There’s a curious problem with entanglement that a lot of people in foundations are trying to tackle at the moment and it is certainly one that bothers me, as it should anyone who wants physics to be consistent in its description of the universe.
Consider a pair of entangled particles separated by lightyears. The act of measurement on one of the particles seems to have an effect on the state of the other instantaneously. In fact we are even free to choose what to measure right before we measure it. Clever physicists have gotten around this problem by positing that the act of measurement does not in fact affect the physical state of the second particle, rather it simply affects our knowledge of that state. What the underlying physical reality actually is (or even if there is an underlying physical reality) is still an open question.
Now, on the other hand, what if we post Alice at our first particle and Bob at our second. Will Alice’s measurement (including her choice of what to measure) have an effect on what Bob might measure for his particle? It is actually a fairly simple matter to show that Bob’s results are completely independent of Alice’s measurement (and any related choices she made).
But wait, isn’t Bob’s measurement a state of knowledge, at least as far as Alice is concerned? Suppose Bob communicates his measurement result to Alice by classical means. In this way the state of the second particle is only a state of knowledge as far as Alice is concerned. But we have seen initially that it is ok for Alice’s measurement of the first particle to affect her knowledge of the state of the second particle. If it can’t affect Bob’s measurement but can affect Alice’s knowledge of Bob’s measurement, what precisely is it that is affected? Is it the classical transmission of Bob’s result to Alice that is affected?
Personally, I find this disturbing and is partly why I don’t entirely buy the “states of knowledge” interpretation, but then again I’m a bit of a neophyte on these things. Perhaps Rob Spekkens can make sense of all of this.