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Re: [Phys-L] electron location & wave function



On 04/16/2013 02:29 PM, Larry Smith wrote:

1. John, are you saying that a quantum of a field is the same thing
as a wave?

I don't know what that means. People use terms like "quantum of
the field" in at at least two inconsistent ways, probably more.

Here's what I have been saying all along:
Q: So you're saying that your cold hydrogen atoms acted like waves?
A: Yes.
Q: But atoms are particles. How did they turn into waves?
A: They were waves all along.
Q: But if they were waves all along, how come nobody ever noticed
before?
A: Because at ordinary temperatures, the wavelength is so short,
and more specifically the coherence length is so short, that
the wave properties all get averaged out, and all that is left
is the classical result. OTOH if you get 'em cold enough, the
de Broglie coherence length gets big, and the atoms become
little fluffy clouds the size of bacteria. They don't bounce
off each other; they diffract right through each other.
Q: So they were waves all along?
A: They were waves all along.

2. The November 2012 issue of AJP has an article by Klein that
asserts that the limit of QM as h approaches 0 is not classical
Newtonian mechanics.

Well, h is not a variable and h is not zero, so the whole idea of
passing to the limit h -> 0 is unphysical.

When sensible people talk about such things, they start by considering
the case where the action (S) is large compared to h. Large S makes a
lot more sense than small h. When you do that, it soon becomes obvious
that the large-S limit does not always correspond to classical physics.
The existence of superfluids and other macroscopic coherent states is
the obvious counterexample.

So, roughly speaking, the classical limit is obtained when the system
is large enough /and messy enough/ that decoherence occurs. There are
ways to predict quantitatively when decoherence will or will not occur.

For anybody who is the least bit interested in such things, a good
place to start is
W. H. Zurek
"Decoherence and the Transition from Quantum to Classical — Revisited"
http://arxiv.org/pdf/quant-ph/0306072v1.pdf