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Wednesday, October 30, 2002 |
"It [the Uncertainty Principal] does say that some pairs of properties are linked in such a way that they cannot both be measured precisely at the same time. In physics, these pairs are called "canonically conjugate variables." One such pair is position and momentum: The more precisely you locate the position of a particle, the less you know about its momentum (and vice versa). Another is time and energy: The more precisely you know the time span in which something occurred, the less you know about the energy involved (and vice versa)."
"From a mathematical point of view, there is nothing the least bit problematic about Heisenberg's uncertainty principle. If you try to translate the sentence, "Electron e is exactly at position x with a momentum of exactly p," into the formal language of quantum theory, you get ungrammatical gibberish, just as you would if you tried to translate "the round square" into the language of geometry."
Thanks to Ian at Psybertron for finding this one.
Well I've been toying with the idea of trying to prove that Identity and Expresscivity in a language are "canonically conjugate variables."
Years ago, the Princeton physicist John Wheeler began to wonder whether Heisenberg's uncertainty principle might not have some deep connection to Gödel's incompleteness theorem (probably the second most misunderstood discovery of the 20th century). Both, after all, seem to place inherent limits on what it is possible to know. But such speculation can be dangerous. "Well, one day [Wheeler recounts] I was at the Institute of Advanced Study, and I went to Gödel's office, and there was Gödel. It was winter and Gödel had an electric heater and had his legs wrapped in a blanket. I said, 'Professor Gödel, what connection do you see between your incompleteness theorem and Heisenberg's uncertainty principle?' And Gödel got angry and threw me out of his office."
... hmm .. would that i was a fly on the wall.
12:14:54 PM 
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© Copyright 2002 Seth Russell.
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