Duality between a deterministic cellular automaton and a bosonic quantum field theory in 1+1 dimensions

TL;DR

This paper establishes an exact correspondence between a deterministic cellular automaton and a bosonic quantum field theory in 1+1 dimensions, suggesting a closer relationship between classical automata and quantum theories than previously believed.

Contribution

It introduces a method to map states of a cellular automaton to those of a quantum field theory, highlighting potential deterministic foundations of quantum physics.

Findings

Exact automaton-field correspondence established

Quantum field theories may be closely related to deterministic automata

Supports the idea of underlying determinism in quantum mechanics

Abstract

Methods developed in a previous paper are employed to define an exact correspondence between the states of a deterministic cellular automaton in 1+1 dimensions and those of a bosonic quantum field theory. The result may be used to argue that quantum field theories may be much closer related to deterministic automata than what is usually thought possible. Version 2 had a minor typo corrected and notation was made more consistent.