Brian- That's a really nice question. All of the answers you suggest
have been advocated at some time or other by some serious physicists.
The interpretation of quantum mechanics has not yet fully settled down,
but we can at least now eliminate some of the possibilities.
In most reasonable interpretations, the particle does not have
completely sharply defined values of position and momentum, ever. After
a measurement, one or the other can be pretty sharply defined, but not
It's tempting to think that all the standard physical variables
actually have definite values, but that somehow we just don't know them
or that they are somehow perturbed by the measurement. However,
experiments following an idea by John Bell have shown that if there are
any 'hidden variables' determining the seemingly random outcomes of
quantum experiments, those variables are not local- i.e. they don't
exist in any particular position but rather all over the place at any
time! These days almost all of us who worry about the interpretation of
quantum mechanics, no matter how much we argue with each other, believe
that your answer "b" is closest to the truth.
If you were to broaden your question to something like "What
actually goes on in a 'measurement'?" I think the closest answer would
(published on 10/22/2007)