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arXiv:1009.2408 · European Journal of Physics

‘Quantum interference with slits’ revisited

Tony Rothman, S. P. Boughn

Published Nov 25, 2010• 4 citations
arXivHTMLPDF

Abstract

Marcella [arXiv:quant-ph/0703126] has presented a straightforward technique employing the Dirac formalism to calculate single- and double-slit interference patterns. He claims that no reference is made to classical optics or scattering theory and that his method therefore provides a purely quantum mechanical description of these experiments. He also presents his calculation as if no approximations are employed. We show that he implicitly makes the same approximations found in classical treatments of interference and that no new physics has been introduced. At the same time, some of the quantum mechanical arguments Marcella gives are, at best, misleading.

DOI
10.1088/0143-0807/32/1/010

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Marcella [arXiv:quant-ph/0703126] has presented a straightforward technique employing the Dirac formalism to calculate single- and double-slit interference patterns. He claims that no reference is made to classical optics or scattering theory and that his method therefore provides a purely quantum mechanical description of these experiments. He also presents his calculation as if no approximations are employed. We show that he implicitly makes the same approximations found in classical treatments of interference and that no new physics has been introduced. At the same time, some of the quantum mechanical arguments Marcella gives are, at best, misleading.
Marcella has presented a straightforward technique employing the Dirac formalism to calculate single-and double-slit interference patterns.He claims that no reference is made to classical optics or scattering theory and that his method therefore provides a purely quantum mechanical description of these experiments.He also presents his calculation as if no approximations are employed.We show that he implicitly makes the same approximations found in classical treatments of interference and that no new physics has been introduced.At the same time, some of the quantum mechanical arguments Marcella gives are, at best, misleading.
Marcella in 2002 published a "quantum-mechanical" treatment of the famous single- and double-slit interference experiment in classical wave optics by a simple assumption that quantum mechanical wave function is a constant anywhere within a slit. Rothman and Boughn in 2011 commented that Marcella introduced no quantum physics into the problem other than\ a symbol substitution p=ℏkp=\hbar kp=ℏk, and the used essentially the classical wave optics. In present comment, we point out that though Marcella made a fundamental mistake, the problem is nevertheless remediable to give the satisfactory quantum mechanical results which are in qualitatively agreement with experimental ones with material particles.
A recently proposed model of the Dirac electron, which has been shown to describe several observed properties of the particle correctly, is in the present paper shown to be also able to explain quantum interference by classical probabilities. According to this model, the electron is not point-like, but rather an “entity with structure”, formed by a fast periodic motion of a “light-like object”, whose momentum (p) causes the angular momentum responsible for the spin, and whose energy (E = pc) is equal to the energy of the electron, mc2. A qualitative description of the model is given, together with the quantitative formulae that allow to discuss interference. Applied to the experimental situation of the “two-slit” experiment, the formulae yield the same time dependence of the detection probability as the quantum mechanical treatment, and hence the same interference pattern. In contrast to quantum mechanics, the pattern is due to “particle interference” rather than to “wave interference”. No wave-particle paradox arises. The merits of the model are summarized, and its physical content discussed.
It was recently argued by Catani et al that it is possible to reproduce the phenomenology of quantum interference classically, by the double-slit experiment with a deterministic, local, and classical model (Quantum 7, 1119 (2023)). The stated aim of their argument is to falsify the claim made by Feynman (in his third book of Lectures on Physics) that quantum interference is ``impossible, absolutely impossible, to explain in any classical way'' and that it ``contains the only mystery'' of quantum mechanics. We here want to point out some problems with their argument.
Young’s double slit experiment was called as "a phenomenon […] has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by ‘explaining’ how it works". To study the mystery, we perform the non-crossing-slit-experiments and crossing-slit experiments and show phenomena: (1) in the same double slit or cross double slit experiments, the non-interference patterns gradually evolve to the interference patterns; (2) in the same single slit or cross single slit experiments, the non-diffraction patterns gradually evolve to the diffraction patterns; (3) in the same two-non-parallel-slits experiment, the non-wave patterns gradually evolve to the hybrid pattern (i.e., interference-pattern-embedded-in-diffraction-pattern); (4) in the same curved-double slit experiments, the non-interference patterns evolve to Seashell-shape interference patterns. The above phenomena show new mysteries that are more mysterious than that of the double slit experiments: it is challenge to consistently explain how they work. Those novel phenomena indicate that the standard theories of the double slit are incomplete. Novel experiments bring the search for the new theory of physical/quantum optics.
Young’s double slit experiment was called as "a phenomenon […] has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by ‘explaining’ how it works". To study the mystery, we perform the non-crossing-slit-experiments and crossing-slit experiments and show phenomena: (1) in the same double slit or cross double slit experiments, the non-interference patterns gradually evolve to the interference patterns; (2) in the same single slit or cross single slit experiments, the non-diffraction patterns gradually evolve to the diffraction patterns; (3) in the same two-non-parallel-slits experiment, the non-wave patterns gradually evolve to the hybrid pattern (i.e., interference-pattern-embedded-in-diffraction-pattern); (4) in the same curved-double slit experiments, the non-interference patterns evolve to Seashell-shape interference patterns. The above phenomena show new mysteries that are more mysterious than that of the double slit experiments: it is challenge to consistently explain how they work. Those novel phenomena indicate that the standard theories of the double slit are incomplete. Novel experiments bring the search for the new theory of physical/quantum optics.