Re: The Electron

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 16:01 -0500 11/10/03, J. Green wrote:
> How much do we really know about the electron?  What, if anything do we know
> about it's inner structure, charge distribution, rotational speed, or if it
> spins at all for that matter?  Why do electrons need to be paired as up and
> down spins?  Fundamental answers are preferred, and those containing
> references to "some guy's theory" will be summarily docked points (unless
> the theory is in fact based on experimental data of course).  Conjecture is
> also welcome (but I imagine someone will take issue with it).  I'm wondering
> if we shrug our shoulders at some questions because we really know less than
> we think we do.  So, what say ye?
There are others on this list who can probably give more cogent
answers to this question, but I think it is safe to say that the
question is not as simple as it may sound. What electron are you
asking about? A "bare" one, or one "dressed" in its electric field?
How much of its mass is due to this "dressing"?

My understanding is that the "bare" electron is, as far as we can
tell, a point particle with no structure. It has a property which is
*called* spin, but is apparently nothing like what we think about
when considering a spinning top. How do you talk about the "spin" of
a point particle? All we can say is that the thing we call "spin"
looks like and combines like an angular momentum. But beyond that, I
don't think we are justified in making any conjectures.

Electrons don't "need" to be paired up as up and down spins, but
since a spin  of one-half of h-bar is a fundamental property of the
electron, if two of them are bound up in the same potential well, and
happen to be in the same energy state, then the Pauli exclusion
principle (which follows from quantum mechanics) tells us that they
cannot both be in the same total state. As it happens, the local
magnetic field can provide a reference direction for the electrons,
which, because of their spin, have a magnetic moment. Again, as a
result of quantum mechanics, the spin is required to be aligned with
the local magnetic field, either parallel or anti-parallel to it.
There is a tiny energy difference in these alignments which allows
the two electrons to sit in what would otherwise be the same state.
In general, if two electrons end up in the same neighborhood, their
interaction energy will be slightly smaller if their spins are
anti-aligned. But this alignment is only "required" if they are
trying to fit themselves into the same quantum-mechanical state, and
need something to differentiate between them.

A good discussion of this very question can be found in Vincent
Icke's book "The Force of Symmetry" (Cambridge U. Press, 1995, ISBN:
0-521-45591-X).

Hugh
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Hugh Haskell
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<mailto:hhaskell@mindspring.com>

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