Afshar experiment

In March 2004, Shahriar S. Afshar announced at Harvard University the results of a variation on the similar two-pin-hole "which-way" experiment, in which he claims to have disproved Bohr's Principle of Complementarity, also reported in the July 24, 2004 edition of New Scientist. [1] [2][3]

Using his experiment it is possible to detect interference fringes even when observing the path of a photon stream, indicating that the wavefunction does not collapse. If his results are verified, it has far-reaching implications for the understanding of the quantum world, and invalidates the Copenhagen interpretation. It would also seem to falsify the Many-worlds interpretation, which predicts that there should be no interference between wave functions in universes that are physically distinguishable. However, it lends support to the Transactional interpretation, which is consistent with the results.

Methodology of the experiment

In this experiment, Afshar creates a setup similar to the double-slit experiment, where the light generated by a laser is passed through two closely spaced pinholes. After this dual pinhole setup, Afshar places a lens, which refocuses the light so that the image of each pinhole is received by a separate photo-detector (Fig. 1).

Fig.1 Experiment without obstructing wire grid

Since there is a one-to-one relationship between the images and the pinholes, a photon that goes through pinhole number one would be seen only by detector number one, and if the it goes through detector two, it would be seen only by detector number two. Therefore, at the image plane, the setup is such that the light behaves as particles and can be assigned to a particular pinhole.

When the light acts as waves, instead of particles, there are special regions that the photons avoid, called the dark fringes. Afshar attempts to check for the wave characteristics of the light in the same experiment by placing a grid of thin wires just before the lens. These wires are carefully 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, and the image quality would be reduced (Fig. 2).

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 slit is closed with what is seen at the photo-detectors when both slits are open. When one slit 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 slits 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

In other words, in this experiment, the light seems to exhibit 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.

Thus this experiment seems to contradict the principle of Complementarity as well as the wavefunction collapse, since it shows both complementary wave and particle characteristics in the same experiment, for the same photons. This experiment has also been conducted with single photons and the results are identical to the high flux experiment.

Controversy

Since this experiment seems to violate a widely-held principle in Quantum mechanics, there has been quite a bit of controversy.

Unruh's rebuttal and Afshar's response

On August 7, 2004, Bill Unruh presented an argument in which he claims to disprove Afshar's results. Because of this, some in the scientific community question the validity of Afshar's experiment.

Unruh offers a simplified version of Afshar's experiment using a series of half-silvered mirrors, a setup which he claims to be equivalent to Shariar Afshar's. He demonstrates that his experiment is consistent with the Copenhagen interpretation and, on that basis, argues that Afshar's results are incorrect. [4]

However, there is a major difference between Unruh's experiment and Afshar's experiment. Whereas Afshar uses a lens to focus two light sources onto two detectors in a way that allows him to exactly identify the path of any photon, the design of Unruh's experiment destroys the path information at the second mirror.

Although Unruh demonstrates that he can detect the path of a photon when one path is blocked, this is tautological: if photons are admitted on only one path, the detectors the beam reaches will agree with the path of the beam. When light travels along both paths, two beams are combined into a single beam with a single direction, and so Unruh's argument is invalid.

Afshar's response, found in his FAQ, compares Unruh's experiment to one in which the wings are removed from an airplane. The experimenter might find that a wingless airplane cannot fly, but such an experiment would not prove anything about the flight capabilities of an intact plane.

Visibility: zero or one?

Harvard professor of physics, Lubos Motl, argues that the contrast with which the wave properties of light are observed in Afshar's experiment converges to zero as the wire grid becomes thin simply because only a very tiny fraction of the photons are used to deduce whether the interference exists or not:

$V\approx 0$

Shahriar Afshar, on the other hand, argues that the visibility is close to 100 percent. According to Motl, the Principle of Complementarity, as well as all other important postulates of quantum mechanics, are preserved, they say. The results of this experiment agree with quantum mechanics; in fact, classical electromagnetism is sufficient to explain it.

Afshar's rebuttal

Let us momentarily agree with Motl that V=0 throughout the experimental setup (including the region where the wires are placed.) In order to evaluate this claim, it is essential to have a definition of V, the visibility of the interference pattern. As defined in the literature,

$V={\frac {I_{\mathrm {max} }-I_{\mathrm {min} }}{I_{\mathrm {max} }+I_{\mathrm {min} }}}$

where I_max is the highest flux (at the middle of a bright fringe) and I_min is the lowest flux (found at the middle of the dark fringe). When Motl claims that V=0 (at the wires), according to the above efinition, we necessarily have I_max = I_min. In other words, there are no dark fringes in the spatial distribution of photons for any sub-ensemble with V=0. In other words, for photons with V=0, there are no regions where they would systematically avoid. Since the distribution of photons in such a decoherent distribution is essentially random, some of these decoherent photons must be blocked by the wires (depending on the actual number of wires in the grid, this amount can be upto 14% of the total flux). Such blockage is ruled out by the results of the experiment. Therefore, V=0 before the lens is a claim not supported by the actual data from the experiment. However, the same experimental data does support V=1 at the wire grid region. A more detailed discussion of this issue can be found in section 3 of Afshar's preprint.

Also, as discussed in his preprint, Afshar has no claim as to a violation of quantum mechanical formalism, or any other postulate therein. The only claim supported by the experiment is a violation of Bohr's Complementarity principle which does not allow presence of interference and "which-way" information in the same experimental setup. Although the classical electromagnetism works well for high flux regimes, it fails to account for experiments where single photons are used and therefore it is irrevlevant to the proper discussion of the experiment. The results of the single-photon experiment were identical to the results obtained in the high flux version.

Motl's clarification

The fluxes I_max and I_min that enter the (correct) definition of the visibility V are the intensities that are observed at the places where the actual photons are absorbed. In the case of Afshar's experiments, most of the photons are absorbed by the detectors. The detectors show no interference behavior whatsoever. I_max and I_min as seen by the detectors are nearly identical, and therefore V approximately equals zero. If one wants to calculate the I_max and I_min only from the photons that are absorbed by the wire grid, then one must also calculate the accuracy K of the "which way information" from the same ensemble of photons. For these photons that (potentially) interact with the wire grid, there will be no significant correlation between the detectors and their chosen pinholes.

The situation is a very rudimentary example of the principle of complementarity in action: the photons that interact with the wire grid allow us to measure the interference pattern, but they don't carry the "which way information", as explained by Unruh, and therefore

$V\approx 1,\quad K\approx 0,$

while the photons that avoid the wires are absorbed by the detectors. These photons carry the "which way information" but they don't create any interference pattern:

$V\approx 0,\quad K\approx 1.$

If we mix both types of photons, we obtain both V,K somewhere in between 0 and 1 so that Englert's "fuzzy" version of the complementarity principle

$V^{2}+K^{2}\leq 1$

will be satisfied. At any rate, the complementarity principle holds perfectly, regardless of the additional comments below.

Afshar's clarification

If I_min=0, then regardless of the actual value of I_max, V≡1, as long as the total flux is not zero. Also, there are two regions in the experiment where measurements are being made. One at the wires, where an indirect measurement of V is being made. The other the image plane where a direct measurement of which-way information is being made. At the wire grid, V=1, and K=0, but at the image plane, V=0, and K=1, while this shows that if each observation plane is considered in isolation, Complementarity holds, however we must consider the entire experimental setup in which V=1 at the wire region and K=1 at the image plane, which is a violation of Complementarity. If the photons passing the wires are assumed to be decoherent, then the impossible challenge to meet, is to show a quantum-mechanical wavefunction that has minima in it without appealing to at least two interfering wavefunctions. If Motl can show that such a decoherent distribution is possible without violating quantum formalism, then his claim could be verified rigorously. Also, appealing to the argument of Unruh, which has been ruled out previoulsy as being inapplicable to an inherently different system, cannot be considered as a valid argument. One has to show how QM provides for a loss of which-way information for the interfering photons without any of the photons interacting with the wires. So far no one has.

External Links

• Analog: A Farewell to Copenhagen?

• Shahriar S. Afshar, "Waving Copenhagen Good-bye: Were the founders of Quantum Mechanics wrong?"
  • "Variation on the (similar two-pin-hole "which-way" experiment". (reported in New Scientist; July 24)
  • www.irims.org/quant-ph/030503/ (Preprint)

• Blog entries
  • Afshar's own blog entry on the subject
  • The Afshar experient: Farewell to Copenhagen?
  • Shahriar S. Afshar: Quantum Rebel (also, from the same blog: [5], [6], [7], [8], etc.)
  • Violation of complementarity?