Collapse of the Wave Function
Note that when a probability function collapses to unity in one place and zero elsewhere, nothing physical is moving from one place to the other. When the nose of one horse crosses the finish line, his probability of winning goes to certainty, and the finite probabilities of the other horses, including the one in the rear, instantaneously drops to zero. This happens faster than the speed of light, since the last horse is in a "spacelike" separation from the first.
Note that probability, like information
, is neither matter nor energy. When a wave function "collapses" or "goes through both slits" in the dazzling two-slit experiment
, nothing physical is traveling faster than the speed of light or going through the slits. No messages or signals can be sent using this collapse of probability.
This is similar to the Einstein-Podolsky-Rosen
experiments, where measurement of one particle transmits nothing physical (matter or energy) to the other "entangled" particle. Instead instantaneous information
has come into the universe. That information, together with conservation of angular momentum, makes the state of the coherently entangled second particle certain, however far away it might be.
Although neither horse races nor John Bell
's famous example of Bertlmann's socks are (normally) influenced by quantum mechanics, the idea of probability collapsing applies to both. The only difference is that in quantum mechanics, we are dealing with a complex probability amplitude that can interfere with itself, as shown in the two-slit case
Superposition of states
(as with Paul Dirac
's diagonal polarizer
that puts a photon in a linear combination of horizontal and vertical polarization states) can only give us the probability (amplitude) for each state. Thus we say that there is an even chance of measuring the diagonally polarized photon in either vertical or horizontal polarization.
In the entangled electron case, once we measure electron 1 as spin up, conservation of angular momentum tells us with certainty that entangled electron 2 is spin down.
That is instantaneously true, just as the winning horse's nose at the finish line collapses the probabilities of other horses to zero, at faster than the speed of light, but with no material/energy flow.
Information is neither matter nor energy. It needs matter for its embodiment and energy for its communication, but information
itself is as abstract as the number 2, or in the electron angular momentum case, 0.
In the two-slit experiment
, here is what happens to the probability amplitude wave function (the blue waves) when the photon is detected at the screen (either a photographic plate or CCD) in the second interference fringe to the right (red spot). The probability simply disappears instantly, apparently
"moving" at faster than the speed of light.