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arXiv:quant-ph/0507044 · Physics Letters A

On the significance of a recent experiment demonstrating quantum interference in time

Lawrence Paul Horwitz

Published Feb 14, 2006• 33 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2006.01.097

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I comment on the interpretation of a recent experiment showing quantum interference in time. It is pointed out that the standard nonrelativistic quantum theory, used by the authors in their analysis, cannot account for the results found, and therefore that this experiment has fundamental importance beyond the technical advances it represents. The recent experiment of Lindner, et al 1, clearly shows the effect of interference in time for a particle wave function. The results are discussed in that paper in terms of a very precise solution of the time-dependent nonrelativistic Schrödinger equation. In this Comment, I wish to point out that the nonrelativistic Schrödinger theory cannot predict interference phenomena in time, and therefore the very striking results of this beautiful experiment have a fundamental importance which goes beyond the technical advances which it represents. It is well known, in fact, that the nonrelativistic quantum theory cannot predict interference in time. For example, Ludwig 2 has pointed out that the time variable cannot be a quantum observable, a prerequisite for the development of interference phenomena, since

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I comment on the interpretation of a recent experiment showing quantum interference in time. It is pointed out that the standard nonrelativistic quantum theory, used by the authors in their analysis, cannot account for the results found, and therefore that this experiment has fundamental importance beyond the technical advances it represents. The recent experiment of Lindner, et al 1, clearly shows the effect of interference in time for a particle wave function. The results are discussed in that paper in terms of a very precise solution of the time-dependent nonrelativistic Schrödinger equation. In this Comment, I wish to point out that the nonrelativistic Schrödinger theory cannot predict interference phenomena in time, and therefore the very striking results of this beautiful experiment have a fundamental importance which goes beyond the technical advances which it represents. It is well known, in fact, that the nonrelativistic quantum theory cannot predict interference in time. For example, Ludwig 2 has pointed out that the time variable cannot be a quantum observable, a prerequisite for the development of interference phenomena, since
Quantum mechanics and general relativity have been each successfully tested in numerous experiments. However, the regime where both theories are jointly required to explain physical phenomena remains untested by laboratory experiments, and is also not fully understood by theory. This contribution reviews recent ideas for a new type of experiments: quantum interference of "clocks", which aim to test novel quantum effects that arise from time dilation. "Clock" interference experiments could be realised with atoms or photons in near future laboratory experiments.
In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well-known text books in quantum mechanics implicitly and/or explicitly use this assumption that is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from nonclassical paths in quantum interference experiments that provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these nonclassical paths is difficult to present. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.