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Old 01-03-2012, 02:03 PM
Omphaloskeptic Omphaloskeptic is offline
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Quote:
Originally Posted by whc.03grady View Post
The assertion of the existence of a state wherein a cat is simultaneously alive and not-alive (viz., in a superposition) would by definition entail a contradiction and is therefore (it seems to me) an assertion we're entitled to ignore. The laws of logic/math are more basic than the laws of physics, after all.
I think there are some misunderstandings in both of these sentences. It is tempting to view logic and mathematics as basic, with physical laws somehow building on these. But physics is fundamentally an empirical science, not a logical one; if empirical physical results contradict logical derivations then it's the logic that's broken, not the physics.

Of course what's more likely than an inconsistency in logic is that there's been an error in the attempt to translate from physical measurements to physical laws to logical statements; and this is what I think is wrong with your first statement. (This is especially easy to do if you're reading popular accounts, which may not be terribly precise in their use of language.) You say that a cat must be either alive or not-alive (excluded middle), and implicitly count this as two distinct well-defined states exhausting all possibilities. At least one of these two properties is empirically shown to fail in quantum mechanics, however. The usual informal way in which physicists talk about this is to label two particular states of the cat system as "alive" and "dead" and then understand that quantum mechanics allows superpositions of these two states. Now you see that there's not actually a logical contradiction. There are more than two possibilities, so excluded middle does not apply, and "not-alive" is not the same as "dead".

So more formally what quantum mechanics predicts--and as already mentioned this has been experimentally verified, though not for actual cats--is that there is a continuum of possible states, each of which has some probabilities of having particular values when actual measurements such as "is the cat alive?" are made. The difference between this prediction and the statistical incomplete-knowledge prediction is that for a superposition there are some measurements that always give the same value.

These measurements are somewhat difficult to describe for cats, but they are pretty easy to describe for an electron, say. If we call |up> and |down> the states in which an electron's z-component of spin (i.e., measured along a chosen z axis) is +1/2 and -1/2 respectively, then measuring the z-component of spin for the state |up>+|down> will give +1/2 half the time and -1/2 half the time. However, measurement of the component of spin along a particular axis orthogonal to the z axis will give +1/2 *all the time*. This is distinct from the statistical case in which you have no information about the electron's spin; in this case measurement along any axis will statistically give +1/2 half the time and -1/2 half the time.