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arXiv:2311.03525 · The European Physical Journal Plus

Comment on “photons can tell ‘contradictory’ answer about where they have been”

Gregory Reznik, Carlotta Versmold, Jan Dziewior, Florian Huber, Harald Weinfurter, Justin Dressel, Lev Vaidman A

Published Feb 21, 2024• 2 citations
arXivHTMLPDF

Abstract

Abstract Yuan and Feng (Eur. Phys. J. Plus 138:70, 2023) recently proposed a modification of the nested Mach–Zehnder interferometer experiment performed by Danan et al. (Phys. Rev. Lett. 111:240402, 2013) and argued that photons give “contradictory” answers about where they have been, when traces are locally imprinted on them in different ways. They concluded that their results are comprehensible from what they call the “three-path interference viewpoint,” but difficult to explain from the “discontinuous trajectory” viewpoint advocated by Danan et al. We argue that the weak trace approach (the basis of the “discontinuous trajectory” viewpoint) provides a consistent explanation of the Yuan–Feng experiment. The contradictory messages of the photons are just another example of photons lying about where they have been when the experimental method of Danan et al. is applied in an inappropriate setup.

DOI
10.1140/epjp/s13360-023-04818-0

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The author of the comment on my work [1] states that the proposed modification of the scheme of the experiment reported in [2] is improper and that the experiment faithfully demonstrates a discontinuous trace of photons.It is difficult to agree with this statement because of the absence of clear and well-founded (see below).In [1], I discussed the recent experiment [2] with a nested Mach-Zehnder interferometer.The authors treated the experiment so that the past of photons is not described by continuous trajectories because photons are detected inside the inner Mach-Zehnder interferometer and are not detected outside it.The idea of a small modification of the scheme of the experiment [2] has been proposed just to detect photons at the input of the inner Mach-Zehnder interferometer.Instead of the vibration of the mirror, the direction of polarization of light is modulated in this scheme.Further, in one of the arms of the inner Mach-Zehnder interferometer, this modulation is converted into a shift of the light beam of orthogonal polarization, which is then transformed to the original polarization.The realization of the idea is as follows.A birefringent plate, a phase compensator, and two polarizers that oriented at the angle of 45° and in parallel to the initial polarization are placed in one of the arms of the inner Mach-Zehnder interferometer.The same polarizers are placed in the other two arms of the nested Mach-Zehnder interferometer.The author of the comment states that such a modification is improper because it "violates the faithfulness of the experiment because it causes different transformations of the polarization record at E into a signal at the detector, depending on the path the beam takes."The author of the comment also claims that "the signal at the detector does not present a faithful indication of the trace inside the interferometer" in the absence of con-

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Abstract Yuan and Feng (Eur. Phys. J. Plus 138:70, 2023) recently proposed a modification of the nested Mach–Zehnder interferometer experiment performed by Danan et al. (Phys. Rev. Lett. 111:240402, 2013) and argued that photons give “contradictory” answers about where they have been, when traces are locally imprinted on them in different ways. They concluded that their results are comprehensible from what they call the “three-path interference viewpoint,” but difficult to explain from the “discontinuous trajectory” viewpoint advocated by Danan et al. We argue that the weak trace approach (the basis of the “discontinuous trajectory” viewpoint) provides a consistent explanation of the Yuan–Feng experiment. The contradictory messages of the photons are just another example of photons lying about where they have been when the experimental method of Danan et al. is applied in an inappropriate setup.
We argue that the modification proposed by Li et al. [Chin. Phys. Lett. 32 (2015) 050303] to the experiment of Danan et al. [Phys. Rev. Lett. 111 (2013) 240402] does not test the past of the photon as characterized by local weak traces. Instead of answering the questions: (i) were the photons in A? (ii) were the photons in B? and (iii) were the photons in C? the proposed experiment measures a degenerate operator answering the questions: (i) were the photons in A? and (ii) were the photons in B and C together? A negative answer to the last question does not tell us if photons were present in B or C. On the other hand, a simple variation of the proposal by Li et al. does provide conceptually better evidence for the past of the pre- and post-selected photon, but this evidence will be in agreement with the results of Danan et al.
Recently, a scheme based on the method of weak measurements to register the trajectories of photons passing through a nested Mach–Zehnder interferometer was proposed [L. Vaidman, Phys. Rev. A 87 , 052104 (2013)] and then realized [A. Danan, D. Farfurnik, S. Bar-Ad, et al., Phys. Rev. Lett. 111 , 240402 (2013)]. Interpreting the results of the experiment, the authors concluded that “the photons do not always follow continuous trajectories.” It is shown in this work that these results can be easily and clearly explained in terms of traditional classical electrodynamics or quantum mechanics implying the continuity of all possible paths of photons. Consequently, a new concept of disconnected trajectories proposed by the authors of work [Phys. Rev. Lett. 111 , 240402 (2013)] is unnecessary.
The author of the comment on my work [1] states that the proposed modification of the scheme of the experiment reported in [2] is improper and that the experiment faithfully demonstrates a discontinuous trace of photons.It is difficult to agree with this statement because of the absence of clear and well-founded (see below).In [1], I discussed the recent experiment [2] with a nested Mach-Zehnder interferometer.The authors treated the experiment so that the past of photons is not described by continuous trajectories because photons are detected inside the inner Mach-Zehnder interferometer and are not detected outside it.The idea of a small modification of the scheme of the experiment [2] has been proposed just to detect photons at the input of the inner Mach-Zehnder interferometer.Instead of the vibration of the mirror, the direction of polarization of light is modulated in this scheme.Further, in one of the arms of the inner Mach-Zehnder interferometer, this modulation is converted into a shift of the light beam of orthogonal polarization, which is then transformed to the original polarization.The realization of the idea is as follows.A birefringent plate, a phase compensator, and two polarizers that oriented at the angle of 45° and in parallel to the initial polarization are placed in one of the arms of the inner Mach-Zehnder interferometer.The same polarizers are placed in the other two arms of the nested Mach-Zehnder interferometer.The author of the comment states that such a modification is improper because it "violates the faithfulness of the experiment because it causes different transformations of the polarization record at E into a signal at the detector, depending on the path the beam takes."The author of the comment also claims that "the signal at the detector does not present a faithful indication of the trace inside the interferometer" in the absence of con-
We present a three-path photon interferometer, theoretically investigate the behavior of the photon passing through it, and revisit the surprising experimental outcomes introduced by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)]. Our study shows that the ``discontinuous trajectory'' behavior of the photon results from the interference of the three propagation paths of the photon, which originate from the light source and end in the detector. If two of the three paths are adjusted in a destructive interference condition, there will be a zero probability domain in the overlap region of these two paths. However, these two paths can still individually interfere with the third path and contribute to the final output. In this condition, the discontinuous trajectory phenomenon appears. Our theory has a clear physical image and agrees with the experimental outcomes very well.
Poto\ifmmode \check{c}\else \v{c}\fi{}ek and Ferenczi [Phys. Rev. A 92, 023829 (2015)] provided an analysis of the experimental evidence obtained by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] for the surprising behavior of photons passing through an interferometer, in particular, motion on disconnected paths. Poto\ifmmode \check{c}\else \v{c}\fi{}ek and Ferenczi reproduced the results of the experiment, but when analyzing its modification, they claimed that the reasoning of Danan et al., which led to disconnected paths, is erroneous. It is argued here that the criticism of Poto\ifmmode \check{c}\else \v{c}\fi{}ek and Ferenczi is unfounded.
Bartkiewicz et al. [Phys. Rev. A 91, 012103 (2015)] provided an alternative analysis of an experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] which presented surprising evidence regarding the past of photons passing through an interferometer. They argued that the quantity used by Danan et al. is not a suitable which-path witness, and proposed an alternative. The weaknesses of the analysis are discussed, and it is argued that the alternative, analyzed properly, provides no new predictions.