Lagrangian Description for Particle Interpretations of Quantum Mechanics -- Entangled Many-Particle Case

TL;DR

This paper develops a Lorentz-invariant Lagrangian framework for entangled many-particle quantum interpretations, revealing retrocausality and enabling a spacetime-based description with single-particle wavefunctions.

Contribution

It extends previous single-particle formulations to many particles, incorporating entanglement and final boundary conditions, and introduces a spacetime approach to quantum interpretations.

Findings

Retains Lorentz invariance in many-particle case

Requires final boundary conditions, implying retrocausality

Allows a spacetime description with single-particle wavefunctions

Abstract

A Lagrangian formulation is constructed for particle interpretations of quantum mechanics, a well-known example of such an interpretation being the Bohm model. The advantages of such a description are that the equations for particle motion, field evolution and conservation laws can all be deduced from a single Lagrangian density expression. The formalism presented is Lorentz invariant. This paper follows on from a previous one which was limited to the single-particle case. The present paper treats the more general case of many particles in an entangled state. It is found that describing more than one particle while maintaining a relativistic description requires the specification of final boundary conditions as well as the usual initial ones, with the experimenter's controllable choice of the final conditions thereby exerting a backwards-in-time influence. This retrocausality then allows an important theoretical step forward to be made, namely that it becomes possible to dispense with the usual, many-dimensional description in configuration space and instead revert to a description in spacetime using separate, single-particle wavefunctions.