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Quantum Gravity?
Do you use the word God because you can't explain otherwise how it
happens? Tsk tsk tsk. Sloppy. Very sloppy. |
#2
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#3
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Russell wrote:
"God does not play dice" is a famous quote of Einstein, in which he expressed, in jokingly colorful language, his serious opinion that some deterministic law lies behind the apparently probabilistic quantum mechanics. It's not quite that simple (as you alluded to below). The one generally accepted axiom of QM -- the Evolution postulate, as couched in Schroedinger's equation -- is deterministic. The probabilistic element only enters into Lueder's Rule or the Projection postulate, which is not widely accepted as a fundamental postulate of QM. That's really the whole impetus behind "interpretations" and "measurement theory": trying to find a way to get a semblance of projection without the extra axiom. All that you can say, as Bohm pointed out directly after writing up a book summarizing the standard (Evolution + Projection) formulation is that the determinism is non-local and the probabilistic element comes from ignoring what's "outside" the system -- just like it does in classical physics (where "outside" means both "outside the domain of interest" AND "outside/under the macroscopic realm"). In fact, you get the probabilistic behavior any time you cut off ANY part of the external environment; the resulting state (relative states) exhibit the very type of "collapse" (from pure state to mixed states) you want. The probabilistic behavior is not fundamental but comes from tracing over the external (and/or microscopic) modes, no different than in classical physics. The one question that usually arises is what about the entire universe? If it has a quantum (pure) state that evolves deterministically, then absent an extra axiom like Projection, literally nothing will happen in the universe so-modelled. That's the famous Problem of Time in quantum cosmology. But the problem seriously begs the question: i.e., that there even IS such a thing as a universal configuration space to draw out a state space from, never mind that the universe might be in one of the states. Number one, you need not even have a global "t" coordinate in the first place, if the global structure of the spacetime is contorted in such a way that time can loop. And even if not, then as Smolin was one of the first to point out, it STILL need not be the case, even in a globally hyperbolic spacetime where there is a "t" coordinate, that you have a configuration space or a pure quantum state. In that case, for all intents and purposes, the entire Universe is an open system, relative states become a necessity, boundaries with the external environment become a necessity, and everything has to be done locally. The result is that probability enters the picture. Not just in quantum theory, but even in classical physics! |
#5
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Shmuel (Seymour J.) Metz wrote:
The one question that usually arises is what about the entire universe? If it has a quantum (pure) state that evolves deterministically, then absent an extra axiom like Projection, literally nothing will happen in the universe so-modelled. That's [i.e. The Problem of Time, which is what this is in reply to, as you would know if you hadn't deleted the rest of the quote above which said it was referring to that!] only true if it has an exact energy, Oh, for God's sake, people! Will you PLEASE look up what you're replying to before you reply (and try not to delete it!) The Problem of Time http://search.yahoo.com/search?p=%22...lem+of+Time%22 Energy and eigenvalues have nothing to do with nothing. The problem of time is related solely to diffeomorphism gauge invariance. |
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