A Process Algebra Approach to Quantum Mechanics

TL;DR

This paper introduces a novel process algebra framework for quantum mechanics that offers a discrete, realist interpretation, resolving paradoxes and divergences while maintaining quantum computational power.

Contribution

It presents a new process algebra approach that extends NRQM with an emergentist, quasi-non-local interpretation, linking to standard quantum mechanics via a process covering map.

Findings

Provides a process algebra model for quantum systems

Demonstrates the link to NRQM through a toy model

Addresses quantum paradoxes with a realist interpretation

Abstract

The process approach to NRQM offers a fourth framework for the quantization of physical systems. Unlike the standard approaches (Schrodinger-Heisenberg, Feynman, Wigner-Gronewald-Moyal), the process approach is not merely equivalent to NRQM and is not merely a re-interpretation. The process approach provides a dynamical completion of NRQM. Standard NRQM arises as a asymptotic quotient by means of a set-valued process covering map, which links the process algebra to the usual space of wave functions and operators on Hilbert space. The process approach offers an emergentist, discrete, finite, quasi-non-local and quasi-non-contextual realist interpretation which appears to resolve many of the paradoxes and is free of divergences. Nevertheless, it retains the computational power of NRQM and possesses an emergent probability structure which agrees with NRQM in the asymptotic quotient. The paper describes the process algebra, the process covering map for single systems and the configuration process covering map for multiple systems. It demonstrates the link to NRQM through a toy model. Applications of the process algebra to various quantum mechanical situations - superpositions, two-slit experiments, entanglement, Schrodinger's cat - are presented along with an approach to the paradoxes and the issue of classicality.