The Afshar experiment (2005 ) is a lovely variant on the famous two-slit experiment. In this experiment, a grid is placed at the location of the dark fringes in what would be an interference pattern, but downstream from that location, the photon beam is subjected to a “which slit” measurement by way of lenses. However, its alleged significance is based on ambiguous and misleading terminology, and it has been widely misunderstood (and its significance has been consequently widely overstated). A colleague of mine recently submitted a paper on the experiment to a peer-reviewed journal in which he questioned claims about the experiment’s alleged implications. He sent me some unfavorable reviews he received, in which both reviewers claimed that the experiment remained a “paradox.” They defended Afshar’s claim that the experiment challenges fundamental principles of quantum theory, such as the idea that one cannot obtain outcomes for two incompatible observables in a single measurement. The latter idea was pointed to by Niels Bohr in his “principle of complementarity” (POC), which Afshar claims to have refuted by his experiment. This brief post is an attempt to update and to correct the record, since key claims regarding the experiment’s significance have in fact long ago been refuted.
While the present writer is not a fan of Bohr’s pronouncements about quantum theory, and has argued elsewhere that his POC fails to pass muster as a interpretive principle, I did analyze the Afshar experiment back in 2005 , showing that there is in fact nothing at all paradoxical about it, and that it does not refute the basic quantum principle that you can’t obtain values for incompatible observables in a single measurement. (The published paper can be found here. It also discusses the application of the Transactional interpretation to the Experiment.)
What the Afshar experiment does is to prepare a photon in a superposition of slits, subject it to a non-disturbing “null” measurement that confirms the prepared state (this is the grid placed at the dark areas for the predicted interference pattern), and then subsequently subject the photon to a “which slit” measurement. This process is fully equivalent (in terms of the quantum formalism) to first preparing a spin-1/2 particle (such as a silver atom) in a state of “spin up along x,” then confirming that it is in that state by having it pass through an x-oriented Stern-Gerlach device with a detector only for the state “spin down along x” (which of course never activates, since the particle was prepared in “spin up”), and finally allowing the particle to continue on to a z-oriented Stern-Gerlach device which detects it in either “spin up along z” or “spin down along z.”
Presumably, Bohr would not have thought that such a spin experiment contradicted his POC, since one can certainly prepare a particle in a state, confirm that state through a null measurement of the same observable, and then subject the particle to a measurement of a non-commuting observable. That sequence of perfectly mundane measurements is all that is going on the in the Afshar experiment, as elegant an experimental exercise in quantum optics as it may be. The only criticism of Bohr’s POC that one might make here is that he didn’t state it very precisely; he sometimes stated it in terms of an “experimental setup” or a “single experiment.” He really intended the idea that one cannot obtain values for incompatible observables in a single measurement, not in a single experiment, because of course one can do a sequence of different measurements in a single experiment.