The linearity of quantum mechanics from the perspective of Hamiltonian cellular automata

Abstract

We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped reversibly on continuum equations describing a set of bandwidth limited harmonic oscillators. They represent the Schroedinger equation. However, modifications reflecting the bandwidth limit are incorporated, i.e., the presence of a time (or length) scale. When this discreteness scale is taken to zero, the usual results are obtained. Thus, the linearity of quantum mechanics can be traced to the postulated action principle of such cellular automata and its conservation laws to discrete ones. The cellular automaton conservation laws are in one-to-one correspondence with those of the related quantum mechanical model, while admissible symmetries are not.

9 pages. Invited talk for the symposium on "Emergent Quantum Mechanics", EmQM13 (Vienna, October 2013); to appear in JPCS

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Cited by in corpus (1)

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