Quantum Origin of (Newtonian) Mass and Galilean Relativity Symmetry

TL;DR

This paper explores the quantum origins of Newtonian mass and Galilean symmetry, proposing a refined group-theoretical framework that revises traditional assumptions and clarifies the role of mass and time symmetry in nonrelativistic physics.

Contribution

It introduces a corrected group-theoretical formulation of nonrelativistic quantum mechanics, emphasizing the role of mass as a Casimir invariant and excluding time translation symmetry to allow interactions.

Findings

Mass identified as a Casimir invariant in the revised symmetry framework

Exclusion of time translation symmetry to permit particle interactions

Clarification of the relation between mathematical representations and physical dynamics

Abstract

The Galilei group has been taken as the fundamental symmetry for 'nonrelativistic' physics, quantum or classical. Our fully group theoretical formulation approach to the quantum theory asks for some adjustments. We present a sketch of the full picture here, emphasizing aspects that are different from the more familiar picture. The analysis involves a more careful treatment of the relation between the exact mathematics and its physical application in the dynamical theories, and a more serious full implementation of the mathematical logic than what is usually available in the physics literature. The article summarizes our earlier presented formulation while focusing on the part beyond, with an adjusted, or corrected, identification of the basic representations having the (Newtonian) mass as a Casimir invariant and the notion of center of mass as dictated by the symmetry. Another result is the necessary exclusion of the time translational symmetry, that otherwise bans interactions between particles.