I think that the unsettling and unsettled conclusion of experiments on this subject is that the measuring alone of one particle can affect a system whose second particle is expected to act independently of the measurement of either particle. Is this a correct, although likely partial, assessment? What's missing?
'One of the principal features of quantum mechanics is that not all the classical physical observables of a system can be simultaneously known with unlimited precision, even in principle. Instead, there may be several sets of observables which give qualitatively different, but nonetheless complete (maximal possible) descriptions of a quantum mechanical system. These sets are sets of "good quantum numbers," and are also known as "maximal sets of commuting observables." Observables from different sets are "noncommuting observables".
A well known example is position and momentum. You can put a subatomic particle into a state of well-defined momentum, but then you cannot know where it is. It's not just a matter of your inability to measure, but rather, an intrinsic property of the particle. Conversely, you can put a particle in a definite position, but then its momentum is completely ill-defined...
...They imagined two physical systems that are allowed to interact initially so that they will subsequently be defined by a single Schrodinger wave equation. (For simplicity, imagine a simple physical realization of this idea - a neutral pion at rest in your lab, which decays into a pair of back-to-back photons. The pair of photons is described by a single two-particle wave function.) Once separated, the two systems (read: photons) are still described by the same wave equation, and a measurement of one observable of the first system will determine the measurement of the corresponding observable of the second system. (Example: the neutral pion is a scalar particle - it has zero angular momentum. So the two photons must speed off in opposite directions with opposite spin. If photon 1 is found to have spin up along the x-axis, then photon 2 must have spin down along the x-axis, since the total angular momentum of the final-state, two-photon, system must be the same as the angular momentum of the initial state, a single neutral pion. You know the spin of photon 2 even without measuring it.) Likewise, the measurement of another observable of the first system will determine the measurement of the corresponding observable of the second system, even though the systems are no longer physically linked in the traditional sense of local coupling.
However, QM prohibits the simultaneous knowledge of more than one mutually noncommuting observable of either system. The paradox of EPR is the following contradiction: for our coupled systems, we can measure observable A of system I (for example, photon 1 has spin up along the x-axis; photon 2 must therefore have x-spin down), and observable B of system II (for example, photon 2 has spin down along the y-axis; therefore the y-spin of photon 1 must be up), thereby revealing both observables for both systems, contrary to QM.
QM dictates that this should be impossible, creating the paradoxical implication that measuring one system should "poison" any measurement of the other system, no matter what the distance between them. (In one commonly studied interpretation, the mechanism by which this proceeds is 'instantaneous collapse of the wave function'. But the rules of QM do not require this interpretation, and several other perfectly valid interpretations exist.) The second system would instantaneously be put into a state of well-defined observable A, and, consequently, ill-defined observable B, spoiling the measurement. Yet, one could imagine the two measurements were so far apart in space that special relativity would prohibit any influence of one measurement over the other. For example, after the neutral-pion decay, we can wait until the two photons are a light year apart, and then "simultaneously" measure the x-spin of photon 1 and the y-spin of photon 2. QM suggests that if say the measurement of the photon 1 x-spin happens first, then this measurement must instantaneously force photon 2 into a state of ill-defined y-spin, even though it is light years away from photon 1.
How do we reconcile the fact that photon 2 "knows" that the x-spin of photon 1 has been measured, even though they are separated by light years of space and far too little time has passed for information to have travelled to it according to the rules of special relativity? There are basically two choices. You can accept the postulates of QM as a fact of life, in spite of its seemingly uncomfortable coexistence with special relativity, or you can postulate that QM is not complete, that there was more information available for the description of the two-particle system at the time it was created, carried away by both photons, and that you just didn't know it because QM does not properly account for it.'math.ucr.edu/
At least, we now know that it is simplistic to limit the phenomenon to measurement alone. That much I knew to question. As for what the whole thing is about, I have some vague idea.
Essentially, you have to get over the idea of "distance." As in "the particles are separated by such a great distance that NOT EVEN LIGHT could have transmitted the signal to tell particle B to have opposite spin as Particle A." (Sorry for the long quote). The quantum entanglement is completely predicted by quantum mechanics, which, we know, is INCOMPATIBLE with General Relativity. Therefore, the action at a distance "paradox" is actually poorly posed, or has been in the cases I've seen. Likely, the next-gen theory will have to explain the phenomenon of entanglement, along with many others, in order to be accepted by much of the community.
