The plain old double slit experiment displays interference when we don't measure which slit the photon passed through, and no interference when it is measured. Let's turn our attention to the case with no detectors at the slits. If instead of a back screen, we replace that with a focusing lens with a screen further back such that the lens focuses the optical image of the slits sharply on the screen further back, then just by looking at which spot the photon ends up in, we can state with absolute certainty which slit the photon passed through.
Afshar introduced detector wires where the interference troughs should have been to detect any photon hitting those wires, but allowing photons to pass through unimpeded in between the narrow wires. The wires have some thickness, and so, a small fraction of the photon still hit them anyway, but the important point is this fraction is pretty low, and consistent with an interference pattern. This is an example of what is known in the literature as a nondestructive measurement.
Anyway, this interference pattern seems to suggest the photon went through both slits. The catch is, at the screen further back, we still detect two sharp spots. The small fraction of photon intercepted by the wires blurs the sharpness a little, but it's still mostly sharp. Now, it appears we also know which slit the photon passed through.
But would you say the presence of the wires causes us to lose information about which slit the photon passed through despite the fact that we still see two sharp spots at the back, and even after knowing which of the two spots it ended up in, we still have to say it went through both slits despite the fact only a small fraction of the photons get intercepted?
Can we make any definite counterfactual statements about which slit the photon passed through even after knowing which spot it ended up in? Or are such questions meaningless?
Best Answer
There is no reason to suppose that the photon which is detected in the top spot in the Afshar experiment when through the bottom slit. The result of the experiment is that you see two spots, corresponding to the two slits, but the spots have been spread out and recombined, and the process does not necessarily keep the photons which went through the bottom (inasmuch as this concept makes sense) going to the top spot, and the phtons which went through the top going to the bottom spot. There is no conservation of momentum, because of the spatial symmetry breaking by both the slits and the wires.
So while the interference pattern contains the information of the slit shape it is not giving you which-way information about the photons, because such information does not exist in quantum mechanics to begin with. This is only arguing against thinking of the quantum wavefunction as a parametrization of ignorance about stuff, and the quantum wavefunction is obviously not a parametrization of ignorance about anything, because only probability calculus is a parametrization of ignorance about things.