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Quantum Mechanics
Introductory Remarks
Humans have divided physics into a few artificial categories, called theories, such as
•
classical mechanics (nonrelativistic and relativistic)
•
electricity & magnetism (classical version)
•
quantum mechanics (nonrelativistic)
•
general relativity (theory of gravity)
•
thermodynamics and statistical mechanics
•
quantum electrodynamics and quantum chromodynamics (relativistic version
of quantum mechanics)
Each of these theories can be taught without much reference to the others. (Whether any
theory can be
learned
that way is another question.) This is a bad way to teach and view
physics, of course, since we live in a single universe that must obey one set of rules.
Really smart students look for the connections between apparently different topics. We
can only really learn a concept by seeing it in context, that is, by answering the question:
how does this new concept fit in with other, previously learned, concepts?
Each of these theories, nonrelativistic classical mechanics for instance, must rest on a set
of statements called
axioms
or
postulates
or
laws
. Laws or Postulates are statements that
are presented without proof; they cannot be proven; we believe them to be true because
they have been experimentally verified. Newton's 2
nd
Law,
net
F
ma
=
r
r
, is a postulate; it
cannot be proven from more fundamental relations. We believe it is true because it has
been abundantly verified by experiment.
Actually, Newton's 2
nd
Law has a limited
regime of validity
. If you consider objects going
very fast (approaching the speed of light) or object very small (microscopic, atomic), then
this "law" begins to make predictions that conflict with experiment. However, within its
regime of validity, classical mechanics is quite correct; it works so well that we can use it
to predict the time of a solar eclipse to the nearest second, hundreds of year in advance. It
works so well, that we can send a probe to Pluto and have it arrive right on target, right
on schedule, 8 years after launch. Classical mechanics is not wrong; it is just incomplete.
If you stay within its wellprescribed limits, it is correct.
Each of our theories,
except
relativistic Quantum Mechanics, has a limited regime of
validity. As far as we can tell, QM (relativistic version) is
perfectly
correct. It works for
all
situations, no matter how small or how fast. Well... this is not quite true: no one
knows how to properly describe gravity using QM, but everyone believes that the basic
framework of QM is so robust and correct, that eventually gravity will be successfully
folded into QM without requiring a fundamental overhaul of our present understanding of
QM. String theory is our current best attempt to combine General Relativity and QM, but
"String Theory" is not yet really a theory, since it cannot yet make predictions that can be
checked experimentally.
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 Fall '08
 STEVEPOLLOCK
 Physics, mechanics, Magnetism, General Relativity, Fundamental physics concepts

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