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Raul told me today that he doesn’t see any connection between Aharonov qCC and Denkmayr (alleged) qCC because Denkmayr doesn’t have a displaced pointer state. A weak values theorist (who asked not to be cited) agreed with our analysis saying “weakly enough” in Denkmayr should have read “linearly” because weak measurement requires linear interaction. Therefore, he said the quadratic interaction of Denkmayr “would seem fatal.” That’s why I think the parallel between Aharonov qCC and Denkmayr qCC would be, as I stated above, Correa’s Eq 5 giving his Eq 7.
This is an interesting issue for weak values in general, because in Denkmayr <SzP1> = 1, <P1> = 0, <SzP2> = 0, and <P2> = 1. If the Bz interaction had been linear, these “observables” would account directly for a reduction in the intensity at detector O (Io) for the absorber in path 2 <P2> = 1, but no change in Io for the absorber in path 1 <P1> = 0. And, there would have been an increase in Io for Bz in path 1 <SzP1> = 1, but no change in Io for Bz in path 2 <SzP2> = 0. As it turns out, the quadratic Bz interaction leads to a decrease in Io for Bz in path 2, which is accounted for by <P2> = 1. This is where we claim qCC is violated, it’s what Correa refers to when he writes, “the quadratic term of the Bz interaction is connected to the ‘where the neutron is’ weak value [<P2> = 1], and hence means they can’t look for the Cheshire Cat with this interaction.” However, these “observables” are used properly to account for what they *did* observe. Stephan Sponar (experimentalist on Denkmayr et al) attended my presentation in Vaxjo two weeks ago and said he understood those four “observables” entailed qCC. But, if that were true, you would have two very different empirical results associated with qCC, one of which makes sense (linear Bz interaction) and one of which doesn’t (quadratic Bz interaction). So, in our paper, we have a section where we explain what <SzP1> = 1, <P1> = 0, <SzP2> = 0, and <P2> = 1 mean in Denkmayr.
Thus, while Denkmayr doesn’t give us qCC, it does show us empirically that weak value “observables” have different meanings in different weak scenarios, which is interesting. I would like to hear from more of the weak values community on this issue.