Classical probabilistic realisation of quantum double-slit interference
arXiv:2607.11580
The paper shows that interference patterns in the double-slit experiment can be reproduced using a classical probabilistic field theory, where conserved charges define particle-like excitations and a complex wave function obeys the Schrödinger equation derived from the Liouville equation.
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.
Additional discussion of one-particle observables, 16 pages