I get the concept of information entropy, and that, for example, a “z” in a telegraphed message in English reduces the entropy of the message by more than an “e.” My misunderstanding came from various vague articles (and some posts) that left me thinking that my scenario was not FTL information transfer because information wasn’t being transferred, rather than because it wasn’t being transfered FTL. Then when I see a term like “choice” rather than your more instructive and entropy- reducing term “uncertainty,” I started to conflate the notion of “choice” with “can’t be the result of a coin flip.” Thanks for your help.
I understand. I have understood. The point of the analogy was not to give another example of things being “entangled,” but the other half of this thread, which is how a variety of scenarios can be concocted that give the illusion of FTL information transfer, but that it all comes down to just that. An illusion.
I think most people, myself included, reacted to statements such as these:
What they suggest, on a straightforward reading, is that you claim that there would be some absolute sense in which one could put an order to events arriving at A and C—i. e. that it looks like A sends a message ‘FTL’ to which C immediately reacts, sends a message back, thus getting a conversation between the two that happens at apparent light speed, by merely following a fixed script. But that’s just not the case—in some reference frames, C will seem to reply before A sends the first message, and hence, it will not ‘look like’ there is communication between the two. And neither reference frame is objectively the right one.
But in the original problem, one could claim that a sort of information exchange has taken place, although it would not be clear in which direction—i. e. which general measured first, thus causing the entangled state to collapse.
In quantum mechanics though there is non-locality, so it is not an illusion in the sensse that there is, or can be, a explanation that is ‘classical-like’ (i.e. realist) and doesn’t involve FTL information transfer (i.e. is local) for what happens. A local realist explanation could explain the correlation between two entangled particles, but Bell’s inequalties shows it would fail in other situations.
What I basically mean is that any explanation of how quantum non-locality doesn’t ‘break’ causality will defy a simple classical analogy.
Well, although it’s often glossed like that, I think one should point out that it’s far from a settled issue, even though some would claim otherwise. On most accounts, the Many Worlds interpretation is thoroughly local—even local realistic, getting around Bell’s theorem by violating the (implicit) assumption that only one outcome of a range of possibilities ever obtains. Even on other interpretations, Bell’s theorem doesn’t force you to give up locality; all that a Bell inequality really is, is just a necessary condition for a certain set of variables (the experimental outcomes) to have a joint probability distribution, so their violation just means that no such distribution exists. And after all, what would be the meaning of the probability for observing, say, some simultaneous spin values for orthogonal directions, when there is no possible way to actually make such an observation?