Or by many worlds: the quarter is both ways in the box. When you each open your boxes, you yourself are pulled into the doubling. Now there are two pairs of you-and-them. In one pair, you hold heads and they hold tails. In the other pair, you hold tails and they hold heads.

Thinking about this makes it clear how communication is impossible. You will always get both answers - for different values of "you".

> then the other is resolved simultaneously.

Relativity of course makes a hash of that.

Still it's as close as you'll get with a classical analogy, and if you only have access to a fixed basis is entirely correct. Expanding beyond the classical explanation is only truly necessary when you start measuring in different bases.

> There is not a fixed state of each 'quarter' in each 'box'. They are truly not determined until one is resolved;

Isn't that unknowable? And aren't both situations (fixed vs undetermined) effectively the same from an observer's point of view?

No. What you are calling 'fixed' is a local hidden variable - an internal state that has yet to be measured but is already determined. This state of affairs is ruled out by Bell's Theorem - https://en.wikipedia.org/wiki/Bell%27s_theorem

That's only true if you take the Copenhagen interpretation. There are other interpretations (like 'consistent histories' for example). See: http://en.wikipedia.org/wiki/Copenhagen_interpretation#Alter...

Other interpretations of quantum mechanics do not generally violate Bell's Theorem, since it appears to be confirmed by experiment. There are other interpretations which choose to abandon locality rather than hidden variables, such as the De Broglie-Bohm pilot wave interpretation. But consistent histories doesn't even do that. It's actually pretty similar to the Copenhagen interpretation.

I didn't say anything about violating Bell's theorem. Yes pilot wave theory is a better alternative that doesn't require spooky action at a distance but consistent histories doesn't require wavefunction collapse (which is a huge source of spookiness as well).