Economical ontological models for discrete quantum systems

Ontological states and dynamics of discrete (pre-)quantum systems

The notion of ontological states is introduced here with reference to the Cellular Automaton Interpretation of Quantum Mechanics proposed by G.'t Hooft. A class of discrete deterministic "Hamiltonian" Cellular Automata is defined that has been shown to bear many features in common with continuum quantum mechanical models, however, deformed by the presence of a finite discreteness scale $l$, such that for $l\rightarrow 0$ the usual properties result -- e.g., concerning linearity, dispersion relations, multipartite systems, and Superposition Principle. We argue that within this class of models o…

Are quantum spins but small perturbations of ontological Ising spins?

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…

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 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 int…

Reality without Realism: On the Ontological and Epistemological Architecture of Quantum Mechanics

First, this article considers the nature of quantum reality (the reality responsible for quantum phenomena) and the concept of realism (our ability to represent this reality) in quantum theory, in conjunction with the roles of locality, causality, and probability and statistics there. Second, it offers two interpretations of quantum mechanics, developed by the authors of this article, the second of which is also a different (from quantum mechanics) theory of quantum phenomena. Both of these interpretations are statistical. The first interpretation, by A. Plotnitsky, "the statistical Copenhagen…

元胞自动机本体论、比特、量子比特与狄拉克方程

Cellular automaton ontology, bits, qubits, and the Dirac equation

本文基于元胞自动机诠释，以经典伊辛链说明本体论状态经置换演化避免叠加，并在连续极限下关联韦尔方程，进而通过引入质量项构造满足本体论的离散确定性狄拉克方程自动机。

强O值语境性：排除量子理论的离散非确定性替代方案

Strong $O$-valued contextuality: ruling out discrete nondeterministic alternatives to quantum theory

研究排除量子理论离散非确定性替代方案，通过构建有限测量配置，采用状态依赖哈迪型测试和广义KS定理两种方式，扩展层理论框架引入强\(O\)值语境性，探讨对多值逻辑及相关协议的影响。