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 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 "instantaneous-action-at-a-distance" that prevents the spherical outgoing wave from acting at more than one place on the screen.

Einstein's idea of "local reality" was that events at one point in spacetime could depend only on the values of continuous functions at that point. In a "complete" physical theory all physical variables should be locally determined by his four-dimensional continuous field of space-time. The two-slit experiment showed Einstein that things appeared to happen simultaneously over a large distance in space. That appeared to violate his special theory of relativity. But the two-slit experiment involved just one photon or electron.

In 1935 Einstein and his Princeton colleagues Boris Podolsky and Nathan Rosen proposed their "EPR" thought experiment that implied two particles could remain correlated, perhaps remain "in contact" over large spatial distances. As far as the probabilistic wave function is concerned, there is nothing different here. When the wave function "collapses," its value goes to zero everywhere, just as for a single particle, but it predicts two places where particles will be found. At the moment of collapse, all their properties are still correlated. After the collapse they are decohered and describable as the product of separate single-particle wave functions.

Schrödinger wrote to Einstein immediately and explained that the two-particle wave function could not be "separated" (this came to be called "nonseparability," closely related to nonlocality). Schrödinger said they remain entangled until some interaction "disentangles" them. A measurement would be such an interaction. Einstein stubbornly insisted on what he called a "separation principle" (Trennungsprinzip) that obtains as soon as the particles are in a spacelike separation, beyond where subluminal signals could be exchanged between them. This was needed for his idea of "local reality."

But Schrödinger understood wave mechanics much better than Einstein. The wave function describes only the possibilities for particle locations (with calculable probabilities). In a two-particle wave function, the possibilities mean either particle can be found anywhere the wave function is non-zero. We cannot know where either one will be found until we make a measurement. At that moment, the other particle will instantly be located where the principles of conservation of energy, momentum, angular momentum, and spin require it to be. It is only after the measurement that we can say the particles are separated. This is the core idea of nonseparability.

And this means that any measurement that collapses the two-particle wave function measures both particles! It is not possible to measure "one" (now, here) and then the "other one" (far away, later). Because the particles are indistinguishable, either one could be anywhere just before the measurement, exactly as the single particle in Einstein's 1927 presentation (or in the two-slit experiment) can be anywhere just before the measurement. We cannot say that the two particles are separated beyond the possibility of speed-of-light contact before the measurement.

Almost 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).

In the two-particle case (instead of just one particle making an appearance), when either particle is measured, we know instantly those properties of the other particle that satisfy the conservation laws, including its location equidistant from, but on the opposite side of, the source, and its other properties such as spin.

We can also ask what happens if Bob is not at the same distance from the origin as Alice. This introduces a positional asymmetry. But there is still no time asymmetry from the point of view of the two-particle wave function collapse.

When Alice detects the particle (with say spin up), at that instant the other particle also becomes determinate (with spin down) at the same distance on the other side of the origin. It now continues, in that determinate state, to Bob's measuring apparatus.

Einstein asked whether a particle has a determinate position just before it is measured. Probably not, but we can say that before Bob's measurement the electron spin he measures was determined from the moment the two-particle wave function collapsed. The two-particle wave function describing the indistinguishable particles cannot be separated into a product of two single-particle wave functions. When either particle is measured, they both become determinate.

This is another example of using one mystery to solve another mystery. This is rarely successful. What it produces is two mysteries!

John Searle says consciousness is a mystery, free will is a mystery, and quantum mechanics is a mystery. These mysteries may be related.

Nonlocality is one of the many quantum mysteries, which are connected with free will now that many philosophers accept the possibility that quantum mechanics introduces some real randomness and absolute chance into the universe.

Until recently, few thinkers have succeeded in getting past the standard argument that indeterminacy may render our decisions random and thus deny us moral responsibility.

But randomness is not the essence of the nonlocality phenomenon. This mysterious phenomenon exhibited in the famous Einstein-Podolsky-Rosen experiments is the apparent transfer of something physical faster than the speed of light. What happens actually is merely an instantaneous change in the information about probabilities (actually complex probability amplitudes).

Roger Penrose thinks that nonlocality can help to explain consciousness.

The Swiss physicists Nicolas Gisin and Antoine Suarez think that nonlocality can explain free will because "something is coming from outside space and time."