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Afshar experiment

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In physics, and more specifically, quantum mechanics, the Afshar experiment is an optical experiment, devised by Shahriar S. Afshar in 2004, that its proponents claim disproves Niels Bohr's principle of complementarity. Since this principle is a central idea of quantum mechanics, the proper interpretation of the experiment has engendered some controversy in the physics community; response papers have been critical of Afshar's interpretation. The controversy has appeared online in blogs, at physics colloquia and academic conferences, and in arXiv e-print archives. Papers by Afshar on the experiment have been published in the American Institute of Physics and SPIE conference proceedings; however, as of May 4, 2006, neither a description of the experiment, nor any discussion of its theoretical interpretation, has been published in a refereed physics journal.

Overview

The principle of complementarity states that two complementary physical observables cannot both be measured for any given quantum particle without one measurement disturbing the other. For example, a particle's position and momentum cannot be observed at the same time: this is Werner Heisenberg's uncertainty principle.

One of Afshar's assertions is that, in his experiment, one can check for interference fringes of a photon stream (a momentum measurement) while at the same time observing the photon's path (a position measurement). Afshar's experiment attempts to do this using a variant of the classic Thomas Young double-slit experiment. Such interferometer experiments typically have two "arms" or paths a photon may take. Afshar attempts to both preserve interference, and to determine "which way" or "Welcher Weg" the photon went. Many of the claims associated with this experiment cut across several conventional ideas in quantum mechanics.

History

Shahriar S. Afshar's experimental work was done initially at the Institute for Radiation-Induced Mass Studies (IRIMS) in 2001 and later reproduced at Harvard University in 2003, while he was a Research Scholar there. He presented his results in a seminar talk in March 2004 entitled Waving Copenhagen Good-bye: Were the founders of Quantum Mechanics wrong? . The experiment was subsequently featured as the cover story in the July 24, 2004 edition of New Scientist. , and published in Proc. SPIE 5866, 229-244 in July of 2005 . Afshar's claim that his experiment invalidates the complementarity principle would have far-reaching implications for the understanding of quantum mechanics, potentially challenging the Copenhagen interpretation and according to John Cramer, the many-worlds interpretation of quantum mechanics. Cramer also asserts that Afshar's results support his transactional interpretation of quantum mechanics.

As of late May, 2005, Afshar has presented his work at various university seminars and in late March of 2005, at the American Physical Society meeting in Los Angeles . His paper has been published by the International Society for Optical Engineering (SPIE) in July, 2005 . Afshar's results have also been reported in the New Scientist as cited above and in other popular science magazines. 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. Among those writing were Alistair Rae (Centre for Photonic Systems, Cambridge University), David Dunstan (Head of the Physics Department, Queen Mary, University of London) and Alwyn Eades (Director of the Microscopy Center, Materials Science Department, Lehigh University) who viewed Afshar's interpretation with skepticism. Afshar's response to their critiques was given in a response letter from Cramer published on August 21, 2004.

Experimental setup and Afshar's interpretation

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 is received by a separate photo-detector (Fig. 1). In this setup, a photon that goes through pinhole number one impinges only on detector number one, and similarly, if it goes through pinhole two. Therefore, if observed at the image plane, the setup is such that the light behaves as a stream of particles and can be assigned to a particular pinhole.

Fig.1 Experiment without obstructing wire grid

When the light acts as a wave, because of interference one can observe that there are regions that the photons avoid, called dark fringes. Afshar now places a grid of thin wires just before the lens (Fig. 2). These wires are placed in previously measured positions of the dark fringes of an interference pattern which is produced by the dual pinhole setup when observed directly. If one of the pinholes is blocked, the interference pattern can no longer be formed, and some of the light will be blocked by the wires. Consequently, one would expect that the image quality is reduced, as is indeed observed by Afshar. Afshar then claims that he can check for the wave characteristics of the light in the same experiment, by the presence of the grid.

Fig. 2 Experiment with obstructing wire grid and one pinhole covered

At this point, Afshar compares the results of what is seen at the photo-detectors when one pinhole is closed with what is seen at the photo-detectors when both pinholes are open. When one pinhole is closed, the grid of wires causes some diffraction in the light, and blocks a certain amount of light received by the corresponding photo-detector. When both pinholes were open, however, the effect of the wires is minimized, so that the results are comparable to the case in which there are no wires placed in front of the lens (Fig.3).

Fig. 3 Experiment with obstructing wire grid and both pinholes open

Afshar's conclusion is that the light exhibits a wave-like behavior when going through the wires, since the light goes through the spaces between the wires when both slits were open, but also exhibits a particle-like behavior after going through the lens, with photons going to a given photo-detector.

This behavior, Afshar argues, contradicts the principle of complementarity, since it shows both complementary wave and particle characteristics in the same experiment for the same photons; although not at the same time, some critics point out, and hence compatible with an interpretation of complementarity more closely tied to the uncertainty principle. Afshar asserts this experiment has also been conducted with single photons and the results are identical to the high flux experiment, although these results were not available at the time of the talk at Harvard.

Theory

In the context of the archetypal double-slit experiment, Bohr's principle of complementarity can be mathematically represented through a relation expressing a limitation on fringe visibility V and path distinguishability D as follows,

D 2 + V 2 ≤ 1 {\displaystyle D^{2}+V^{2}\leq 1\,}

This complementarity relation is known as the Englert-Greenberger duality relation.

Afshar claims that his experiment violates this limitation (and hence the principle of complementarity), however it is unclear how generic this relation is and whether it extends to cover more complicated experimental setups such as Afshar's.

Critiques

Though Afshar's work is still the subject of ongoing interpretation and discussion, a significant portion of the scientific community is of the opinion that Afshar's experiment does not refute complementarity.

Some general criticisms are:

Bohr's philosophical views on the Complementarity Principle are generally seen as in accordance with the Schrodinger wave equation. Since the latter is obeyed in Afshar's experiment it is not obvious how complementarity can be violated.
The modern understanding of quantum decoherence and its destruction of quantum interference provides a mechanism for understanding the appearance of wavefunction collapse and the transition from quantum to classical. As such there is no need, in the decoherence view, for an a priori introduction of a classical-quantum divide as enshrined by complementarity. Any experiment that claims to violate complementarity needs to address this issue.

A more specific criticism is that when fringes are not visible, due to there only being a single photon in a pure state in the apparatus, V and D are defined directly in terms of the photon's quantum amplitudes for passing through pin-hole 1 or pin-hole 2, ψ 1 {\displaystyle \psi _{1}} and ψ 2 {\displaystyle \psi _{2}} , respectively:


D = | | ψ 1 | 2 − | ψ 2 | 2 | | ψ 1 | 2 + | ψ 2 | 2 {\displaystyle D={\frac {||\psi _{1}|^{2}-|\psi _{2}|^{2}|}{|\psi _{1}|^{2}+|\psi _{2}|^{2}}}}
V = 2 | ψ 1 | 2 | ψ 2 | 2 | ψ 1 | 2 + | ψ 2 | 2 . {\displaystyle V={\frac {2|\psi _{1}|^{2}|\psi _{2}|^{2}}{|\psi _{1}|^{2}+|\psi _{2}|^{2}}}.}

and hence the Englert-Greenberger duality relation is algebraically satisfied as an equality:

V 2 + D 2 = 1 {\displaystyle {\begin{matrix}V^{2}+D^{2}=1\end{matrix}}}

so it is unclear how the inequality:

V 2 + D 2 ≤ 1 {\displaystyle {\begin{matrix}V^{2}+D^{2}\leq 1\end{matrix}}}

can be violated by multiple photons passing through the apparatus as fringes build up.

The following is a partial list of other specific critiques of Afshar's experimental design and analysis. Afshar's rebuttals are available on his Q&A archive and FAQ .

  • Aurelien Drezet, University of Graz Institut of experimental physics, Austria,
  • Ole Steuernagel, School of Physics, Astronomy and Mathematics, University of Hertfordshire,

Notes

  1. ^ Gregg Jaeger, Abner Shimony, Lev Vaidman "Two interferometric complementarities" Phys. Rev. A, Vol. 51, 54 (1995))
  2. ^ Bethold-Georg Englert "Fringe Visibility and Which-Way Information: An Inequality" Phys. Rev. Lett., Vol. 77, 2154 (1996)
  3. ^ Daniel M. Greenberger, Allaine Yasin ,"Simultaneous wave and particle knowledge in a neutron interferometer" Phys. Lett. A 128, 391, (1988)
  4. "There is absolutely nothing mysterious about Afshar's experiment." "And of course, the conventional quantum mechanics is compatible with the principle of complementarity." Lubos Motl at
  5. "Bohr would have had no problem whatsoever with this experiment within his interpretation. Nor would any other interpretation of quantum mechanics. It is simply another manifestation of the admittedly strange, but utterly comprehensible (it can be calculated with exquisite precision), nature of quantum mechanics." Bill Unruh at
  6. "It was claimed that this experiment could be interpreted as a demonstration of a violation of the principle of complementarity in quantum mechanics. Instead, it is shown here that it can be understood in terms of classical wave optics and the standard interpretation of quantum mechanics." Ole Steuernagel at
  7. Wojciech H. Zurek, Decoherence and the transition from quantum to classical, Physics Today, 44, pp 36-44 (1991); and an updated version from 2003:
  8. Aurelien Drezet, Complementarity and Afshar's experiment, University of Graz Institute of experimental physics, Austria, for details of the duality inequality.

.

References

  • John G. Cramer, "A Farewell to Copenhagen?" (2005), Analog Science Fiction and Fact. (A non-technical discussion in a popular forum)
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