Classical probabilistic realisation of quantum double-slit interference
Abstract
We demonstrate how the interference effects for a quantum particle in the double-slit experiment can be described by classical probabilities. We investigate a classical field theory for a complex scalar field with probabilistic initial conditions. A central element are conserved charges leading to the concept of particles. These are statistical observables which describe properties of the probability distribution for field configurations. The conserved charges define subsystems for particle excitations of a vacuum state. The classical probability distribution for the one-particle subsystem can be expressed in terms of a complex wave function. The Liouville equation for the classical probability distribution implies that the time evolution of this wave function obeys the Schrödinger equation for a quantum particle in a potential. The potential arises from space-dependent external fields in the otherwise relativistic classical field theory. It can be chosen arbitrarily, realizing the typical quantum effects of interference, tunneling or discrete energy spectra.
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BibTeX
@misc{wetterich2026classical,
title = {{Classical probabilistic realisation of quantum double-slit interference}},
author = {Christof Wetterich},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.11580},
eprint = {2607.11580},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.11580},
}
RIS
TY - UNPB
TI - Classical probabilistic realisation of quantum double-slit interference
AU - Christof Wetterich
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2607.11580
UR - https://arxiv.org/abs/2607.11580
AB - We demonstrate how the interference effects for a quantum particle in the double-slit experiment can be described by classical probabilities. We investigate a classical field theory for a complex scalar field with probabilistic initial conditions. A central element are conserved charges leading to the concept of particles. These are statistical observables which describe properties of the probability distribution for field configurations. The conserved charges define subsystems for particle excitations of a vacuum state. The classical probability distribution for the one-particle subsystem can be expressed in terms of a complex wave function. The Liouville equation for the classical probability distribution implies that the time evolution of this wave function obeys the Schrödinger equation for a quantum particle in a potential. The potential arises from space-dependent external fields in the otherwise relativistic classical field theory. It can be chosen arbitrarily, realizing the typical quantum effects of interference, tunneling or discrete energy spectra.
ER -