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Discrete Time Leads to Quantum-Like Interference of Deterministic Particles

Andrei Khrennikov·Yaroslav Volovich
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Abstract

In this note we demonstrate that a quantum-like interference picture could appear as a statistical effect of interference of deterministic particles, i.e. particles that have trajectories and obey deterministic equations, if one introduces a discrete time. The nature of the resulting interference picture does not follow from the geometry of force field, but is strongly attached to the time discreetness parameter. As a demonstration of this concept we consider a scattering of charged particles on the charged screen with a single slit. The resulting interference picture has a nontrivial minimum-maximum distribution which vanishes as the time discreetness parameter goes to zero that could be interpreted as an analog of quantum decoherence.

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Andrei Khrennikov, Yaroslav Volovich. 2002-03-04. Discrete Time Leads to Quantum-Like Interference of Deterministic Particles. https://arxiv.org/abs/quant-ph/0203009

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