NonseparabilityThe idea of something measured in one place "influencing" measurements far away challenged what Einstein thought of as "local reality." It came to be known as "nonlocality," but it always contained something else called "nonseparability." Einstein called it "spukhaft Fernwirkung" or "spooky action at a distance." Erwin Schrödinger called two particles "verschrankt" or "entangled" when their quantum properties had become correlated by an interaction. Entangled particles cannot be separated without an external interaction. The question for Einstein and Schrödinger was how long the particles could retain their correlation as they traveled a great distance apart. Once de-correlated or "decohered," their two-particle wave function can be described as the product of two single-particle wave functions and there will no longer be any quantum interference (or the appearance of communications or interactions between them) between them. But entangled particles, it turns out, cannot be decohered without an external interaction of some kind (like a measurement). Einstein had objected to nonlocal phenomena as early as the Solvay Conference of 1927, when he criticized the collapse of the wave function as involving "instantaneous-action-at-a-distance" (his spukhafte Fernwerkung or "spooky action at a distance") that prevents the spherical outgoing wave from acting at more than one place on the screen. He probably had seen this nonlocality as early as his light-quantum hypothesis paper of 1905. Single-particle nonlocality can be defined in terms of the volume in phase space where the wave function has non-zero values. There are possibilities of finding the particle anywhere in this volume (with a calculable probability for each possibility). A particle appears when one of those possibilities becomes actual and the particle is localized. This can be the result of an observer making a measurement or a random environmental interaction. The "collapse" of the wave function is then simply the instantaneous disappearance, the going to zero, of all the non-actualized possibilities when the nonlocal wave becomes a localized particle. Einstein insisted that when two particles have separated enough there would come a distance where interactions between them are no longer possible. He called this his Trennungsprinzip or separability principle. We can now understand the "nonseparability" of two entangled particles in terms of this nonlocality. Two entangled particles are described by a two-particle wave function that can not be factored into the product of two single-particle wave functions. The entangled particles share the same volume of nonlocality, i.e., where the two-particle wave function has non-zero values. This means that either particle has the same possibility (with calculable probability) of appearing at any particular location. Just as with the single-particle nonlocality, we cannot say where the particles "are." Either one may be anywhere inside the nonlocality volume up to the moment of "collapse" of the two-particle wave function. So far this is what Richard Feynman called the "only mystery" in quantum mechanics. He mistakenly advised you not to try to understand it or visualize it, but information physics will help you to do both, for single particles, such as the two-slit experiment, and for the two-particle Einstein-Podolsky-Rosen thought experiment. When the entangled particles experience a random environmental interaction (described as "decoherence"), or an experimental measurement by an observer, the two-particle wave function "collapses." All the possibilities/probabilities that are not actualized go to zero, just as with the single particle wave function. But now, two particles appear, simultaneously in a special frame in which their center of mass is not moving. In other frames, one may appear to appear before the other. Just as with the single particle, the localization of the two particles can be anywhere there was a possibility. But now fundamental conservation principles constrain their local appearances.The two particles appear simultaneously, usually in a spacelike separation, now disentangled, and symmetrically located about the point of the interaction which entangled them.
Einstein's Introduction of AsymmetryAlmost every presentation of the EPR paradox begins with something like "Alice observes one particle..." and concludes with the question "How does the second particle get the information needed so that Bob's later measurements correlate perfectly with Alice?" There is a fundamental asymmetry in this framing of the EPR experiment. It is a surprise that Einstein, who was so good at seeing deep symmetries, did not consider how to remove the asymmetry. Consider this reframing: Alice's measurement collapses the two-particle wave function. The two indistinguishable particles simultaneously appear at locations in a space-like separation. The frame of reference in which the source of the two entangled particles and the two experimenters are at rest is a special frame in the following sense. As Einstein knew very well, there are frames of reference moving with respect to the laboratory frame of the two observers in which the time order of the events can be reversed. In some moving frames Alice measures first, but in others Bob measures first. If there is a special frame of reference (not a preferred frame in the relativistic sense), surely it is the one in which the origin of the two entangled particles is at rest. Assuming that Alice and Bob are also at rest in this special frame and equidistant from the origin, we arrive at the simple picture in which any measurement that causes the two-particle wave function to collapse makes both particles appear simultaneously at determinate places with fully correlated properties (just those that are needed to conserve energy, momentum, angular momentum, and spin).