Re: a question on incompatibility of properties in a one particle system
From: Bilge (dubious_at_radioactivex.lebesque-al.net)
Date: 10/17/04
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Date: Sun, 17 Oct 2004 09:28:49 -0000
richardconers@yahoo.com:
>I understand that quantum mechanics asserts that position and momentum
>(velocity?) cannot be simultaneously determined. Yet, what happens
>when you measure the position of an electron as precisely as possible?
The momentum is completely indeterminate.
>Suppose you shoot an electron at a phosphorus screen. At the moment
>of impact, you have an exact measure of the position of the electron,
>relative to the screen.
No, you only think that's the case. We're talking about really
small numbers here. Remember that we can pin down the position
and momentum of an electron to that of an atomic orbital.
> You know the momentum/velocity of the screen
>relative to itself (i.e., 0). That must mean that you have no
>information whatever about the momentum of the electron. But you do.
>You know that the absolute magnitude of the velocity of the electron
>is surely less than or equal to what it was before the moment of
>impact. Or can electrons, when striking an object at relative rest,
>ricochet off that object at a greater velocity than when the electron
>was approaching the object that it will strike?
The first thing is that velocity is not a quantum observable, momentum
is and the momentum is -i\hbar\grad\Psi, not mv. The second thing is
you shouldnt think of the indeterminacy as a lack of precision. Think
of it as literally meaning what it implies. A precise position measurement
implies the momentum was really indeterminate, not that it really had
a value but you can't measure the value.
>Are there laws of thermodynamics that atomic particles obey, and
>some they don't obey?
Atoms and other particles not only obey the laws of thermodynamics,
but the quantum theory that describes them resolved a long standing
problem with classical physics called gibb's paradox. Because of the
uncertainty relations, identical particles really are indistinguishable
particles, e.g., two electrons in a single state have to be treated
as a single state, not two electrons. Gibb's paradox was the result
of a _classical_ counting argument in which interchanging two particles
defined a different state of the system and overcounted the number of
states by N!, giving an entropy which was too large.
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