Zafa Pi said:
I gave what I consider a coherent definition of locality. The experiment could either be classical or quantum and could include EPR.
The big assumption that EPR violates is Bell's notion of locality.
Basically: the probability of Bob getting a particular result can only depend on facts about Bob and his detector and the particle being measured by the detector.
The predictions of QM for EPR, in contrast, say that the probability of Bob's result can depend on Alice's result. That's what makes it nonlocal, in Bell's sense. Bob's result doesn't depend on Alice's
choice, so EPR doesn't allow FTL communication, but it does depend on Alice's result.
We can picture it this way:
This picture represents regions of spacetime relevant for a single "round" of an EPR-type experiment. Region 1 is where (and when) Alice performs her measurement, and Region 2 is where Bob performs his measurement. Regions 3 and 5 are in the causal past of Alice (her "backwards lightcone"), and Regions 4 and 5 are in the causal past of Bob.
Locality in the sense of Bell says that Bob's result, in Region 2, can only depend on facts about his causal past, which means facts about regions 4 & 5. If Alice's result in Region 1 reveals information about Bob's result in Region 2, and that information is unavailable in Regions 4 & 5, then that means that the information is nonlocal in the sense of Bell.
That's exactly what EPR does. In the anti-correlated spin-1/2 version of EPR, if Alice in region 1 measures spin-up for her particle along axis \vec{\alpha}, then she immediately knows something about Bob's result in region 2: She knows that he did not (or will not, if it hasn't happened yet) measure spin-up along that axis. So this is definite information about Bob's result. And it is nonlocal in the sense that no amount of information about conditions in regions 4 and 5 can tell you this fact.
For comparison purposes, we can consider a classical analog of EPR: In Region 5, somebody (call him Charlie) takes a pair of shoes, takes two identical white shoe boxes, and puts one shoe in each box. Then he mixes up the boxes and sends one box to Alice and another box to Bob. Later, in region 1, Alice opens her box, and finds a left shoe. She immediately knows that Bob found (or will find, if it hasn't happened yet) a right shoe. So that's seemingly similar nonlocal information. However, in the classical case, it's not true that "no amount of information about conditions in regions 4 and 5 can tell you this fact". If you had a video of Charlie putting the shoes into boxes and shuffling them, then you could slow the video down. By paying close attention, you could figure out at each moment which box contained the left shoe and which box contained the right shoe. Then you could see which box was sent to Alice and which was sent to Bob. That would allow you to predict what result Bob would get, based only on facts about region 5.
The quantum version does not allow the prediction of Bob's result based on information about Region 5.