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The Quantum Mechanical Two-Slit Interference Experiment Modelled Using Spherical Waves

Panayiotis Nicos Kaloyerou

Published Aug 26, 2025• 0 citations
Publisher

Abstract

Abstract The 2011 experiment by Kocsis et al., using the weak measurement protocol, confirmed the distinctive particle trajectory pattern given by the Bohm-de Broglie causal interpretation model of the quantum version of Young's two-slit experiment. The model uses Gaussian wave-packets. Given that the original (classical) Young's two-slit experiment was modelled by Fresnel in terms of Huygens' spherical waves, we thought it would be interesting to test whether a spherical wave model of the quantum Young's two-slit experiment would yield a similar description, in particular, whether or not the distinctive particle trajectory pattern confirmed by experiment would be reproduced. PACS NO. 03.65.-w

DOI
10.21203/rs.3.rs-2963522/v1

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Abstract The 2011 experiment by Kocsis et al., using the weak measurement protocol, confirmed the distinctive particle trajectory pattern given by the Bohm-de Broglie causal interpretation model of the quantum version of Young's two-slit experiment. The model uses Gaussian wave-packets. Given that the original (classical) Young's two-slit experiment was modelled by Fresnel in terms of Huygens' spherical waves, we thought it would be interesting to test whether a spherical wave model of the quantum Young's two-slit experiment would yield a similar description, in particular, whether or not the distinctive particle trajectory pattern confirmed by experiment would be reproduced. PACS NO. 03.65.-w
Abstract Young’s double slit experiments, which represent the mystery of quantum mechanics, have been interpreted by quantum probability waves and de Broglie-Bohm’s trajectory/pilot waves. To study in detail, the double slit experiments are extended to the cross double slit experiments. We argue that an interpretation must be able to explain all of the double slit and cross double slit experiments consistently. To test the interpretations, the comprehensive double slit experiments have been performed, which challenge both the wave interpretation and the trajectory interpretation. The cross double slit experiments and comprehensive double slit experiments provide a new tool for studying the mystery of double slit, wave-particle duality, complementarity principle, wave theory and trajectory theory. In this article, we review the cross double slit experiments and comprehensive double slit experiments, and report new experiments.
Young’s double slit experiments, which represent the mystery of quantum mechanics, have been interpreted by quantum probability waves and by de Broglie-Bohm trajectories/pilot waves. Computer simulations of Bohm’s theory predict that (1) trajectories cannot cross, and (2) there is a triangle-shape area behind the double slit, in which there is no trajectory, i.e., no photons. In this article, we report the observations of novel comprehensive double slit experiments, which show that trajectories exist and cross in the triangular area. We show new phenomena that, in 2D cross double slit experiments and which way 2D cross double slit experiments, photons propagate along trajectories in the far field, and behave as particle and distribute as wave.
The standard quantum theory has not taken into account the size of quantum particles, the latter being implicitly treated as material points. The recent interference experiments of Zeilinger [3] with large molecules like fullerenes and the thought experiments of Bozic et al [7] with asymmetrical Young slits make it possible today to take into account the particle size. We present here a complete study of this phenomenon where our simulations show differences between the particles density after the slits and the modulus square of the wave function. Then we propose a crucial experiment that allows us to reconsider the wave-particle duality and to test the existence of the Broglie-Bohm trajectories for indistinguishable particles.
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.
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.