Action principle for cellular automata and the linearity of quantum mechanics
arXiv:1312.1615 · doi:10.1103/PhysRevA.89.012111
Abstract
We introduce an action principle for a class of integer valued cellular automata and obtain Hamiltonian equations of motion. Employing sampling theory, these discrete deterministic equations are invertibly mapped on continuum equations for a set of bandwidth limited harmonic oscillators, which encode the Schrödinger equation. Thus, the linearity of quantum mechanics is related to the action principle of such cellular automata and its conservation laws to discrete ones.
6 pages; presented in part in invited talks at "Wigner 111 Scientific Symposium" (11-13 Nov 2013, Budapest) and "EmQM13 - Emergent Quantum Mechanics" (3-6 Oct 2013, Vienna)
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