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Unformatted text preview: 1 of 6 Quantum Mechanics Introductory Remarks Humans have divided physics into a few artificial categories, called theories, such as classical mechanics (non-relativistic and relativistic) electricity & magnetism (classical version) quantum mechanics (non-relativistic) 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, non-relativistic 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 well-prescribed 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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