Quantum Mechanics and Relativity --- Their Unification by Local Time ---

TL;DR

This paper derives a quantum-mechanical Hamiltonian incorporating gravitational potential within the framework of local times, bridging quantum mechanics and relativity, and explaining stellar stability phenomena.

Contribution

It introduces a novel derivation of a gravitational Hamiltonian using local times consistent with relativity, connecting quantum mechanics to gravitational phenomena.

Findings

Derived a Hamiltonian used in stellar stability analysis.

Linked quantum local times with general relativity.

Provided a new perspective on unifying quantum mechanics and relativity.

Abstract

A quantum-mechanical Hamiltonian with a gravitational potential is derived in the framework of local times. This Hamiltonian is the one used by E. H. Lieb (Bull. Amer. Math. Soc. 22(1990), 1-49) in his explanation of stability and instability of cold stars. Our procedure deriving the Hamiltonian is based on an analysis of the process of the observation with the background of the notion of quantum-mechanical local times compatible with general theory of relativity.