I think you're being a bit hard on Schrรถdinger here. I thought the whole point of Schrรถdinger's cat was to point out that the "observers cause collapse" idea was kind of stupid.

Hal Finney: "...at the time I discovered an analysis of a related idea at http://www.flownet.com/gat/QM.pdf".

That's a great link--thanks! That puzzle puzzled me for years, ever since I read about some EPR experiments in Scientific American as a kid, and wondered why they didn't just tweak the experiment a bit to make it actually interesting. That paper is the best explanation I've seen by far.

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.)

Regarding Larry's question about how close the photons have to be before they merge --

The solution to that problem comes from the fact that Eliezer's experiment is (necessarily) simplifying things. I'm sure he'll get to this in a later post so you might be better off waiting for a better explanation (or reading Feynman's QED: The Strange Theory of Light and Matter, which I think is a fantastically clear explanation of this stuff.) But if you're willing to put up with a poor explanation just to get it quicker...

In reality, you don't have just one initial amplitude of a photon at exactly time T. To get the full solution, you have to add in the amplitude of the photon arriving a little earlier, or a little later, and with a little smaller or a little larger wavelength, and even travelling faster or slower or not in a straight line, and possibly interacting with some stray electron along the way, and so on for a ridiculously intractable set of complications. Each variation or interaction shows up as a small multiplier to your initial amplitude.

But fortunately, most of these interactions cancel out over long distances or long times, just like the case of the two photons hitting opposite detectors, so in this experiment you can treat the photon as just having arrived at a certain time and you'll get very close to the right answer.

Or in other words--easier to visualize but perhaps misleading--the amplitude of the photons is "smeared out" a little in space and time, so it's not too hard to get them to overlap enough for the experiment to work.

--Jeff