# Afshar experiment

The Afshar experiment is a variation of the double slit experiment in quantum mechanics, devised and carried out by Shahriar Afshar while at the private, Boston-based Institute for Radiation-Induced Mass Studies (IRIMS).[1] The results were presented at a Harvard seminar in March 2004.[2] Afshar claimed that the experiment gives information about which of two paths a photon takes through the apparatus while simultaneously allowing interference between the two paths to be observed, by showing that a grid of wires, placed at the nodes of the interference pattern, does not alter the beams.[3] Afshar claimed that the experiment violates the principle of complementarity of quantum mechanics,[4] which states roughly that the particle and wave aspects of quantum objects cannot be observed at the same time, and specifically the Englert–Greenberger duality relation.[5] The experiment has been repeated by a number of investigators but its interpretation is controversial, and some disagree that it violates complementarity, while also disagreeing amongst themselves as to why.[6][7][8][9][10]

## Overview

Afshar's experiment uses a variant of Thomas Young's classic double-slit experiment to create interference patterns to investigate complementarity. One of Afshar's assertions is that, in his experiment, it is possible to check for interference fringes of a photon stream (a measurement of the wave nature of the photons) while at the same time determining each photon's "which-path" information (a measurement of the particle nature of the photons).[3][11] In his experiment, pinhole A is correlated to detector 1 when pinhole B is closed, and pinhole B is correlated to detector 2 when pinhole A is closed. Afshar's claim for the violation of the principle of complementarity depends crucially on his assertion that these correlations remain, and thus which-path information is preserved, when both pinholes are open, and cites Wheeler[12] in support.[5]

## History

Shahriar S. Afshar's experimental work was done initially at the Institute for Radiation-Induced Mass Studies (IRIMS) in Boston in 2001 and later reproduced at Harvard University in 2003, while he was a research scholar there.[1] The results were presented at a Harvard seminar in March 2004,[2] and published as conference proceeding by The International Society for Optical Engineering (SPIE).[3] The experiment was featured as the cover story in the July 24, 2004 edition of New Scientist.[1][13] The New Scientist feature article itself generated many responses, including various letters to the editor that appeared in the August 7 and August 14, 2004 issues, arguing against the conclusions being drawn by Afshar, with John G. Cramer's response.[14] Afshar presented his work also at the American Physical Society meeting in Los Angeles, in late March 2005.[15] His peer-reviewed paper was published in Foundations of Physics in January 2007.[5]

## Experimental setup

Fig.1 Experiment without obstructing wire grid
Fig.2 Experiment with obstructing wire grid and one pinhole covered
Fig.3 Experiment with wire grid and both pinholes open. The wires lie in the dark fringes and thus block very little light

The experiment uses a setup similar to that for the double-slit experiment. In Afshar's variant, light generated by a laser passes through two closely spaced circular pinholes (not slits). After the dual pinholes, a lens refocuses the light so that the image of each pinhole falls on separate photon-detectors (Fig. 1). With Pinhole 2 closed, a photon that goes through Pinhole 1 impinges only on Photon Detector 1. Similarly, with Pinhole 1 closed, a photon that goes through Pinhole 2 impinges only on Photon Detector 2. With both pinholes open, Afshar claims, citing Wheeler[12] in support, that Pinhole 1 remains correlated to Photon Detector 1 (and vice versa for Pinhole 2 to Photon Detector 2), and therefore that which-way information is preserved when both pinholes are open.[5]

When the light acts as a wave, because of quantum interference one can observe that there are regions that the photons avoid, called dark fringes. A grid of thin wires is placed just before the lens (Fig. 2) so that the wires lie in the dark fringes of an interference pattern which is produced by the dual pinhole setup. If one of the pinholes is blocked, the interference pattern will no longer be formed, and the grid of wires causes appreciable diffraction in the light and blocks some of it from detection by the corresponding photon detector. However, when both pinholes are open, the effect of the wires is negligible, comparable to the case in which there are no wires placed in front of the lens (Fig.3), because the wires lie in the dark fringes of an interference pattern. The effect is not dependent on the light intensity (photon flux).

To establish violation of the principle of complementarity, Afshar considers the case in which both pinholes are open and asserts both high visibility V of interference as well as high distinguishability D (corresponding to which-path information), so that V2 + D2 > 1.[5] His claim depends heavily on whether which-path information is preserved when both pinholes are open.

## Afshar's Interpretation

Afshar's conclusion is that, when both pinholes are open, the light exhibits wave-like behavior when going past the wires, since the light goes through the spaces between the wires but avoids the wires themselves, but also exhibits particle-like behavior after going through the lens, with photons going to a correlated photo-detector. Afshar argues that this behavior contradicts the principle of complementarity to the extent that it shows both wave and particle characteristics in the same experiment for the same photons.

## Reception

### Specific criticism

A number of scientists have published criticisms of Afshar's interpretation of his results, some of which reject the claims of a violation of complementarity, while differing in the way they explain how complementarity copes with the experiment. Afshar has responded to these critics in his academic talks, his blog, and other forums. For example, one paper contests Afshar's core claim, that the Englert–Greenberger duality relation is violated. The researchers re-ran the experiment, using a different method for measuring the visibility of the interference pattern than that used by Afshar, and found no violation of complementarity, concluding "This result demonstrates that the experiment can be perfectly explained by the Copenhagen interpretation of quantum mechanics."[8]

Below is a synopsis of papers by several critics highlighting their main arguments and the disagreements they have amongst themselves:

• Ruth Kastner, Committee on the History and Philosophy of Science, University of Maryland, College Park.[6][16]
Kastner's criticism, published in a peer-reviewed paper, proceeds by setting up a thought experiment and applying Afshar's logic to it to expose its flaw. She proposes that Afshar's experiment is equivalent to preparing an electron in a spin-up state and then measuring its sideways spin. This does not imply that one has found out the up-down spin state and the sideways spin state of any electron simultaneously. Applied to Afshar's experiment: "Nevertheless, even with the grid removed, since the photon is prepared in a superposition S, the measurement at the final screen at t2 never really is a 'which-way' measurement (the term traditionally attached to the slit-basis observable ${\displaystyle {\mathcal {O}}}$), because it cannot tell us 'which slit the photon actually went through.'
• Daniel Reitzner, Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia.[17]
Reitzner performed numerical simulations, published in a preprint, of Afshar's arrangement and obtained the same results that Afshar obtained experimentally. From this he argues that the photons exhibit wave behavior, including high fringe visibility but no which-way information, up to the point they hit the detector: "In other words the two-peaked distribution is an interference pattern and the photon behaves as a wave and exhibits no particle properties until it hits the plate. As a result a which-way information can never be obtained in this way."
• W. G. Unruh, Professor of Physics at University of British Columbia[18]
Unruh, like Kastner, proceeds by setting up an arrangement that he feels is equivalent but simpler. The size of the effect is larger so that it is easier to see the flaw in the logic. In Unruh's view that flaw is, in the case that an obstacle exists at the position of the dark fringes, "drawing the inference that IF the particle was detected in detector 1, THEN it must have come from path 1. Similarly, IF it were detected in detector 2, then it came from path 2." In other words, he accepts the existence of an interference pattern but rejects the existence of which-way information.
• Luboš Motl, Former Assistant Professor of Physics, Harvard University.[19]
Motl's criticism, published in his blog, is based on an analysis of Afshar's actual setup, instead of proposing a different experiment like Unruh and Kastner. In contrast to Unruh and Kastner, he believes that which-way information always exists, but argues that the measured contrast of the interference pattern is actually very low: "Because this signal (disruption) from the second, middle picture is small (equivalently, it only affects a very small portion of the photons), the contrast V is also very small, and goes to zero for infinitely thin wires." He also argues that the experiment can be understood with classical electrodynamics and has "nothing to do with quantum mechanics".
• Aurelien Drezet, Néel Institute, Grenoble, France.[20][21]
Drezet argues that the classical concept of a "path" leads to much confusion in this context, but "The real problem in Afshar's interpretation comes from the fact that the interference pattern is not actually completely recorded." The argument is similar to that of Motl's, that the observed visibility of the fringes is actually very small. Another way he looks at the situation is that the photons used to measure the fringes are not the same photons that are used to measure the path. The experimental setup he analyzes is only a "slightly modified version" of the one used by Afshar.
• Ole Steuernagel, School of Physics, Astronomy and Mathematics, University of Hertfordshire, UK.[7]
Steuernagel makes a quantitative analysis of the various transmitted, refracted, and reflected modes in a setup that differs only slightly from Afshar's. He concludes that the Englert-Greenberger duality relation is strictly satisfied, and in particular that the fringe visibility for thin wires is small. Like some of the other critics, he emphasizes that inferring an interference pattern is not the same as measuring one: "Finally, the greatest weakness in the analysis given by Afshar is the inference that an interference pattern must be present."
• Andrew Knight argues that Afshar’s claim to violate complementarity is a simple logical inconsistency: by setting up the experiment so that photons are spatially coherent over the two pinholes, the pinholes are necessarily indistinguishable by those photons.[22] “In other words, Afshar et al. claim in one breath to have set up the experiment so that pinholes A and B are inherently indistinguishable by certain photons [specifically, photons that are produced to be spatially coherent over the width spanned by pinholes that are thus incapable of distinguishing them], and in another breath to have distinguished pinholes A and B with those same photons.”

### Specific support

• Flores et al. criticize Kastner's setup and propose an alternative experimental setup.[23] By removing the lens of Afshar and causing two beams to overlap at a small angle, Flores et al. aimed to show that conservation of momentum guarantee the preservation of which-path information when both pinholes are open.

## References

1. ^ a b c Chown, Marcus (2004). "Quantum rebel wins over doubters". New Scientist. 183 (2457): 30–35.(subscription required)
2. ^ a b S. S. Afshar (2004). "Waving Copenhagen Good-bye: Were the founders of Quantum Mechanics wrong?". Harvard Seminar Announcement. Retrieved 2013-12-01.
3. ^ a b c S. S. Afshar (2005). Roychoudhuri, Chandrasekhar; Creath, Katherine (eds.). "Violation of the principle of complementarity, and its implications". Proceedings of SPIE. The Nature of Light: What Is a Photon?. 5866: 229–244. arXiv:quant-ph/0701027. Bibcode:2005SPIE.5866..229A. doi:10.1117/12.638774.
4. ^ J. Zheng; C. Zheng (2011). "Variant simulation system using quaternion structures". Journal of Modern Optics. 59 (5): 484. Bibcode:2012JMOp...59..484Z. doi:10.1080/09500340.2011.636152.
5. S. S. Afshar; E. Flores; K. F. McDonald; E. Knoesel (2007). "Paradox in wave-particle duality". Foundations of Physics. 37 (2): 295–305. arXiv:quant-ph/0702188. Bibcode:2007FoPh...37..295A. doi:10.1007/s10701-006-9102-8.
6. ^ a b R. Kastner (2005). "Why the Afshar experiment does not refute complementarity?". Studies in History and Philosophy of Modern Physics. 36 (4): 649–658. arXiv:quant-ph/0502021. Bibcode:2005SHPMP..36..649K. doi:10.1016/j.shpsb.2005.04.006.
7. ^ a b O. Steuernagel (2007). "Afshar's experiment does not show a violation of complementarity". Foundations of Physics. 37 (9): 1370. arXiv:quant-ph/0512123. Bibcode:2007FoPh...37.1370S. doi:10.1007/s10701-007-9153-5.
8. ^ a b V. Jacques; et al. (2008). "Illustration of quantum complementarity using single photons interfering on a grating". New Journal of Physics. 10 (12): 123009. arXiv:0807.5079. Bibcode:2008NJPh...10l3009J. doi:10.1088/1367-2630/10/12/123009.
9. ^ D. D. Georgiev (2007). "Single photon experiments and quantum complementarity" (PDF). Progress in Physics. 2: 97–103. Archived from the original (PDF) on 2010-09-27. Retrieved 2009-08-15.
10. ^ D. D. Georgiev (2012). "Quantum histories and quantum complementarity". ISRN Mathematical Physics. 2012: 327278. doi:10.5402/2012/327278. Archived from the original on 2012-09-26. Retrieved 2012-02-25.
11. ^ S. S. Afshar (2006). "Violation of Bohr's complementarity: One slit or both?". AIP Conference Proceedings. 810: 294–299. arXiv:quant-ph/0701039. Bibcode:2006AIPC..810..294A. doi:10.1063/1.2158731.
12. ^ a b Wheeler, John (1978). Mathematical foundations of quantum theory. Elsevier. p. 9-48.
13. ^ Afshar's Quantum Bomshell Science Friday
14. ^ J. G. Cramer (2004). "Bohr is still wrong". New Scientist. 183 (2461): 26.
15. ^ S. S. Afshar (2005). "Experimental Evidence for Violation of Bohr's Principle of Complementarity". APS Meeting, March 21–25, los Angeles, California: 33009. Bibcode:2005APS..MARP33009A.
16. ^ R. E. Kastner (2006). "The Afshar Experiment and Complementarity". APS Meeting, March 13–17, Baltimore, Maryland: 40011. Bibcode:2006APS..MARD40011K.
17. ^ D. Reitzner. "Comment on Afshar's experiments". arXiv:quant-ph/0701152. Cite journal requires |journal= (help)
18. ^ W. Unruh (2004). "Shahriar Afshar – Quantum Rebel?".
19. ^ L. Motl (2004). "Violation of complementarity?".
20. ^ Aurelien Drezet (2005). "Complementarity and Afshar's experiment". arXiv:quant-ph/0508091.
21. ^ Aurelien Drezet (2011). "Wave particle duality and the Afshar experiment" (PDF). Progress in Physics. 1: 57–67. arXiv:1008.4261. Archived from the original (PDF) on 2011-10-11. Retrieved 2012-02-25.
22. ^ Andrew Knight (2020). "No Paradox in Wave-Particle Duality". arXiv:2006.05315.
23. ^ E. Flores and E. Knoesel. "Why Kastner analysis does not apply to a modified Afshar experiment". arXiv:quant-ph/0702210. Cite journal requires |journal= (help)
24. ^ J. G. Cramer (2005). "A farewell to Copenhagen?". Analog Science Fiction and Fact. Archived from the original on 2004-12-08. Retrieved 2004-12-21.