Related papers: The Dirac Equation, Mass and Arithmetic by Permutations of Automaton States

The Dirac Equation, Mass and Arithmetic by Permutations of Automaton States

URL: http://arxiv.org/abs/2504.06883v1
Date: Wed, 09 Apr 2025 13:37:12 GMT
Title: The Dirac Equation, Mass and Arithmetic by Permutations of Automaton States
Authors: Hans-Thomas Elze,
Abstract summary: We construct a new Necklace of Necklaces'' automaton with a torus-like topology that lends itself to represent the Dirac equation in 1 + 1 dimensions.<n>As discussed earlier, such deterministic models of discrete spins or bits unavoidably become quantum mechanical, when only slightly deformed.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: The cornerstones of the Cellular Automaton Interpretation of Quantum Mechanics are its underlying ontological states that evolve by permutations. They do not create would-be quantum mechanical superposition states. We review this with a classical automaton consisting of an Ising spin chain which is then related to the Weyl equation in the continuum limit. Based on this and generalizing, we construct a new ``Necklace of Necklaces'' automaton with a torus-like topology that lends itself to represent the Dirac equation in 1 + 1 dimensions. Special attention has to be paid to its mass term, which necessitates this enlarged structure and a particular scattering operator contributing to the step-wise updates of the automaton. As discussed earlier, such deterministic models of discrete spins or bits unavoidably become quantum mechanical, when only slightly deformed.

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