momentum and energy formulas

Confirmation of E=mc^2 from elementary principles

Simplification of relativistic dynamics understanding

Abstract

The expressions of momentum and energy of a particle in special relativity are often derived in a quite unconvincing manner in elementary text, by resorting either to electrodynamic or quantum considerations, or via the introduction of the less-than-elementary concept of a four-vector. It is instead possible, by exploiting considerations introduced by P. Epstein and A. Einstein and exploited later by Feynman, to obtain a fully elementary derivation of these expressions and of the $E=mc^2$ formula exploiting only Lorentz transformations and the postulate of the conservation of quantities defined for point-like particles which reduce to the Newtonian expressions of momentum and energy in the classical limit.