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arXiv:1402.4315

Comments to Asking Photons Where They Have Been (A Danan et al, Phys. Rev. Lett. 111, 240402 (2013))

B. E. Y. Svensson

Published Feb 18, 2014• 0 citations
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Abstract

I critize some of the conclusions in the paper by Danan et al, in particular their claim that '(S)ome (of the photons) have been inside the nested interferometer ... but they never entered and never left (it) ...'. A standard quantum-mechanical analysis also casts doubts on their statement that '(o)nly the description with forward and backward evolving quantum states provides a simple and intuitive picture of pre- and postselected quantum particles.'

DOI
10.48550/arxiv.1402.4315

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I critize some of the conclusions in the paper by Danan et al, in particular their claim that '(S)ome (of the photons) have been inside the nested interferometer ... but they never entered and never left (it) ...'. A standard quantum-mechanical analysis also casts doubts on their statement that '(o)nly the description with forward and backward evolving quantum states provides a simple and intuitive picture of pre- and postselected quantum particles.'
In an recent work with the title ``Asking Photons Where They Have Been,'' Danan et al. experimentally demonstrate an intriguing behavior of photons in an interferometer [Phys. Rev. Lett. 111, 240402 (2013)]. In their words: ``The photons tell us that they have been in the parts of the interferometer through which they could not pass.'' They interpret the results using the two-state vector formalism of quantum theory and say that, although an explanation of the experimental results in terms of classical electromagnetic waves in the interferometer is possible (and they provide a partial description), it is not so intuitive. Here we present a more detailed classical description of their experimental results, showing that it is actually intuitive. The same description is valid for the quantum wave function of the photons propagating in the interferometer. In particular, we show that it is essential that the wave propagates through all parts of the interferometer to describe the experimental results. We hope that our work helps to give a deeper understanding of these interesting experimental results.
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.
In a paper titled ``Asking photons where they have been? Danan, Farfurnik, Bar-Ad and Vaidman describe an experiment with pre and post selected photons going through nested Mach-Zehnder interferometers. They find that some of the mirrors leave no footprints on the signal and interpret this as evidence that the photon skipped these mirrors and by a discontinuous path. I review the experiment and analyze it within the orthodox framework of quantum mechanics. The picture of interfering multiple trajectories provide a satisfactory explanation of the experimental findings and the absence of footprints.
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.
Using the most basic mathematical tools, I present the full analysis of the experiment decribed in [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, {\em Phys. Rev. Lett.} {\bf 111}, 240402 (2013)]. First, I confirm that the data presented therein are in full agreement with the standard quantum mechanics. I then show other symptoms of presence of photons at all mirrors in the setup. I then analytically explain both the absence of peaks a Readers of [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, {\em Phys. Rev. Lett.} {\bf 111}, 240402 (2013)] are made to expect and presence of those not discussed in the Reference.