I am not sure I understand the problem. What would an answer to your question look like? But I’ll try to answer your numbered objections and see if that helps.
In your first numbered point, why are you concerned with the phases of the photons? You seem to be thinking that the photons are waves, ie streams of photons, but I believe they are intended to be literal single photons, which do not interact at the mirror. (Indeed you have this in your second numbered point.) Would the experiment be clearer with s/photon/electron? (In which case you need some other device than a half-silvered mirror to get the 50% transmission effect, but that shouldn’t be a problem.)
Your second point seems to contain a non-sequitur. You say that the photons do not interact, and therefore any statistical effect must come from the sources. I don’t think that follows. This is precisely the point Eliezer is making, that human intuition breaks down in this case and you have to do the math. When you do so, you find that the amplitude for “one photon at each detector” is zero, so you will never observe that result.
On second thought, however, it seems to me that we can explain this in terms of photon interactions, although not at the mirror. Consider that there are two ways to get one photon in each detector: Both deflected, or both went straight. Now look at the path D->E. It `contains’ two single-photon amplitudes: A deflected B->D photon, and a straight C->E photon. These two photons have opposite quantum (not electrical!) phases and therefore cancel. Thus the interaction doesn’t occur at the mirror, but at the detector.
I don’t believe this is EPR at all, it is bog-standard QM with a slightly unusual interaction, namely the rotation by 90 degrees.
I am not sure I understand the problem. What would an answer to your question look like? But I’ll try to answer your numbered objections and see if that helps.
In your first numbered point, why are you concerned with the phases of the photons? You seem to be thinking that the photons are waves, ie streams of photons, but I believe they are intended to be literal single photons, which do not interact at the mirror. (Indeed you have this in your second numbered point.) Would the experiment be clearer with s/photon/electron? (In which case you need some other device than a half-silvered mirror to get the 50% transmission effect, but that shouldn’t be a problem.)
Your second point seems to contain a non-sequitur. You say that the photons do not interact, and therefore any statistical effect must come from the sources. I don’t think that follows. This is precisely the point Eliezer is making, that human intuition breaks down in this case and you have to do the math. When you do so, you find that the amplitude for “one photon at each detector” is zero, so you will never observe that result.
On second thought, however, it seems to me that we can explain this in terms of photon interactions, although not at the mirror. Consider that there are two ways to get one photon in each detector: Both deflected, or both went straight. Now look at the path D->E. It `contains’ two single-photon amplitudes: A deflected B->D photon, and a straight C->E photon. These two photons have opposite quantum (not electrical!) phases and therefore cancel. Thus the interaction doesn’t occur at the mirror, but at the detector.
I don’t believe this is EPR at all, it is bog-standard QM with a slightly unusual interaction, namely the rotation by 90 degrees.