The Planck law for particle with rest mass

TL;DR

This paper derives a generalized Planck law for particles with rest mass, revealing its quantum origin and implications for black hole formation, extending classical black body radiation principles.

Contribution

It introduces a quantum-based derivation of the Planck law for massive particles and explores the effects of quantum potential on scale invariance and black hole formation.

Findings

Derived Planck law for particles with rest mass

Identified quantum potential as origin of the law

Discussed implications for small black holes

Abstract

In this work the author derives the Plank law for particles with rest mass that in the limit of photons with null rest mass leads to the known Plank law for the black body radiation. The paper shows that the relation has a pure quantum origin deriving it from the quantum potential of the hydrodynamic model. The paper puts under light how these laws originates by the scale invariance breaking due to the quantum potential. The paper also briefly analyzes the consequences of this symmetry breaking on the small-size black holes formation.