Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0309012

Interference as a statistical consequence of conjecture on time quant

Andrei Yu. Khrennikov, Yaroslav Volovich

Published Aug 31, 2003• 2 citations
arXivHTMLPDF

Abstract

We analyze statistical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. We study particle dynamics with discrete time. We show that a quantum-like interference pattern could appear as a statistical effect for deterministic particles, i.e. particles that have trajectories and obey deterministic dynamical equations, if one introduces a discrete time. As a demonstration of this concept we consider particle scattering on a screen with a slit. We study how resulting interference picture depends on the parameters of the model. The resulting interference picture has a nontrivial minimum-maximum distribution which vanishes, as the time discreteness parameter goes to zero. This picture is qualitatively the same as one obtained in quantum experiments. The picture includes some interesting nonclassical properties such as a 'black' region behind the center of the slit.

DOI
10.48550/arxiv.quant-ph/0309012

Related papers

Discrete Time Dynamical Models and Their Quantum Like Context Dependant Properties

Andrei Yu. Khrennikov, Yaroslav Volovich

In this paper we demonstrate that a quantum-like interference pattern could appear as a statistical effect of interference of deterministic particles, i.e. particles that have trajectories and obey deterministic dynamical 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 several numerical experiments of 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. This picture is qualitatively the same as the one one obtained in quantum experiments.

•Jan 1, 2003•0 citations

Discrete Time Leads to Quantum-Like Interference of Deterministic Particles

Andrei Yu. Khrennikov, Yaroslav Volovich

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.

arXiv:quant-ph/0203009•Mar 4, 2002•9 citations

The deterministic set of operators, quantum interference phenomena, and quantum reality

Jeff Tollaksen, Yakir Aharonov

We develop an approach to quantum interference phenomenon which makes the characteristics of the problem more conspicuous and brings out more physical concepts. We do this by discussing the idea of deterministic quantum experiments using the Heisenberg picture. The variables that are relevant for describing interference are modular variables. These variables obey non-local equations of motion and can be used to follow the time evolution of a system without disturbing it. We present a physical explanation for the different behaviors of a single particle when the distant slit is open or closed: instead of having a quantum wave that passes through all slits, we have a localized particle with non-local interactions with the other slit(s). While the Heisenberg picture and the Schrodinger pictures are equivalent formulations of quantum mechanics, nevertheless, the results discussed here support a new approach to quantum mechanics which has led to new insights, new intuitions, new experiments, and even the possibility of new devices that were missed from the old perspective.

Journal of Physics Conference Series•Dec 1, 2009•4 citations

Classical probabilistic realisation of quantum double-slit interference

Christof Wetterich

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.

quant-pharXiv:2607.11580•Jul 14, 2026•0 citations

Simple interpretation of the double-slit experiment

Salim Yasmineh

This paper aims to understand how sequential, separate and independent impacts of particles on the screen of a double-slit experiment produce an interference pattern when both slits are open and how no such pattern is produced when detectors are placed at the slits. These strange phenomena can be explained by conjecturing the existence of a certain " thickness " of time. This conjecture is falsifiable, fits the observed results and maximizes simplicity for explaining other quantum phenomena without contradicting the established principles and laws of quantum mechanics.

•Nov 28, 2017•0 citations

How Could Classical Electrons Acquire Double-Slit Quantum Interference via Interacting with Stochastic Quantum Fields

Jau Tang, Chien-Cheng Chang

Quantum interference is traditionally interpreted as evidence of intrinsic wave–particle duality, invoking self-interference and wavefunction superposition. Here, we propose an alternative causal framework in which interference arises from interactions between a classical electron and a quantized electromagnetic field. In this picture, electrons follow definite, localized trajectories and produce discrete detection events, while the observed interference pattern emerges statistically from stochastic, nonlocal momentum transfers mediated by quantized field modes. Numerical simulations of the double-slit experiment show that dot-like interference fringes arise without invoking wavefunction collapse or intrinsic matter waves. Doubling the electron mass narrows the fringe spacing in agreement with de Broglie scaling, indicating that the effective wavelength emerges dynamically from particle–field coupling rather than representing an inherent property of the particle. The formulation is based on a rigorously defined Hamiltonian and derived equations describing electromagnetic coupling between particles and the slit environment. Although neutral particles such as neutrons or atoms carry no net charge monopoles, they possess electric or magnetic dipole and higher multipole moments that enable electromagnetic interactions with the slit apparatus, allowing discrete momentum transfer through the quantized field. Our simulations show that interference fringes arise from intermittent singleparticle detection events caused by stochastic momentum impulses from quantized electromagnetic modes. These results suggest a reinterpretation of wave–particle duality: the apparent wave-like behavior of matter may arise from interaction with the inherently wave-like quantized electromagnetic field—whose quanta are photons, the massless U(1)-gauge bosons—rather than from an intrinsic wave nature of the particles themselves. Our analysis is rigorous and is not speculative, because the proposed Hamiltonian for this system is physical. Within this nonlocal hidden-variable framework, the dot-like interference pattern observed in the double-slit experiment emerges from individual electrons traversing one slit at a time while receiving discrete momentum impulses from stochastic, spatially extended quantized electromagnetic fields.

International Journal of Quantum Technologies•Apr 6, 2026•0 citations
We analyze statistical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. We study particle dynamics with discrete time. We show that a quantum-like interference pattern could appear as a statistical effect for deterministic particles, i.e. particles that have trajectories and obey deterministic dynamical equations, if one introduces a discrete time. As a demonstration of this concept we consider particle scattering on a screen with a slit. We study how resulting interference picture depends on the parameters of the model. The resulting interference picture has a nontrivial minimum-maximum distribution which vanishes, as the time discreteness parameter goes to zero. This picture is qualitatively the same as one obtained in quantum experiments. The picture includes some interesting nonclassical properties such as a 'black' region behind the center of the slit.
In this paper we demonstrate that a quantum-like interference pattern could appear as a statistical effect of interference of deterministic particles, i.e. particles that have trajectories and obey deterministic dynamical 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 several numerical experiments of 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. This picture is qualitatively the same as the one one obtained in quantum experiments.
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.
We develop an approach to quantum interference phenomenon which makes the characteristics of the problem more conspicuous and brings out more physical concepts. We do this by discussing the idea of deterministic quantum experiments using the Heisenberg picture. The variables that are relevant for describing interference are modular variables. These variables obey non-local equations of motion and can be used to follow the time evolution of a system without disturbing it. We present a physical explanation for the different behaviors of a single particle when the distant slit is open or closed: instead of having a quantum wave that passes through all slits, we have a localized particle with non-local interactions with the other slit(s). While the Heisenberg picture and the Schrodinger pictures are equivalent formulations of quantum mechanics, nevertheless, the results discussed here support a new approach to quantum mechanics which has led to new insights, new intuitions, new experiments, and even the possibility of new devices that were missed from the old perspective.
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.
This paper aims to understand how sequential, separate and independent impacts of particles on the screen of a double-slit experiment produce an interference pattern when both slits are open and how no such pattern is produced when detectors are placed at the slits. These strange phenomena can be explained by conjecturing the existence of a certain " thickness " of time. This conjecture is falsifiable, fits the observed results and maximizes simplicity for explaining other quantum phenomena without contradicting the established principles and laws of quantum mechanics.
Quantum interference is traditionally interpreted as evidence of intrinsic wave–particle duality, invoking self-interference and wavefunction superposition. Here, we propose an alternative causal framework in which interference arises from interactions between a classical electron and a quantized electromagnetic field. In this picture, electrons follow definite, localized trajectories and produce discrete detection events, while the observed interference pattern emerges statistically from stochastic, nonlocal momentum transfers mediated by quantized field modes. Numerical simulations of the double-slit experiment show that dot-like interference fringes arise without invoking wavefunction collapse or intrinsic matter waves. Doubling the electron mass narrows the fringe spacing in agreement with de Broglie scaling, indicating that the effective wavelength emerges dynamically from particle–field coupling rather than representing an inherent property of the particle. The formulation is based on a rigorously defined Hamiltonian and derived equations describing electromagnetic coupling between particles and the slit environment. Although neutral particles such as neutrons or atoms carry no net charge monopoles, they possess electric or magnetic dipole and higher multipole moments that enable electromagnetic interactions with the slit apparatus, allowing discrete momentum transfer through the quantized field. Our simulations show that interference fringes arise from intermittent singleparticle detection events caused by stochastic momentum impulses from quantized electromagnetic modes. These results suggest a reinterpretation of wave–particle duality: the apparent wave-like behavior of matter may arise from interaction with the inherently wave-like quantized electromagnetic field—whose quanta are photons, the massless U(1)-gauge bosons—rather than from an intrinsic wave nature of the particles themselves. Our analysis is rigorous and is not speculative, because the proposed Hamiltonian for this system is physical. Within this nonlocal hidden-variable framework, the dot-like interference pattern observed in the double-slit experiment emerges from individual electrons traversing one slit at a time while receiving discrete momentum impulses from stochastic, spatially extended quantized electromagnetic fields.