Yan Feng

I love photons, especially their polarization states. That's a cute photon doll, I have never seen such a thing before. Here's an idea on how to find out more about a single photon's polarization that than traditional QM allows:

A single photon in coherent superposition expresses a fully characterized polarization state. For example, we can make a photon equivalent to elliptical polarization, given the wave function: A |R> + Be^(i theta) |R> and e.g. 0.6 for A and 0.8 for B. The phase then provides an angle, not just an ellipse shape, so we can be sure a filter tuned to that wave would let the photon through (as it would also have ideal 100% transmission for the equivalent classical polarized light beam.) If I am a confidante of the photon’s creator, I can know just how to orient the right filter (say, combo of QWP and LPF) to get all “hits” etc.

But if I don’t already know, I can’t find out for sure: all I can do is try a filter and orientation and I might get transmission or not. Either way, the photon is “ruined” by either being absorbed or changed into the new filter’s base. (Projection postulate? I wonder why that doesn’t have its own Wikipedia article.) All I really know is, that photon couldn’t have been the orthogonal to the filter base if it went through. But if the trait is “real” (unlike the literal contradiction in Fourier analysis of exact momentum and exact position), why can’t I find out? (I know, doing so might lead to weird effects in entangled states, like FTL communication, but suppose it didn’t?)

This seems silly, like a kid saying “If you don’t know, I’m not going to tell you!” In some other comments around, I explained how we might circumvent that restriction by using the accumulation of angular momentum. First, a quick primer on birefringent half-wave plates: A HWP reverses the rotational sense (spin), by swapping the values of A and B. Hence 0.6 for A and 0.8 for B turns into 0.8 for A and 0.6 for B, etc. (you may be surprised, but it does - known fact, and to be consistent with the affect on the classical wave.) It therefore must accumulate a bit of angular momentum from the spin flipping, each time a photon (whether a "new" photon, or the "same one" ! - passes through it.)

OK, try this: keep reflecting a photon around with mirrors, sending it through the same half-wave plate over and over (re-flipped by a second HWP if needed.) If we did it enough, all those transits would build up detectable angular momentum in the HWP. That measurement would be along a range, not an either/or as required by the PP because the result needs to be consistent with sending many many “separate” photons through (indistinguishability.)

IOW, if the photon came out of a linear polarizer, the many transits wouldn’t build up net spin since the average effect is no rotation. Maybe it wouldn’t work, but it’s worth mulling over. It seems to resemble “weak measurements” as propounded by Yakir Aharonov.

tyrannogenius