A Machian reformulation of Quantum Mechanics

TL;DR

This paper reformulates non-relativistic quantum mechanics in a fully relational, Machian framework, removing the concept of absolute space and linking quantum dynamics directly to the system's mass distribution.

Contribution

It introduces a novel Machian reformulation of the Schrödinger equation, emphasizing relational properties over absolute references in quantum mechanics.

Findings

Quantum theory becomes fully relational in positions and momenta.

No reference to absolute space remains in the reformulated theory.

The approach parallels classical Machian mechanics reformulations.

Abstract

The widely known but also somewhat esoteric Mach principle envisages a fully relational formulation of physical theories without any reference to a concept of `absolute space'. When applied to classical mechanics, under the guise of an extended symmetry group, this procedure is known to lead to an equation of motion with inertial-like forces that are sourced by the mass distribution of the system itself. In this paper we follow a similar procedure and reformulate the Schr\"odinger equation of non-relativistic quantum mechanics in a fully Machian way. Just like its classical counterpart, the resulting quantum theory is fully relational in the positions and momenta of the bodies comprising a given physical system, leaving no room for the notion of absolute space.