Relativistic Derivations of de Broglie and Planck-Einstein Equations

TL;DR

This paper demonstrates that special relativity uniquely constrains the relationship between a particle's four-momentum and its wave properties, deriving the de Broglie and Planck-Einstein equations from relativistic principles.

Contribution

It provides a relativistic derivation showing the exclusive form of relations between particle momentum-energy and wave characteristics, confirming de Broglie and Planck-Einstein equations.

Findings

Relativistic constraints lead to unique proportional relations

Derivation of de Broglie and Planck-Einstein equations from relativity

Confirmation of the fundamental link between particle and wave properties

Abstract

We show how Special Relativity sets tight constraints on the form of possible relations that may exist between the four-momentum of a particle and the wave four-vector. More specifically, we demonstrate that there is just one way, according to Special Relativity, to relate the finite energy and momentum of a corpuscle with the characteristics of a plane wave, frequency, wave vector and amplitude: that is by laws of direct proportionality like de Broglie equation and Planck-Einstein equation.