Are Quantum-Classical Hybrids Compatible with Ontological Cellular Automata?

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 of whether quantum-classical hybrids can be described consistently in this framework. We consider chains of ‘...

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Main Author: Hans-Thomas Elze
Format: Article
Language:English
Published: MDPI AG 2022-03-01
Series:Universe
Subjects:
Online Access:https://www.mdpi.com/2218-1997/8/4/207
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author Hans-Thomas Elze
author_facet Hans-Thomas Elze
author_sort Hans-Thomas Elze
collection DOAJ
description 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 of 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 can be studied. We found that such hybrid character of composites, generally, does not persist under interactions and, therefore, cannot be upheld consistently, or even as a fundamental notion <i>à la</i> Kopenhagen interpretation, within CAI.
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spelling doaj.art-aa01e3092a0a43ea9066f8b34dc7e1e42023-12-01T21:29:54ZengMDPI AGUniverse2218-19972022-03-018420710.3390/universe8040207Are Quantum-Classical Hybrids Compatible with Ontological Cellular Automata?Hans-Thomas Elze0Dipartimento di Fisica “Enrico Fermi”, Università di Pisa, Largo Pontecorvo 3, I-56127 Pisa, ItalyBased 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 of 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 can be studied. We found that such hybrid character of composites, generally, does not persist under interactions and, therefore, cannot be upheld consistently, or even as a fundamental notion <i>à la</i> Kopenhagen interpretation, within CAI.https://www.mdpi.com/2218-1997/8/4/207quantum-classical hybrid systemcellular automatonising spinqubitontological stateBaker–Campbell–Hausdorff formula
spellingShingle Hans-Thomas Elze
Are Quantum-Classical Hybrids Compatible with Ontological Cellular Automata?
Universe
quantum-classical hybrid system
cellular automaton
ising spin
qubit
ontological state
Baker–Campbell–Hausdorff formula
title Are Quantum-Classical Hybrids Compatible with Ontological Cellular Automata?
title_full Are Quantum-Classical Hybrids Compatible with Ontological Cellular Automata?
title_fullStr Are Quantum-Classical Hybrids Compatible with Ontological Cellular Automata?
title_full_unstemmed Are Quantum-Classical Hybrids Compatible with Ontological Cellular Automata?
title_short Are Quantum-Classical Hybrids Compatible with Ontological Cellular Automata?
title_sort are quantum classical hybrids compatible with ontological cellular automata
topic quantum-classical hybrid system
cellular automaton
ising spin
qubit
ontological state
Baker–Campbell–Hausdorff formula
url https://www.mdpi.com/2218-1997/8/4/207
work_keys_str_mv AT hansthomaselze arequantumclassicalhybridscompatiblewithontologicalcellularautomata