2023/08/04 by A. V. Nenashev, Nenashev, A. V., S. D. Baranovskiǐ +3
Physics and Astronomy · #Classical Physics (physics.class-ph) #Experimental and Theoretical Physics Studies #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #History and Philosophy of Physics (physics.hist-ph) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2308.02612
openalex publication_date 2023/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are several ways to derive Einstein's celebrated formula for the energy of a massive particle at rest, E=mc2. Noether's theorem applied to the relativistic Lagrange function provides an unambiguous and straightforward access to energy and momentum conservation laws but those tools were not available at the beginning of the twentieth century and are not at hand for newcomers even nowadays. In a pedestrian approach, we start from relativistic kinematics and analyze elastic and inelastic scattering processes in different reference frames to derive the relativistic energy-mass relation. We extend the analysis to Compton scattering between a massive particle and a photon, and a massive particle emitting two photons. Using the Doppler formula, it follows that E=ℏ ω for photons at angular frequency ω where ℏ is the reduced Planck constant. We relate our work to other derivations of Einstein's formula in the literature.