Are Quantum-Classical Hybrids compatible with Ontological Cellular Automata?

TL;DR

This paper investigates whether quantum-classical hybrids can be modeled within the Cellular Automaton Interpretation of quantum mechanics, finding that such hybrids generally cannot be consistently maintained under interactions.

Contribution

It demonstrates that quantum-classical hybrids are incompatible with the CAI framework due to the disruptive effects of an identified error mechanism.

Findings

Hybrid models lose consistency under interactions.

Classical chains can become quantum-like due to error mechanisms.

Quantum-classical hybrids cannot be fundamental in CAI.

Abstract

Based on the concept of ontological states and their dynamical evolution by permutations, as assumed in the Cellular Automaton Interpretation (CAI) of quantum mechanics, we address the issue whether quantum-classical hybrids can be described consistently in this framework. We consider chains of 'classical' two-state Ising spins and their discrete deterministic dynamics as an ontological model with an unitary evolution operator generated by pair exchange interactions. A simple error mechanism is identified, which turns them into quantum mechanical objects, chains of qubits. Consequently, an interaction between a quantum mechanical and a 'classical' chain can be introduced and its consequences for this quantum-classical hybrid be studied. We find that such hybrid character of composites, generally, does not persist under interactions and, therefore, cannot be upheld consistently, or even as a fundamental notion as in Kopenhagen interpretation, within CAI.