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American Journal of Modern Physics

An Attempt to Describe Quantum Interference on two Slits in Classical Terms

Vladimir K. Ignatovich, K. E. Batkov

Published Jun 9, 2015• 0 citations
OpenAlex

Abstract

An idea of interpretation of quantum interference in classical terms is presented. Classical propagation of an electron through a slit in a perfectly conducting screen is considered. The change of the electron trajectory under influence of a nearby slit in the same screen is evaluated. The goal of this study is to see whether the influence of the second slit on the electron trajectory can be interpreted as interference in quantum mechanics.

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An idea of interpretation of quantum interference in classical terms is presented. Classical propagation of an electron through a slit in a perfectly conducting screen is considered. The change of the electron trajectory under influence of a nearby slit in the same screen is evaluated. The goal of this study is to see whether the influence of the second slit on the electron trajectory can be interpreted as interference in quantum mechanics.
We consider a classical analogue of the well known quantum two-slit experiment. Charged particles are scattered on flat screen with two slits and hit the second screen. We show that the probability distribution on the second screen when both slits are open is not given by the sum of distributions for each slit separately, but has an extra interference term that is given with the quantum rule of the addition of probabilistic alternatives. We show that the proposed classical model has a context dependence and could be adequately described with contextual formalism.
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.
Single-slit and two-slit interferometer measurements of electrons are analyzed within the realistic model of particle propagation. In a step by step procedure we show that all current models of interference are essentially non-local and demonstrate that the treatment of the quantum theory of motion is the simplest model for the scalar problem. In particular we give a novel interpretation of the quantum potential Q, which should be regarded as a non-classical and essentially statistical term describing the changes of the quantum ensemble due to a change of the physical environment.
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.
This paper discusses up to what point the fundamental two slits electron diffraction experiment can be modelled as a purely classical electromagnetic scattering problem [1]. The trajectories of single point charges (electrons with no spin) are computed as they pass, one by one, between two ungrounded perfectly conducting spheres, all computations being exclusively based on classical electromagnetic theory [2]. The computed particles trajectories clearly exhibit “interference like” behavior like those predicted by quantum theory, namely• Particles trajectories deviations depending on the accelerating voltage, spheres radii, separation (gap) and initial particle coordinates• Trajectories exhibiting velocity/energy discontinuities similar to quantum trajectories• Depending on the overall system dimensions, the energy jumps associated to observed trajectory discontinuity have been found to bear a clear association to the energy jumps in quantum systems as expressed in terms of Pank ́s constant h.