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

Bianca Rizzo, Hans-Thomas Elze

Published 2020-12-30Version 1

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.