Multipartite Cellular Automata and the Superposition Principle

Abstract

Cellular automata can show well known features of quantum mechanics, such as a linear updating rule that resembles a discretized form of the Schrödinger equation together with its conservation laws. Surprisingly, a whole class of "natural" Hamiltonian cellular automata, which are based entirely on integer-valued variables and couplings and derived from an Action Principle, can be mapped reversibly to continuum models with the help of Sampling Theory. This results in "deformed" quantum mechanical models with a finite discreteness scale $l$, which for $l\to 0$ reproduce the familiar continuum limit. Presently, we show, in particular, how such automata can form "multipartite" systems consistently with the tensor product structures of nonrelativistic many-body quantum mechanics, while maintaining the linearity of dynamics. Consequently, the Superposition Principle is fully operative already on the level of these primordial discrete deterministic automata, including the essential quantum effects of interference and entanglement.

12 pages; accepted for publication - Int. J. Qu. Info

References in corpus (4)

• Spacetime could be simultaneously continuous and discrete in the same way that information can
• Dissipation and quantization for composite systems
• Are nonlinear discrete cellular automata compatible with quantum mechanics?
• The linearity of quantum mechanics from the perspective of Hamiltonian cellular automata

Cited by in corpus (6)

• Probability theory as a physical theory points to superdeterminism
• Multi-Time Wave Functions
• Quantum models as classical cellular automata
• Ontological states and dynamics of discrete (pre-)quantum systems
• Qubit exchange interactions from permutations of classical bits
• On configuration space, Born's rule and ontological states