The Master Magician
In a previous article the quantum wave function is depicted as a spinning spiral. Waves incident upon infinite potential barriers are considered. In each case the reflected wave is added to the incident wave, forming a standing wave.
In quantum theory the waves are associated with a stream of particles (e.g. electrons) traveling in the +x-direction. Classically the same density of particles would be expected in any volume, with half the particles traveling toward positive x and half toward negative x. According to Bornís interpretation of the standingY waves, however, there are "quantum surprises." The probability of finding particles in a given Dx is not constant, but ranges from zero right at a standing wave node to a maximum at a wave anti-node.
Experiment indicates that the quantum surprises reflect reality. There are at least two suggested explanations for these results: (1) At wave nodes the particles are present but defy detection, and (2) The particles are never at the nodes.
One might at first be inclined toward the first view. After all, in going from anti-node to anti-node a particle must travel through a node, right? Here again experiment suggests that the correct answer to that question is "Wrong!" It appears that a particle may actually cease to exist on one side of a node, and simultaneously appear on the other side a finite distance away! The more general proposition, that an event at one point in space might simultaneously trigger a complementary one at some point a finite distance away, has puzzled physicists ever since Bohr proposed instantaneous jumps between orbitals in his Hydrogen atom. Since then many other examples of such odd behavior have been discovered. (See, for example, "Quantum Entanglement" on the Internet.)
The hypothesis that an event can happen at one point in space, and simultaneously trigger a complementary event at a distant point with no influence traveling from one point to another at anything less than infinite speed, is often referred to as "non-locality." Einstein, who never believed that information can be transferred at speeds in excess of c (the speed of light), called it "spooky action at a distance."
It appears to be nothing less than magic. And thus far only "The Old One" seems to know the secret. Then again, perhaps the secret is that there is no trickery involved. We have long grown accustomed to the fact that the world of the super small can be counterintuitive. And this counterintuitive reality is never more manifest than in the now-you-see-it, now-you-donít behavior of elementary particles. If there are sleights of a mighty hand at work, thus far no one has detected them.
The student may be well-advised to get used to it. For it appears to be how Nature works in the domain of the very small. It is as if the conservation laws, of momentum, charge, etc., are enforced through all of space instantaneously. There appear to be no hidden variables or other mechanisms that explain such phenomena in macroscopic terms. The mathematics of probability, in tandem with the conservation laws, appear to be running the show.
Einstein, in his celebrated debates with Bohr, apparently got it wrong. It appears that God really does play dice with the universe. Or, to paraphrase Richard Feynman, microscopic reality really is magical.
G.R.Dixon, July 2013.