Are quantum spins but small perturbations of ontological Ising spins?

TL;DR

This paper presents a classical, deterministic ontological model based on Ising spins that mimics quantum mechanics and shows how small modifications can lead to genuine quantum behavior, supporting an epistemic view of quantum phenomena.

Contribution

It introduces a classical ontological model with discrete dynamics that can be deformed into a true quantum theory, bridging classical and quantum descriptions.

Findings

Model resembles a discrete free field theory.

Small deformations produce genuine quantum behavior.

Supports epistemic interpretation of quantum mechanics.

Abstract

The dynamics-from-permutations of classical Ising spins is generalized here for an arbitrarily long chain. This serves as an ontological model with discrete dynamics generated by pairwise exchange interactions defining the unitary update operator. The model incorporates a finite signal velocity and resembles in many aspects a discrete free field theory. We deduce the corresponding Hamiltonian operator and show that it generates an exact terminating Baker-Campbell-Hausdorff formula. Motivation for this study is provided by the Cellular Automaton Interpretation of Quantum Mechanics. We find that our ontological model, which is classical and deterministic, appears as if of quantum mechanical kind in an appropriate formal description. However, it is striking that (in principle arbitrarily) small deformations of the model turn it into a genuine quantum theory. This supports the view that quantum mechanics stems from an epistemic approach handling physical phenomena.