I understand that the positions and momentums of elementary particles
is described in terms of probability theory in quantum mechanics. Is
probability theory the "ultimate" explanation for the "states" of
elementary particles, or will future scientists find descriptions or
models in terms of something more fundamental than current models
that does not use probability theory?
Good question. Unfortuantely, we can't possibly answer it, because we
don't know what will be discovered in the future. The probabilistic model
of quantum mechanics has bothered physicists since it came out, but so far
nobody has found a better model (or even another model that works as well).
A lot of folks would LOVE to find a different model, though. So, we'll
certainly TRY to find "descriptions or models in terms of something...
that does not use probability theory," but I can't say what will actually
be found. We just don't know!
Richard Barrans Jr., Ph.D.
You're not really asking a question about physics, are you? I
mean, a physical theory can't possibly encompass a description of its
own limitations, any more than you can see what you can't see because
it's behind you. Follow? What you've got here is a question of
metaphysics, the study of how we know what we know. I suppose it is
conceivable that someone could, using pure logic and mathematics, come
up with some kind of constraint on the nature of physical theory, and
thereby show that certain kinds of theories -- for example those that
involve only perfect certainties, like classical mechanics -- can't
describe reality. That would be quite interesting. But I don't see
how it could be done. Anyway, no one's ever done it.
Incidentally, you may read somewhere that Bell's Inequality and
related experiments on photo polarization teleportation establish
something along the lines you're thinking. This would be nonsense.
The work in question, while quite interesting for a variety of other
reasons, only shows on this score that the known forms of purely local
mechanics (i.e. classical mechanics) are not consistent with
experiment. Which we knew already, long ago.
Dr. C Grayce
You are asking a question not in physics but in metaphysics, or, if
you prefer, a metaquestion about physics: a question about the nature
of the questions that physics can (and cannot) answer.
Whether we will always find ourselves working with probability in
our fundamental physics depends on whether the Universe is
deterministic. If the Universe is deterministic, then everything that
has happened or will ever happen is now and forever fixed, down to the
last wiggle of the tiniest particle at the other end of the galaxy
ninety billions years hence. Beginning from a complete description of
the Universe at any single instant in its history, a mathematical
computation can be made of the exact value of any measurable quantity
at any other time.
If and only if the Universe is deterministic can there someday be a
theory of mechanics that is not probabilistic.
We don't yet know if the Universe is deterministic. Quantum
mechanics says it cannot be macroscopically observed to be so, but
that is not the same thing.
Furthermore, assuming the assertions of quantum mechanics stand up
for all future time unaltered would seem rash: Newtonian mechanics
appeared to be the final theory of mechanics for almost 300 years.
Quantum mechanics only 65 years old.
Let me also point out that even if human scientists never construct
a more correct mechanics, that does not imply that such does not
exist. It is not obvious that all knowledge is within the capability
of our intelligence to deduce and comprehend. You would hardly doubt
that a horse could never comprehend calculus -- the most correct
theory of mechanics may analogously be beyond the grasp of homo sapiens.
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Update: June 2012