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:1008.0424

A suggested experiment to distinguish between the Bohmian Interpretation and the Standard Quantum Mechanics

Ke-Xia Jiang, Ke San-Min

Published Aug 2, 2010• 0 citations
arXivHTMLPDF

Abstract

Based on the double-slit experiment of electrons, we suggest a proposal of thought experiment to distinguish between the Bohmian Interpretation (BI) and the Standard Quantum Mechanics (SQM). We mainly focus on the discussion of the meaning of the wave function (Schrödinger-$ψ$). The key technique is require to insert some slow-electrons or weak electron current into the space between the double-slit and the detector plane. We find that the two theories finally give out two totally different results about the affections which the externally inserted electrons cause to the original pattern of the interference fringes. Under the BI, the externally inserted electrons also can be influenced by the Quantum Potential (QP) in a totally same way with the electrons which come from the slits, so the positions they arrived at are preferred to certain bright zones, and the interference pattern will become more clearer. While under the SQM, the Schrödinger-$ψ$ does not represent an objectively real field, but only a mathematical construction of the probability characteristics of the particle itself, so the externally inserted electrons and the electrons which come from the slits have no correlations with each other. No any priority positions at the detector plane the externally inserted electrons will arrive. And the affections are only the addition of a uniform bright background. In such a meaning, the dark zones of the fringes of the interference pattern have been filled.

DOI
10.48550/arxiv.1008.0424

Related papers

On a new prediction of Causal Quantum Mechanics for the two-slit interference experiment with electrons

Eduardo Sergio Santini, Germán M. Chiappe, González, Rafael

The causal quantum mechanics (i.e. Bohmian or de Broglie-Bohm or Bohm-de Broglie quantum mechanics) has made possible to calculate the trajectories of electrons in a typical double-slit experiment [C. Philippidis et al., Il Nuovo Cimento, 52 B, 15-28 (1979)]. The trajectories do not correspond to an uniform movement but to an accelerated one. The acceleration is caused by the quantum potential. From the quantum theoretical point of view, there is a probability for the electron to emit photons, with a certain emission power, during its movement from the slits to the screen. We find a quantum general formula for the emission power of photons, valid independently of the interpretation. Then, according to the Copenhagen interpretation, this formula gives a strictly zero value for the emission power because the electron moves as a free particle after it leaves the slit and before reach the screen. Then, there is no emission of photons. In the case of the causal interpretation, the emission power results, for a concrete real experiment, in a very tiny but not a zero value, driven by the square of the quantum potential gradient. We give an idea of the type of spectrum that could be measured. A brief idea of a possible experimental arrangement in order to detect this effect, is given.

arXiv:1801.02096•Jan 6, 2018•0 citations

Bohmian prediction about a two double-slit experiment and its disagreement with standard quantum mechanics

Mehdi Golshani, Omid Akhavan

The significance of proposals that can predict different results for standard and Bohmian quantum mechanics have been the subject of many discussions over the years. Here, we suggest a particular experiment (a two double-slit experiment) and a special detection process, that we call selective detection, to distinguish between the two theories. Using our suggested experiment, it is shown that the two theories predict different observable results at the individual level for a geometrically symmetric arrangement. However, their predictions are the same at the ensemble level. On the other hand, we have shown that at the statistical level, if we use our selective detection, then either the predictions of the two theories differ or where standard quantum mechanics is silent or vague, Bohmian quantum mechanics makes explicit predictions.

arXiv:quant-ph/0103101•Mar 17, 2001•32 citations

Interpretations of quantum mechanics

Robert B. Griffiths

Jean Bricmont’s review of Travis Norsen’s Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory (Physics Today, April 2018, page 58) stresses the virtues of Louis de Broglie and David Bohm’s pilot-wave interpretation of quantum mechanics, also referred to as Bohmian mechanics (BM), but the review omits mention of some of that interpretation’s rather serious defects. As Bricmont notes, in BM the standard Schrödinger wavefunction ψ(r, t) for a particle is augmented with a classical trajectory r(t) that is interpreted as the actual precise physical position of the particle as a function of time. Sometimes that Bohmian trajectory can provide a helpful intuitive picture, but in other cases it is quite misleading.John Bell presented an example of how Bohmian trajectories can mislead: a modified double-slit experiment with a lens placed right after each slit so that the emerging beams cross on their way to two distant detectors located beyond the crossing point.11. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge U. Press (1987). The beam from the lower slit arrives at the upper detector, and that from the upper slit at the lower detector. If a particle arrives at the upper detector, which slit did it pass through?Bell claims that the naive answer—that the particle came from the lower slit, based on the intuition that particles move in straight lines in a vacuum—is wrong. He notes that a Bohmian particle cannot cross the symmetry plane separating the upper slit and detector from their lower counterparts, and thus a particle arriving at the upper detector actually came from the upper slit: first it moved downward, but when it arrived in the region where the beams cross, it “bounced” back upward toward the upper detector.Years ago I published an analysis that contradicted Bell and showed that the answer he regarded as naive—the particle passes through the crossing region without bouncing—was perfectly good quantum mechanics.22. R. B. Griffiths, Phys. Lett. A 261, 227 (1999). https://doi.org/10.1016/S0375-9601(99)00542-3 I am still waiting for someone in the Bohmian community to publish a reply.Norsen is troubled because the nonlocal, often superluminal influences needed to make sense of BM are hard to reconcile with special relativity. Indeed, the widely accepted no-signaling principle of quantum mechanics asserts that those influences cannot transmit information, so a direct experimental detection of them is out of reach. Defenders of BM say they know that nonlocal influences exist because quantum mechanics violates Bell’s inequalities. But as I and others have pointed out, the hidden variables used in derivations of Bell inequalities are fundamentally classical,33. See R. B. Griffiths, Found. Phys. 41, 705 (2011), and references therein. https://doi.org/10.1007/s10701-010-9512-5 in contrast to the representation of quantum properties by Hilbert subspaces, as introduced by John von Neumann.44. J. von Neumann, Mathematical Foundations of Quantum Mechanics, R. T. Beyer, trans., Princeton U. Press (1955), chap. 3.5. Projectors on those subspaces do not generally commute, which clearly distinguishes quantum physics from classical. Thus that feature, rather than a failure of locality, is why Bell’s inequalities do not agree with quantum theory and experiment.The BM particle trajectories are instances of classical hidden variables, so the nonlocality of the pilot-wave interpretation of quantum mechanics is not surprising. Indeed, when proper account is taken of noncommutativity, one can show that quantum theory satisfies a principle of locality that Albert Einstein might well have agreed with: Objective properties of an isolated individual system do not change when something is done to another, noninteracting system.33. See R. B. Griffiths, Found. Phys. 41, 705 (2011), and references therein. https://doi.org/10.1007/s10701-010-9512-5 Thus a consistent Hilbert-space formulation of quantum theory without hidden variables removes any worry about a conflict with special relativity.Although Bohmian mechanics was worthy of consideration and has been useful in the development of quantum foundations, ignoring more recent developments is not the way to honor the memory of one of the great physicists of the last century. I hope that a second edition of Norsen’s well-written book will take account of more recent work.ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge U. Press (1987). Google Scholar2. R. B. Griffiths, Phys. Lett. A 261, 227 (1999). https://doi.org/10.1016/S0375-9601(99)00542-3, Google ScholarCrossref3. See R. B. Griffiths, Found. Phys. 41, 705 (2011), and references therein. https://doi.org/10.1007/s10701-010-9512-5, Google ScholarCrossref4. J. von Neumann, Mathematical Foundations of Quantum Mechanics, R. T. Beyer, trans., Princeton U. Press (1955), chap. 3.5. Google Scholar© 2019 American Institute of Physics.

Physics Today•Oct 1, 2019•5 citations

Exploration of Alternative Interpretation Approaches to the Physical Mechanism of Electron Double-Slit Interference

Shandong Zhao, Jianshu Luo

The thesis offers an innovative analysis of quantum mechanics. Firstly, it clearly expounds the characteristics of quantum mechanics in measurement and other aspects, and proposes seven criteria for judging scientific nature. Then, it points out that there are some key problems with the orthodox assumptions of quantum mechanics, such as unclear physical mechanisms, lack of rigorous logic, difficulty in falsification, and incomplete main considerations.Regarding the double-slit interference experiment, the thesis conducts a comprehensive derivation and demonstration, proposing a unique interpretation. The traditional view holds that the interference is caused by the wave nature of electrons, while this thesis suggests that it is the periodic fluctuating Coulomb force field in the double-slit slits. A large number of electrons interact with it, undergo regular deflection to form a probability distribution, and then superimpose to produce interference fringes. This interpretation challenges the traditional cognition of the wave nature of microscopic particles in quantum mechanics, prompting us to re-think the basic concepts and experimental interpretations of quantum mechanics from the new perspective of the Coulomb force field, providing new ideas and directions for the study of quantum mechanics.

•Jan 3, 2025•0 citations

The Double-Slit Experiment Reinterpreted: Matter-Wave Propagation and the Physical Mechanism of Quantum Interference

YOUNG HO GOH

The double-slit experiment has stood for a century as the paradigmatic demonstration of quantum superposition: the standard interpretation holds that a particle passes through both slits simultaneously, existing in a superposition of two spatially separated states. This paper proposes a physically distinct alternative: the particle's matter wave — a real physical wave propagating through space in accordance with de Broglie's relation λ = h/p — passes through both slits, while the particle itself (matter) remains in an undetermined state until a constructive interference maximum is formed at the detection screen. The particle does not simultaneously occupy two locations; the wave does. This distinction eliminates the need for superposition as an ontological commitment while fully reproducing the observed interference pattern. We further show that the disappearance of the interference pattern upon which-path measurement is explained without invoking wavefunction collapse: the measurement interaction redirects the matter wave to a single-slit geometry, eliminating the two-wave interference condition. Three experimentally testable predictions distinguish this framework from the standard interpretation: (1) weak-measurement trajectory reconstruction should reveal single particle paths inconsistent with simultaneous two-slit passage; (2) diffraction fringe spacing should depend on the mass density of the slit material, because denser slit edges generate a steeper refractive-index gradient for the matter wave; (3) the fringe pattern should exhibit a density-dependent phase shift measurable with current matter-wave interferometry technology. This reinterpretation requires no new mathematical formalism — the Schrödinger equation and Born's rule are retained — but replaces the ontological claim of simultaneous multi-location existence with the physically consistent picture of matter-wave propagation through an undetermined-state particle.

•Apr 22, 2026•0 citations

When quantum mechanics becomes less weird

Youssef El Fidali

Abstract For about a century, physicists have been debating over the behavior of particles on a microscopic scale. Although the principle of the wave-particle duality is accepted in the scientific community, many experiments with puzzling results are still challenging quantum mechanics until now, such as the double slit experiment, entanglement, interferences of a single electron, or delayed choice quantum eraser. In this article, we shall bring forth explanations for some of these experiments. Unlike standard quantum mechanics (SQM) built by Schr¨odinger1 and P.Dirac2 which considers that the wave function is an abstract mathematical tool, our model takes up the concept of the pilot wave once initiated by physicists De Broglie and D.Bohm,3 who suggested that the wave associated to a quantum object has a real existence and that it is not simply a wave of probability. We shall discuss how this old-new conception of reality renders quantum mechanics ultimately less mysterious than it seems.

•Mar 14, 2023•0 citations
Based on the double-slit experiment of electrons, we suggest a proposal of thought experiment to distinguish between the Bohmian Interpretation (BI) and the Standard Quantum Mechanics (SQM). We mainly focus on the discussion of the meaning of the wave function (Schrödinger-ψψψ). The key technique is require to insert some slow-electrons or weak electron current into the space between the double-slit and the detector plane. We find that the two theories finally give out two totally different results about the affections which the externally inserted electrons cause to the original pattern of the interference fringes. Under the BI, the externally inserted electrons also can be influenced by the Quantum Potential (QP) in a totally same way with the electrons which come from the slits, so the positions they arrived at are preferred to certain bright zones, and the interference pattern will become more clearer. While under the SQM, the Schrödinger-ψψψ does not represent an objectively real field, but only a mathematical construction of the probability characteristics of the particle itself, so the externally inserted electrons and the electrons which come from the slits have no correlations with each other. No any priority positions at the detector plane the externally inserted electrons will arrive. And the affections are only the addition of a uniform bright background. In such a meaning, the dark zones of the fringes of the interference pattern have been filled.
The causal quantum mechanics (i.e. Bohmian or de Broglie-Bohm or Bohm-de Broglie quantum mechanics) has made possible to calculate the trajectories of electrons in a typical double-slit experiment [C. Philippidis et al., Il Nuovo Cimento, 52 B, 15-28 (1979)]. The trajectories do not correspond to an uniform movement but to an accelerated one. The acceleration is caused by the quantum potential. From the quantum theoretical point of view, there is a probability for the electron to emit photons, with a certain emission power, during its movement from the slits to the screen. We find a quantum general formula for the emission power of photons, valid independently of the interpretation. Then, according to the Copenhagen interpretation, this formula gives a strictly zero value for the emission power because the electron moves as a free particle after it leaves the slit and before reach the screen. Then, there is no emission of photons. In the case of the causal interpretation, the emission power results, for a concrete real experiment, in a very tiny but not a zero value, driven by the square of the quantum potential gradient. We give an idea of the type of spectrum that could be measured. A brief idea of a possible experimental arrangement in order to detect this effect, is given.
The significance of proposals that can predict different results for standard and Bohmian quantum mechanics have been the subject of many discussions over the years. Here, we suggest a particular experiment (a two double-slit experiment) and a special detection process, that we call selective detection, to distinguish between the two theories. Using our suggested experiment, it is shown that the two theories predict different observable results at the individual level for a geometrically symmetric arrangement. However, their predictions are the same at the ensemble level. On the other hand, we have shown that at the statistical level, if we use our selective detection, then either the predictions of the two theories differ or where standard quantum mechanics is silent or vague, Bohmian quantum mechanics makes explicit predictions.
Jean Bricmont’s review of Travis Norsen’s Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory (Physics Today, April 2018, page 58) stresses the virtues of Louis de Broglie and David Bohm’s pilot-wave interpretation of quantum mechanics, also referred to as Bohmian mechanics (BM), but the review omits mention of some of that interpretation’s rather serious defects. As Bricmont notes, in BM the standard Schrödinger wavefunction ψ(r, t) for a particle is augmented with a classical trajectory r(t) that is interpreted as the actual precise physical position of the particle as a function of time. Sometimes that Bohmian trajectory can provide a helpful intuitive picture, but in other cases it is quite misleading.John Bell presented an example of how Bohmian trajectories can mislead: a modified double-slit experiment with a lens placed right after each slit so that the emerging beams cross on their way to two distant detectors located beyond the crossing point.11. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge U. Press (1987). The beam from the lower slit arrives at the upper detector, and that from the upper slit at the lower detector. If a particle arrives at the upper detector, which slit did it pass through?Bell claims that the naive answer—that the particle came from the lower slit, based on the intuition that particles move in straight lines in a vacuum—is wrong. He notes that a Bohmian particle cannot cross the symmetry plane separating the upper slit and detector from their lower counterparts, and thus a particle arriving at the upper detector actually came from the upper slit: first it moved downward, but when it arrived in the region where the beams cross, it “bounced” back upward toward the upper detector.Years ago I published an analysis that contradicted Bell and showed that the answer he regarded as naive—the particle passes through the crossing region without bouncing—was perfectly good quantum mechanics.22. R. B. Griffiths, Phys. Lett. A 261, 227 (1999). https://doi.org/10.1016/S0375-9601(99)00542-3 I am still waiting for someone in the Bohmian community to publish a reply.Norsen is troubled because the nonlocal, often superluminal influences needed to make sense of BM are hard to reconcile with special relativity. Indeed, the widely accepted no-signaling principle of quantum mechanics asserts that those influences cannot transmit information, so a direct experimental detection of them is out of reach. Defenders of BM say they know that nonlocal influences exist because quantum mechanics violates Bell’s inequalities. But as I and others have pointed out, the hidden variables used in derivations of Bell inequalities are fundamentally classical,33. See R. B. Griffiths, Found. Phys. 41, 705 (2011), and references therein. https://doi.org/10.1007/s10701-010-9512-5 in contrast to the representation of quantum properties by Hilbert subspaces, as introduced by John von Neumann.44. J. von Neumann, Mathematical Foundations of Quantum Mechanics, R. T. Beyer, trans., Princeton U. Press (1955), chap. 3.5. Projectors on those subspaces do not generally commute, which clearly distinguishes quantum physics from classical. Thus that feature, rather than a failure of locality, is why Bell’s inequalities do not agree with quantum theory and experiment.The BM particle trajectories are instances of classical hidden variables, so the nonlocality of the pilot-wave interpretation of quantum mechanics is not surprising. Indeed, when proper account is taken of noncommutativity, one can show that quantum theory satisfies a principle of locality that Albert Einstein might well have agreed with: Objective properties of an isolated individual system do not change when something is done to another, noninteracting system.33. See R. B. Griffiths, Found. Phys. 41, 705 (2011), and references therein. https://doi.org/10.1007/s10701-010-9512-5 Thus a consistent Hilbert-space formulation of quantum theory without hidden variables removes any worry about a conflict with special relativity.Although Bohmian mechanics was worthy of consideration and has been useful in the development of quantum foundations, ignoring more recent developments is not the way to honor the memory of one of the great physicists of the last century. I hope that a second edition of Norsen’s well-written book will take account of more recent work.ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge U. Press (1987). Google Scholar2. R. B. Griffiths, Phys. Lett. A 261, 227 (1999). https://doi.org/10.1016/S0375-9601(99)00542-3, Google ScholarCrossref3. See R. B. Griffiths, Found. Phys. 41, 705 (2011), and references therein. https://doi.org/10.1007/s10701-010-9512-5, Google ScholarCrossref4. J. von Neumann, Mathematical Foundations of Quantum Mechanics, R. T. Beyer, trans., Princeton U. Press (1955), chap. 3.5. Google Scholar© 2019 American Institute of Physics.
The thesis offers an innovative analysis of quantum mechanics. Firstly, it clearly expounds the characteristics of quantum mechanics in measurement and other aspects, and proposes seven criteria for judging scientific nature. Then, it points out that there are some key problems with the orthodox assumptions of quantum mechanics, such as unclear physical mechanisms, lack of rigorous logic, difficulty in falsification, and incomplete main considerations.Regarding the double-slit interference experiment, the thesis conducts a comprehensive derivation and demonstration, proposing a unique interpretation. The traditional view holds that the interference is caused by the wave nature of electrons, while this thesis suggests that it is the periodic fluctuating Coulomb force field in the double-slit slits. A large number of electrons interact with it, undergo regular deflection to form a probability distribution, and then superimpose to produce interference fringes. This interpretation challenges the traditional cognition of the wave nature of microscopic particles in quantum mechanics, prompting us to re-think the basic concepts and experimental interpretations of quantum mechanics from the new perspective of the Coulomb force field, providing new ideas and directions for the study of quantum mechanics.
The double-slit experiment has stood for a century as the paradigmatic demonstration of quantum superposition: the standard interpretation holds that a particle passes through both slits simultaneously, existing in a superposition of two spatially separated states. This paper proposes a physically distinct alternative: the particle's matter wave — a real physical wave propagating through space in accordance with de Broglie's relation λ = h/p — passes through both slits, while the particle itself (matter) remains in an undetermined state until a constructive interference maximum is formed at the detection screen. The particle does not simultaneously occupy two locations; the wave does. This distinction eliminates the need for superposition as an ontological commitment while fully reproducing the observed interference pattern. We further show that the disappearance of the interference pattern upon which-path measurement is explained without invoking wavefunction collapse: the measurement interaction redirects the matter wave to a single-slit geometry, eliminating the two-wave interference condition. Three experimentally testable predictions distinguish this framework from the standard interpretation: (1) weak-measurement trajectory reconstruction should reveal single particle paths inconsistent with simultaneous two-slit passage; (2) diffraction fringe spacing should depend on the mass density of the slit material, because denser slit edges generate a steeper refractive-index gradient for the matter wave; (3) the fringe pattern should exhibit a density-dependent phase shift measurable with current matter-wave interferometry technology. This reinterpretation requires no new mathematical formalism — the Schrödinger equation and Born's rule are retained — but replaces the ontological claim of simultaneous multi-location existence with the physically consistent picture of matter-wave propagation through an undetermined-state particle.
Abstract For about a century, physicists have been debating over the behavior of particles on a microscopic scale. Although the principle of the wave-particle duality is accepted in the scientific community, many experiments with puzzling results are still challenging quantum mechanics until now, such as the double slit experiment, entanglement, interferences of a single electron, or delayed choice quantum eraser. In this article, we shall bring forth explanations for some of these experiments. Unlike standard quantum mechanics (SQM) built by Schr¨odinger1 and P.Dirac2 which considers that the wave function is an abstract mathematical tool, our model takes up the concept of the pilot wave once initiated by physicists De Broglie and D.Bohm,3 who suggested that the wave associated to a quantum object has a real existence and that it is not simply a wave of probability. We shall discuss how this old-new conception of reality renders quantum mechanics ultimately less mysterious than it seems.