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arXiv:1811.09488 · Physica Scripta

Computer model of the two-pinhole interference experiment using two-dimensional Gaussian wave-packets

P N Kaloyerou, A M Ilunga

Published Apr 2, 2019• 2 citations
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Abstract

Abstract The two-slit interference experiment has been modeled a number of times using Gaussian wave-packets and the Bohm–de Broglie causal interpretation. Here we consider the experiment with pinholes instead of slits and model the experiment in terms of two-dimensional Gaussian wave-packets and the Bohm–de Broglie causal interpretation.

DOI
10.1088/1402-4896/ab1547

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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 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, the accelerated electrons should, with a certain probabil-ity, emit photons during its movement from the slits to the screen. According to the Copenhagen interpretation we found that this quantity is strictly zero because the electron moves as a free particle along its path after it leaves the slit and before reach the screen. Then, there is no emission of photons. On the other hand, by using the Bohm-de Broglie (BdB) approach we calculate the emission power, giving a general formula and which results, for a concrete real experiment, in a very tiny but not a vanishing value. We give an idea of the type of spectrum that could be measured. Therefore we have shown that the theoretical predictions of the usual quan-tum mechanics and that of Bohm-de Broglie’s interpretation are different. An experiment could determine the correct prediction.
Abstract Chapter 11 introduces the essential mystery of quantum mechanics, shows how it is resolved, and then goes on to examine related phenomena. The mystery is how individual photons, not electromagnetic waves, can give rise to the interference pattern seen in the two-slit experiment. They are shown to do so because the relevant quantum amplitude is a linear combination of two terms, leading to the pattern when neither slit is identified as the one the photon went through, but collapsing to one term and no pattern if the slit is identified. Similar results are shown to occur when individual electrons are incident on the two slits, and when large molecules, which have de Broglie wavelengths, are scattered by diffraction gratings. Many other interference experiments are described, including those where a photon was shown to be in two places simultaneously and one where a photon displayed both wave and particle features.