The Afshar experiment is an optical experiment, devised and carried out by Shahriar Afshar in 2004, which investigates the principle of complementarity in quantum mechanics. The result of the experiment, that a grid of wires can be ignored when both slits are open, is in accordance with the standard predictions of quantum mechanics; however, it is controversially claimed to violate complementarity and specifically the Englert–Greenberger duality relation;  others disagree.
Afshar's experiment uses a variant of Thomas Young's classic double-slit experiment to create interference patterns to investigate complementarity. Such interferometer experiments typically have two "arms" or paths a photon may take. 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 observing each photon's path (a measurement of the particle nature of the photons).
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. The results were presented at a Harvard seminar in March 2004, and published as conference proceeding by the International Society for Optical Engineering (SPIE). The experiment was featured as the cover story in the July 24, 2004 edition of New Scientist. 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. Afshar presented his work also at the American Physical Society meeting in Los Angeles, in late March 2005. His peer-reviewed paper was published in Foundations of Physics in January 2007.
Afshar claims that his experiment invalidates the complementarity principle and has far-reaching implications for the understanding of quantum mechanics, challenging the Copenhagen interpretation. According to Cramer, Afshar's results support Cramer's own transactional interpretation of quantum mechanics and challenge the many-worlds interpretation of quantum mechanics. This claim has not been published in a peer reviewed journal.
Experimental setup 
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). A photon that goes through pinhole number one impinges only on detector number one, and similarly, if it goes through pinhole two it impinges only on detector number two, which is why we see the pinholes separately in the image plane close to the mirrors before the photon-detectors.
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 some of the light will be blocked by the wires. Consequently, the image quality is reduced.
When one pinhole is closed, the grid of wires causes appreciable diffraction in the light, and blocks a certain amount of light received 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, which the photons avoid. The effect is not dependent on the light intensity (photon flux).
Afshar's conclusion is that 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, when both slits were open, but also exhibits particle-like behavior after going through the lens, with photons going to a given photo-detector. Afshar argues that this behavior contradicts the principle of complementarity, since it shows both complementary wave and particle characteristics in the same experiment for the same photons.
Specific critiques 
A number of scientists have published criticisms of Afshar's interpretation of his results. They are united in their rejection of 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.
The most recent work claims that Afshar's core claim, that the Englert–Greenberger duality relation is violated, is not true. They 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." Below is a synopsis of the papers by critics highlighting their main arguments, and the disagreements they have amongst themselves:
Some researchers claim that, while the fringe visibility is high, no which-way information ever exists:
- Ruth Kastner, Committee on the History and Philosophy of Science, University of Maryland, College Park.
- Kastner's criticism, published in a peer-reviewed paper, proceeds by setting up a gedanken 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 ), because it cannot tell us 'which slit the photon actually went through.' In addition she underscores her conclusion with an analysis of the Afshar setup within the framework of the transactional interpretation of quantum mechanics. A follow-up e-print by Kastner "On Visibility in the Afshar Experiment" argues that the commonly referenced inverse relationship between visibility parameter V and which-way parameter K does not apply to the Afshar setup, which post-selects for "which slit" after allowing interference to take place.
- Kastner's setup has been criticised, and an alternative proposed: Why Kastner analysis does not apply to a modified Afshar experiment (by Eduardo Flores and Ernst Knoesel [2007/02]) Abstract:
In an analysis of the Afshar experiment R.E. Kastner points out that the selection system used in this experiment randomly separates the photons that go to the detectors, and therefore no which-way information is obtained. In this paper we present a modified but equivalent version of the Afshar experiment that does not contain a selection device. The double-slit is replaced by two separate coherent laser beams that overlap under a small angle. At the intersection of the beams an interference pattern can be inferred in a non-perturbative manner, which confirms the existence of a superposition state. In the far field the beams separate without the use of a lens system. Momentum conservation warranties that which-way information is preserved. We also propose an alternative sequence of Stern–Gerlach devices that represents a close analogue to the Afshar experimental set up.
- Daniel Reitzner (Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia), Comment on Afshar’s experiments arXiv:quant-ph/0701152 (2007).
- 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."
Other researchers agree that the fringe visibility is high and that the which-way information is not simultaneously measured, but they believe that the which-way information does exist under some circumstances.
- W. G. Unruh, Professor of Physics at University of British Columbia
- Unruh, who has published his objections on the web pages of his university, is probably the most prominent critic of Afshar's interpretation. He, 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 when Afshar puts in the wire grid.
- Tabish Qureshi (Centre for Theoretical Physics, Jamia Millia Islamia, New Delhi), 
- Qureshi, in his paper published in a peer-reviewed journal, does a wave-packet analysis of the Afshar experiment, and argues that even though Afshar's experiment has genuine interference, individual detectors clicking do not give which-path information. Through a mathematical analysis he shows that in the region of overlap of the wave-packets, if the state is such that the modulus square of the wave-function gives an interference pattern, the which-path information is necessarily lost.
Another group does not question the which-way information, but rather contends that the measured fringe visibility is actually quite low:
- Luboš Motl, Former Assistant Professor of Physics, Harvard University.
- 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.
- 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.
- 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."
Others question Afshar's interpretation and offer alternatives:
- Entanglement and quantum interference (by Paul O'Hara [2006/09]) Abstract:
In the history of quantum mechanics, much has been written about the double-slit experiment, and much debate as to its interpretation has ensued. Indeed, to explain the interference patterns for subatomic particles, explanations have been given not only in terms of the principle of complementarity and wave-particle duality but also in terms of quantum consciousness and parallel universes. In this paper, the topic will be discussed from the perspective of spin-coupling in the hope of further clarification. We will also suggest that this explanation allows for a realist interpretation of the Afshar Experiment.
Specific support 
There also is support for the Afshar interpretation from John Cramer:
See also 
- Wheeler's delayed choice experiment
- Delayed choice quantum eraser
- Weak measurement
- Wheeler–Feynman absorber theory
- S. S. Afshar (2005). "Violation of the principle of complementarity, and its implications". Proceedings of SPIE 5866: 229–244. arXiv:quant-ph/0701027. doi:10.1117/12.638774.
- J. Zheng and C. Zheng (2011). "Variant simulation system using quaternion structures". Journal of Modern Optics. Bibcode:2012JMOp...59..484Z. doi:10.1080/09500340.2011.636152.
- 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.
- R. Kastner (2005). "Why the Afshar experiment does not refute complementarity?". Studies in History and Philosophy of Modern Physics 36 (4): 649–658. doi:10.1016/j.shpsb.2005.04.006.
- 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.
- 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.
- D. D. Georgiev (2007). "Single photon experiments and quantum complementarity". Progress in Physics 2: 97–103.
- D. D. Georgiev (2012). "Quantum histories and quantum complementarity". ISRN Mathematical Physics 2012: 327278.
- S. S. Afshar (2006). "Violation of Bohr's complementarity: One slit or both?". AIP Conference Proceedings 810: 294–299. arXiv:quant-ph/0701039. doi:10.1063/1.2158731.
- M. Chown (2004). "Quantum rebel". New Scientist 183 (2457): 30–35.
- S. S. Afshar (2004). "Waving Copenhagen Good-bye: Were the founders of Quantum Mechanics wrong?". Harvard seminar announcement.
- Afshar's Quantum Bomshell Science Friday
- J. G. Cramer (2004). "Bohr is still wrong". New Scientist 183 (2461): 26.
- S. S. Afshar (2005). "Experimental Evidence for Violation of Bohr's Principle of Complementarity". APS Meeting, March 21–25, Los Angeles, California.
- J. G. Cramer (2005). "A farewell to Copenhagen?". Analog Science Fiction and Fact.
- R. E. Kastner (2006). "The Afshar Experiment and Complementarity". APS Meeting, March 13–17, Baltimore, Maryland.
- W. Unruh (2004). "Shahriar Afshar – Quantum Rebel?".
- T. Qureshi (2012). "Modified two-slit experiments and complementarity". Journal of Quantum Information Science 2: 34–39. doi:10.4236/jqis.2012.22007.
- L. Motl (2004). "Violation of complementarity?".
- Aurelien Drezet (2005). "Complementarity and Afshar's experiment". arXiv:quant-ph/0508091 [quant-ph].
- Aurelien Drezet (2011). "Wave particle duality and the Afshar experiment". Progress in Physics 1: 57–67. arXiv:1008.4261v1.
Further reading 
- Mir; Lundeen; Mitchell; Steinberg; Garretson; Wiseman (2007). "A double-slit 'which-way' experiment on the complementarity--uncertainty debate". New Journal of Physics 9 (8): 287–287. arXiv:0706.3966. Bibcode:2007NJPh....9..287M. doi:10.1088/1367-2630/9/8/287.