How perturbing a classical 3-spin chain can lead to quantum features

TL;DR

This thesis explores how classical cellular automata models, specifically a 3-spin chain, can exhibit quantum features like superposition when perturbed, supporting the idea that quantum phenomena may emerge from deterministic classical systems.

Contribution

It demonstrates that quantum superpositions can arise in a deterministic cellular automaton model through perturbations, bridging classical and quantum descriptions.

Findings

Superposition states emerge from classical spin chains under perturbations

Quantum features can be modeled within a deterministic cellular automaton framework

Perturbations induce a transition from classical spins to qubits

Abstract

In this thesis we will work under the premises of the Cellular Automata Interpretation of QM, by Gerard 't Hooft, according to whom particles evolve following the rules of Cellular Automata (CA), a mathematical model consisting of discrete units that evolve following deterministic laws in discrete space and time. The states of a Cellular Automaton are, by definition, classical and thus deterministic and do not form superpositions. Since it is not possible to know how to demonstrate the underlying classical deterministic structure and dynamics at the smallest microscopic scales at present, what we pursue in this thesis, besides summarizing the concept of the Cellular Automaton Interpretation, is to show that quantum phenomena, in particular superposition states, can arise in a deterministic model because of the limited precision of measurements. In order to do that, we follow the path of a recent article by Elze, considering a triplet of Ising spins and their dynamics in a CA context, which is possible to formalize using Pauli matrices and quantum mechanics operators. We will thus observe how the system will shift from a triplet of Ising spins to a triplet of qubits due to the arising of superposition after applying some perturbations on the Hamiltonian and the dynamics operators.