Wikipedia has a most comprehensive page on the
Interpretations of Quantum Mechanics.
As with our analysis of
positions on the free will problem, there are many interpretations, some very popular (with many adherents), some with only a few supporters. The popular views are defended in hundreds or journal articles and published books. Just as with philosophers, the supporters of an interpretation often have their own jargon which sometimes makes communication between the different positions difficult.
The standard "orthodox" interpretation of quantum mechanics includes a
projection postulate. This is the idea that once one of the
possible locations for a particle becomes
actual at one position, the probabilities for actualization at all other positions becomes instantly zero. This sudden disappearance of possibilities/probabilities at locations remote from where a particle is actually found is called
nonlocality. It was first seen as early as 1905 by
Albert Einstein.
"Projection" or "reduction of the wave packet" is known as the "
collapse of the wave function," although the wave itself function does not "collapse." All that changes is our
knowledge about the particle, where it is actually found. What changes is only
abstract immaterial information about the particle's location.
In the
two-slit experiment, for example, the wave function actually does not change at all, since it just depends on the boundary conditions in the experiment, which do not change because one particle has been found. Every future experiment with the same conditions has exactly the same wave function and thus the same probabilities for finding a particle. Unless, of course, we change from one slit open to both open, or vice versa.
Another similar particle entering the same space, after the first particle has been detected and thus removed from the space, would have the same probability distribution, since the wave function is determined by the solution of the Schrödinger equation, given the boundary conditions for the space and the wavelength of the particle.
The wave function is simply
immaterial information. It remains a mystery how it controls (if it controls) the motions of individual particles so their the predicted probabilities agree perfectly with the statistics of large numbers of identical experiments.
Today there appear to be about as many unorthodox "no collapse" interpretations, denying
Dirac's projection postulate, as there are more standard views.
No-Collapse Interpretations
Collapse Interpretations