Equality of Inertial and Gravitational Masses for Quantum Particle

TL;DR

This paper proves the equality of inertial and gravitational masses for nonrelativistic quantum particles, explores limitations of many-particle quantum mechanics for macroscopic bodies, and discusses the role of gravity in quantum state reduction.

Contribution

It provides a proof of mass equivalence in quantum mechanics independent of the equivalence principle and generalizes Bargmann's theory to connect gravity with quantum state reduction.

Findings

Mass equality holds for quantum particles without relying on the equivalence principle.

Many-particle quantum mechanics cannot describe macroscopic bodies.

Gravity may influence quantum state vector reduction, supporting Penrose's hypothesis.

Abstract

We investigate the interaction of the gravitational field with a quantum particle. First, we give the proof of the equality of the inertial and the gravitational mass for the nonrelativistic quantum particle, independently of the equivalence principle. Second, we show that the macroscopic body cannot be described by the many-particle Quantum Mechanics. As an important tool we generalize the Bargmann's theory of ray representations and explain the connection with the state vector reduction problem. The Penrose's hypothesis is discussed, i.e. the hypothesis that the gravitational field may influence the state vector reduction.