vanhees71 said:
I think we had this discussion a while ago. In fact in the here described EPR-paradox version with angular momentum (spin) a la Bohm, it's easy to see that of course the conservation laws hold event by event. To prove this, of course, you have to measure the angular-momentum component in the same direction on both particles, because you can only determine one momentum component due to the commutator relations of angular-momentum components. The ##J=0## state of the total system is an exception, because for this state all three components take simultaneously the same value, 0.
If you measure different components of the angular momentum on both particles, of course you cannot verifty angular-momentum conservation, because the outcomes of the measurements are random with a probabilities for the possible outcome for the two angular-momentum components given by Born's rule. This also includes, of course, the violations of Bell's inequality, which cannot be described with local deterministic hidden-variable theories. This has, however, nothing to do with the claim that the conservation laws only hold "on average".
I'll try to read the papers, as soon as I find the time.
Now that would be, as Peter Donis said, an interpretation of the mainstream view of Bell state data.
The mainstream view of the data is that when Alice and Bob measure a Bell state (say, a triplet state in the symmetry plane) at some particular SG magnet orientation, then both will always get the same result, half the time they will both get +1 and half the time they will both get -1. If Bob changes his SG magnet orientation making an angle ##\theta## with Alice's orientation, then they will observe "average-only" conservation. By that I mean that if Alice partitions the data according to her equivalence relation (her +1 and -1 results), she will see that Bob's results average to ##\pm \cos{\theta}##, respectively. If Bob partitions that same data according to his equivalence relation, he will see that Alice's results average to ##\pm \cos{\theta}##. I'm using the phrase "average-only" conservation per standard physics lingo to characterize this mainstream view of Bell state data as follows.
Alice can say that if Bob had not changed his SG magnet orientation, he would have measured +1 when she measured +1, as required to conserve spin angular momentum. So, when he measured at angle ##\theta## with respect to her, he should have gotten the projection of his +1 result, i.e., ##\cos{\theta}## (analogously with their -1 result). So, his results are only satisfying the conservation of spin angular momentum on average according to her partition of the data. Indeed, his results are not a Gaussian about ##\cos{\theta}##, but they give a binary distribution whereby he
never measures ##\cos{\theta}## (thus, "average-only" conservation). Of course, Bob can say the same thing about Alice's results per his partition of the data.
This is totally analogous to their partitions of M4 when they occupy different reference frames related by Lorentz boosts, i.e., uniform relative motion. There Bob can partition the events of M4 per his equivalence relation (his surfaces of simultaneity) and say that Alice's meter sticks are short and her clocks run slow. And, of course, Alice can partition the events of M4 per her equivalence relation (her surfaces of simultaneity) and say that Bob's meter sticks are short and his clocks run slow. This is called the relativity of simultaneity and was a key concept in Einstein's development of special relativity (according to John Norton, anyway).
You can make the analogy stronger by noting that the different SG orientations are related by spatial rotations and spatial rotations relate inertial reference frames in both Galilean and Lorentz transformations. So, you could characterize the relativity of simultaneity and "average-only" conservation as consequences of the relativity principle (as Einstein did for the former), i.e., "no preferred reference frame." But, that would be a proposal, as Peter Donis said, because these facts could also hold where there is a preferred reference frame. Indeed, Unnikrishnan is a strong advocate for a preferred reference frame, that's why he does not support our proposal to invoke NPRF to explain his average conservation. He believes average conservation is enough to resolve the mystery of entanglement and a universal preferred reference frame resolves other mysteries for him.
Sorry for the confusion. Despite the fact that I've been teaching college physics for over 40 years, I'm not a very good teacher as it turns out :-(
