Proposed is a development of our previous model of «toy quantum mechanics» with hidden variables, which does not contradict to Bell’s Theorem. The model here is cellular automaton describing two-particles experiment with entangled states.
We clarify the meaning of Bell's theorem and its implications for the construction of hidden variable theories by considering an example system consisting of two entangled spin-1/2 particles. Using this example, we present a simplified version of Bell's theorem and describe several hidden variable theories that agree with the predictions of quantum mechanics. These example theories clarify some subtle points, which are often misunderstood, regarding what it is that Bell's theorem actually establishes. \n
Since Richard Feynman introduced the notion of quantum computation in 1982, various models of "quantum computers" have been proposed (R. Feynman, 1992). These models include quantum Turing machines and quantum circuits. We define another quantum computational model, one dimensional quantum cellular automata, and demonstrate that any quantum Turing machine can be efficiently simulated by a one dimensional quantum cellular automaton with constant slowdown. This can be accomplished by consideration of a restricted class of one dimensional quantum cellular automata called one dimensional partitioned quantum cellular automata. We also show that any one dimensional partitioned quantum cellular automaton can be simulated by a quantum Turing machine with linear slowdown, but the problem of efficiently simulating an arbitrary one dimensional quantum cellular automaton with a quantum Turing machine is left open. From this discussion, some interesting facts concerning these models are easily deduced.
Quantum entanglement, a phenomenon where two or more particles become linked and share the same fate, has captivated physicists and philosophers alike. While established in quantum mechanics, its application to complex systems, particularly cellular automata, presents a fascinating challenge and opportunity. This paper explores the potential of extending the concept of quantum entanglement beyond individual particles to propose a dynamic, multi-level entanglement structure within cellular automata simulations. We hypothesize that this approach, driven by chaotic behavior observed in cellular automata, could yield emergent phenomena, including "quantum foam" behavior, offering novel insights into the fundamental nature of reality. The core mechanism involves introducing a novel evolution rule based on chaotic dynamics, incorporating feedback loops and probabilistic branching to generate complex entanglement patterns. This work aims to advance our understanding of entanglement's role in complex systems and potentially lead to new computational models.
Simple algebraic cellular automata and a diffusion confinement are used to model quantum behavior of a relativistic particle in a 1-D box. Comparisons and contrasts are drawn between such a quantum cellular automaton (QCA) and both orthodox and unorthodox interpretations of quantum mechanics. The persistent tension between deterministic pictures and probabilistic descriptions of quantum reality are clarified for the case of a 1-D quantum particle viewed as a cellular automaton surging for survival in space and time.