Thermodynamic Gravity and the Schrodinger Equation

TL;DR

This paper presents a Machian, thermodynamic approach to derive the Schrödinger equation and Planck constant by modeling the universe as a gravitationally entangled statistical ensemble, linking quantum phenomena to cosmic-scale interactions.

Contribution

It introduces a novel Machian model that derives quantum mechanics from thermodynamic and gravitational principles, connecting microscopic quantum behavior to the universe's large-scale structure.

Findings

Schrödinger equation derived from Machian thermodynamics

Planck constant emerges from ensemble discreteness

Quantum probabilities linked to cosmic ensemble finiteness

Abstract

We adopt a 'thermodynamical' formulation of Mach's principle that the rest mass of a particle in the Universe is a measure of its long-range collective interactions with all other particles inside the horizon. We consider all particles in the Universe as a 'gravitationally entangled' statistical ensemble and apply the approach of classical statistical mechanics to it. It is shown that both the Schrodinger equation and the Planck constant can be derived within this Machian model of the universe. The appearance of probabilities, complex wave functions, and quantization conditions is related to the discreetness and finiteness of the Machian ensemble.