Eliezer: “Why can’t you signal using an entangled pair of photons that both start out polarized up-down? By measuring A in a diagonal basis, you destroy the up-down polarization of both photons. Then by measuring B in the up-down/left-right basis, you can with 50% probability detect the fact that a measurement has taken place, if B turns out to be left-right polarized … the answer turns out to be simple: If both photons have definite polarizations, they aren’t entangled.”
You can adjust this slightly so that answer no longer applies. Start with two entangled photons A and B that we know have opposite polarizations, so they really are entangled. At A we have a detector behind a filter that can be rotated either vertically or at a 45 degree angle. This is our signal source.
At B, we use a mirror that reflects, say, vertically polarized photons and transmits horizontally polarized; then we recombine the beams from slightly different angles onto a detector. So if we were to send B photons that have gone through a vertical or horizontal filter, we get no interference pattern at the detector, but if we send it photons that went through a diagonal filter, one would show up.
Now if we put the diagonal filter on at A, we know the diagonal polarization at B, and therefore do not know the horizontal/vertical polarization, and so we get an interference pattern. If we put vertical filter on at A, we know the vertical polarization at B, and the interference pattern disappears. Thus we seem to have faster-than-light (or back in time, if you prefer) communication.
(Of course this doesn’t actually work, but I think it’s a lot harder to explain why in understandable terms.)
Eliezer: “Why can’t you signal using an entangled pair of photons that both start out polarized up-down? By measuring A in a diagonal basis, you destroy the up-down polarization of both photons. Then by measuring B in the up-down/left-right basis, you can with 50% probability detect the fact that a measurement has taken place, if B turns out to be left-right polarized … the answer turns out to be simple: If both photons have definite polarizations, they aren’t entangled.”
You can adjust this slightly so that answer no longer applies. Start with two entangled photons A and B that we know have opposite polarizations, so they really are entangled. At A we have a detector behind a filter that can be rotated either vertically or at a 45 degree angle. This is our signal source.
At B, we use a mirror that reflects, say, vertically polarized photons and transmits horizontally polarized; then we recombine the beams from slightly different angles onto a detector. So if we were to send B photons that have gone through a vertical or horizontal filter, we get no interference pattern at the detector, but if we send it photons that went through a diagonal filter, one would show up.
Now if we put the diagonal filter on at A, we know the diagonal polarization at B, and therefore do not know the horizontal/vertical polarization, and so we get an interference pattern. If we put vertical filter on at A, we know the vertical polarization at B, and the interference pattern disappears. Thus we seem to have faster-than-light (or back in time, if you prefer) communication.
(Of course this doesn’t actually work, but I think it’s a lot harder to explain why in understandable terms.)