What a perfectly charming "dialogue," Physicist -- and so helpful a description of the "ins-and-outs" of nonlocality! Thank you so very much!
I have a couple questions begging for answers (that I do not have): Is a photon "material?" Where does each of the paired photons get its "instruction set" from?
Yes, no more or less than an electron, an atom, or a kumquat.
Where does each of the paired photons get its "instruction set" from?
The point is that there is no instruction set. Any instruction set would cause the photons to satisfy Bell's Inequality, but experimentally they don't.
To create entangled photons such as the ones that are described in the dialogue, it is necessary that they result from the same quantum wavefunction (for example, the two-photon decay of the pi0 meson). The original wavefunction only contained a certain amount of information, and that information gets imparted to the daughter photons. But the photons themselves are in an indeterminate polarization state, until one of them is measured. When the polarization of one of them is measured, it collapses into a well-defined polarization state.
When the other photon is measured, its polarization collapses into a well-defined state, too...but remember, there was only a limited amount of information to begin with. The two states, though initally undetermined, must necessarily collapse in a correlated way. Note that QM predicts (in fact, requires) this correlation based strictly on the amount of information in existence, without postulating either a local instruction set or any sort of signal from one photon to the other.
Einstein thought that the photons carried the information with them, in the form of "hidden variables", but he never had the chance to know Bell's Inequality, let alone the result of the Aspect experiment that confirmed the violation of it. Bohm came up with an interpretation involving superluminal signals (which nevertheless could not in principle be used for communication). I myself don't favor this interpretation, as it postulates an untestable mechanism that is not required for the theory, but it does hold exactly the same mathematical water as the Copenhagen Interpretation.
I myself am of the opinion that QM may be better off without an interpretation, although I realize that one is necessary for a lay audience. If I started throwing equations around, you'd all say, "that's fine, but what's really going on?" The problem is that words will never get it right, whereas the formalism does.