The optical experiment by Shahriar Afshar was a cover story in New Scientist in 2004.
light --->
photon detector B
| / /
| / /
hole A
| • grid
| • interference of the
| • two waves
hole B
| \ \
| \ \
photon detector A
Plane waves of light enter from the left. They are diffracted by the two holes. They form an interference pattern in the spatial volume right of the holes. We put obstacles to the dark spots of the interference pattern, the "grid" in the diagram. The grid might block, say, 20% of the routes (without the interference pattern).
We have two photon detectors at the bottom of two tubes. From the geometry it is obvious that the detector A will detect almost exclusive the wave which went through the hole A, and the same for B.
Diffraction at the grid will scatter some photons to the wrong detector, but not many, because the grid is located at the dark spots.
Afshar's setup contains a lens which focuses the light from the holes. The lens can, in principle, collect 100% of the light that goes through each hole. The lens offers a better "distinguishability" D of the paths, as defined by B.-G. Englert. If a photon does not make it from the hole A to the detector A, it is not "distinguished".
The standard way to analyze the experiment is to calculate the diffraction of the waves at the holes, and the interference of the classical plane waves. We get the intensities at each detector A and B.
Suppose that the intensity of light is so low that we send only one photon per second.
When we measure a photon at a detector, we may interpret that the wave which described the process "collapses" to a single photon at the detector.
Suppose that the detector A measured a photon. Is there sense in saying that the photon passed through the hole A?
The wave at the detector A is able to avoid the grid because it interferes with the wave that went through the hole B. Without the help of the B wave, it might bump into the grid.
The interference of the two waves A and B near the grid is a linear phenomenon. In a linear system we can sensibly talk about the origin of some wave.
In that sense, we may say that the wave at the detector A comes through the hole A. But the wave gets "help" from the B wave in avoiding the grid.
In quantum mechanics, we are really not allowed to talk about the "paths" of photons before the measurement. Everything has to the treated as a wave. In the strict sense, the photon at the detector A did not have any path.
But informally we can say that the wave at the detector A really comes through the hole A.
The experiment is in harmony with all the interpretations of quantum mechanics.
The interpretation by various authors
Shahriar Afshar claimed that the experiment clashes with "complementarity". We do not think so. The particle nature of light is only present when the photon is measured. Everything else is a wave.
William Unruh (2004) claims that a setup with half-silvered mirrors is equivalent to Afshar's experiment, and one cannot deduce which path the photon took:
The setup of Unruh is not very much equivalent. If we calculate a plane wave backward in time in Unruh's diagram from the detector 5, the backward wave will be divided evenly between the paths 1 and 2.
In our diagram, calculating back from the detector A, the wave will almost exclusively go through the hole A.
Lubos Motl calculates the effect of the wire thickness in the grid.
If the wires are thick, there is a big difference in the wave intensity at the detector A when 1) both holes are open, and 2) only one hole is open. But thick wires scatter some light to the "wrong" detector.
The distinguishability value D defined by B.-G. Englert is bad if the wires are thick: for the reflected and absorbed photons we do not know the path.
Motl correctly states that the experiment is a classical one and can be calculated using Maxwell's equations. There is nothing in the experiment which clashes with complementarity.
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