| MadSci Network: Physics |
Great question!
According to the standard interpretation of quantum mechanics, the two photons are each in a superposition of possible states. When one is measured, the other one collapses from a superposition to a definite state. This is different from your card example because this collapse is an actual change, each photon changing from a superposition to a definite state.
But, you ask, what if the standard interpretation only talks about what we can *know* about the photons, not what state the photons are actually in? In order words, what if there are "hidden variables" -- the information inside your envelopes -- that physics doesn't know about? Then quantum mechanics doesn't appear so spooky after all -- it's just a matter of learning what those hidden variables are.
Until 1964, the above question was just a matter of metaphysics and philosophy; many thought that the question would never be resolved. But that's the year that the physics world was shocked by Bell's theorem. Bell showed that there was a testable difference between two photons that had hidden variables and two photons which were really in superpositions. The experiment was performed, and quantum mechanics was vindicated: the experiment proved that there were no "hidden variables" that could explain quantum mechanics in a more realistic way. Superpositions were apparently "real"!
Well, almost. Turns out that Bell's theorem (and the associated experiment) rules out "local" hidden-variables, the sort of secret information that hides with the photons themselves. Bell's theorem doesn't rule out hidden variables that depend on the future. If the photons somehow "know" what measurements will be made on them in the future, they would theoretically be able to put themselves in the appropriate states, right from the start. If this is the case, your card analogy might be the way nature works after all, but only if there's a magician who has knowledge about the future who chooses which card to put in which envelope.
There happens to be a theory, called the transactional interpretation, which uses this sort of backwards-causality to explain all the strange things about quantum mechanics in a completely realistic way -- if you allow the possibility of backwards-causation on a quantum scale. This is the only quantum mechanics theory I know of which both satisfies Bell's theorem and allows quantum states to have real (though unknown) values before they are measured. However, apart from the philosophical advantages of explaining quantum mechanics in a more realistic way, there do not appear to be any experiments which could distinguish the transactional interpretation from the standard interpretation of quantum mechanics.
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