Local Quantum Theory with Fluids in Space-Time

TL;DR

This paper introduces a Lorentz-covariant local hidden variable theory in space-time that reproduces quantum predictions and is compatible with relativistic quantum electrodynamics, challenging the notion that locality and quantum mechanics are incompatible.

Contribution

It presents a novel local hidden variable interpretation of quantum mechanics in space-time, incorporating fluid-like wavefunctions and local interactions, compatible with relativistic quantum theory.

Findings

The theory reproduces all empirical predictions of standard quantum mechanics.

It provides a local, Lorentz-covariant framework consistent with Bell's theorem.

Illustrative examples demonstrate the model's application to quantum phenomena.

Abstract

In 1948, Schwinger developed a local Lorentz covariant formulation of relativistic quantum electrodynamics in space-time which is fundamentally inconsistent with any delocalized interpretation of quantum mechanics. An interpretation compatible with Schwinger's theory is presented, which makes all of the same empirical predictions as conventional delocalized quantum theory in configuration space. This is an explicit, unambiguous, and Lorentz-covariant 'local hidden variable theory' in space-time, whose existence proves definitively that such theories are possible. There is no inconsistency with Bell's theorem because this a local many-worlds theory. Each physical system is characterized by a wave-field, which is a set of indexed piece-wise single-particle wavefunctions in space-time, each with with its own coefficient, along with a memory which contains the separate local Hilbert-space quantum state at each event in space-time. Each single-particle wavefunction of a fundamental system describes the motion of a portion of a conserved fluid in space-time, with the fluid decomposing into many classical point particles, each following a world-line and recording a local memory. Local interactions between two systems take the form of local boundary conditions between the differently indexed pieces of those systems' wave-fields, with new indexes encoding each orthogonal outcome of the interaction. The general machinery is introduced, including the local mechanisms for entanglement and interference. The experience of collapse, Born rule probability, and environmental decoherence are discussed, and a number of illustrative examples are given.