The cellular automaton interpretation of quantum mechanics

Jean Michel Sellier, Kristina G. Kapanova, Ivan Dimov

Simon Berkovich

Luke Schaeffer

Darrin W.S. Belousek, E. Henigin, Douglas A. Hott +1 more

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.

Fabrizio Tamburini, Ignazio Francesco Licata

A deterministic reformulation of quantum mechanics is thought to be able to bypass the usual philosophical interpretations of probability and stochasticity of the standard quantum mechanical scenarios. Recently ’t Hooft proposed a different perspective based on the ontological formulation of quantum mechanics, obtained by writing the Hamiltonian of a quantum system in a way to render it mathematically equivalent to a deterministic system. The ontological deterministic models consist of elementary cells, also called cellular automata, inside which the quantities describing the dynamics oscillate in periodic orbits, extending and replacing the quantum mechanical classical language based on harmonic oscillators. We show that the structure of the cellular automaton sets finds a clear physical interpretation with the Majorana infinite-component equation: the cellular automata are elementary building blocks generated by the Poincaré group of spacetime transformations with positive-definite energy down to the Planck scales, with a close relation to the Riemann Hypothesis.

Gerard ’t Hooft

Quantum Physics; Mathematical Applications in the Physical Sciences; History and Philosophical Foundations of Physics