Two particles fly apart, created in the same nuclear micro-event. When they are too far apart to communicate (remembering the light velocity limit), each has its spin measured. Probability of the spin being plus or minus is exactly 50% for each particle. However, experiment shows that the two particles always, invariably, have the same spin. It is like two coin tosses in two different cities always coming up either both heads or both tails, never one heads and one tails, even when the coin tossers are not linked by telephone or other means of communication.
Standard quantum-theory explanation of the spin measurement for a single particle is that the spin direction is undecided until the act of measurement occurs, i.e. that the act of measurement determines the result. How then can the measurement of one particle’s spin determine the spin of a second particle which is beyond the reach of communication?
I want to propose another interpretation, which is more in line with Betchov’s model of the peak of non-linearity added to the Schrodinger wave equation. In this model, the extremely rapidly resonating peak becomes a representation of the particle associated with the wave. In this view, indeterminacy disappears and a more classical view, one which Einstein would like, is possible.
Perhaps what a particle will do (i.e. what spin direction it will exhibit) does not depend on chance (which “50% probability” implies), but on the incredibly precise timing of its origin in its past history. The timing would be less than a pica-second, to catch the peak of non-linearity in a particular position rather than its alternative. It is not that we (as experimenters) must be incredibly precise — quite the opposite; we can do anything we like, yet we ne-cessarily catch the peak (i.e. the particle) in one or the other of its configurations. And since the two particles emerged in the same fraction of a pica-second from the same experiment, they must necessarily have the same spin no matter how far apart they are. because the spin direction is determined only by the event at the origin. Nothing mysterious in it at all, as soon as we give up the indeterminacy interpretation which has now become standard for quantum theory.
As I prepare to recycle my cans, I take the ends off and step on the cylinder. The cylinder is perfectly round to start with, and any two points on the circumference could become the end-points of the flattened sheet as I step on it. The probability is the same initially for all the almost infinite number of point pairs around the circumference, which means that the probability for any particular pair of points is almost zero. The metal cylinder rolls on the kitchen floor in a state of indeterminacy, yet in spite of the vanishingly small probability of ANY pair of points being “it”, I have to catch it SOMEWHERE — and once I do, one of these infinitesimal probabilities suddenly jumps to one. Yet there was nothing special about that point-pair to start with, it was in every way just like the innumerable other pairs.
Mysterious? Not at all. It only means that what happens in the real world is a matter of history (what IN PARTICULAR happened), not a matter of science (what IN GENERAL must happen according to some law). This is somewhat related to what is meant by “symmetry breaking”.
Even that supreme paradigm of chance, the toss of a coin or of dice, is like that. Several outcomes are possible, but only one materializes, because of the temporal micro-structure of the tossing event. Nothing ever really happens by coincidence.
The two particles flying apart simply shared a common history. They did not need to communicate.