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Re: EPSILON_ZERO, OK ?



Somehow this didn't get posted this morning. I'll try again.

At 8:33 PM -0800 3/3/00, David Bowman wrote:
Regarding Leigh's comment:

Dirac's paper also showed that if there existed even one monopole in the
Universe its charge was determined (to within an integer multiple) by the
quantization of angular momentum in the electromagnetic field.

As I recall the result had nothing to do with angular momentum (although
the quantum of action, h-bar, does appear). Rather, he showed that if
(in cgs Gaussian units) there is any isolated electric charge q_e and
there is also any isolated magnetic charge q_m anywhere in the universe
then the product q_e*q_m was quantized as q_e*q_m = [integer]*h-bar*c/2.
This quantization condition came about because of the need to have the
particle wave functions single-valued throughout all of space. This
quantization condition has a consequence that if there happened to be any
magnetic monopole anywhere in the universe then all electric charges in
the universe must be integer multiples of a fundamental electric charge
e = h-bar*c/(2*q_m). If we invert this expression and solve for
q_m and use the experimental value of the fine structure constant we get
a value of q_m which is (137/2)*e.

I think that is the same thing, isn't it David? Your interpretation
(and perhaps the way that Dirac stated it originally) is essentially
the Bohr-Stoner quantization criterion, another guise of the law of
quantization of angular momentum. As I recall one integrates ExB dV
for a monopole and a (quantized) electric charge over all space and
one obtains a total angular momentum in the field. In that sense the
Bohr-Stoner criterion implies single-valuedness to the wave function
of a hydrogen atom, but it is also interpretable as meaning that the
angular momentum of an atom is quantized. While the former reading
is very clear to a theoretician (and even to me), the latter reading
is the one I would use to explain it conceptually to a student who
has learned already about quantization of angular momentum (say, in
a chemistry course) but who knows little of wave functions.

I haven't performed the calculation in all my years of teaching, so
I'm not at all clear on the details, but I seem to remember reading
a Dirac paper in the sixties in Science in which he coined the term
"dyon" for the magnetic monopole. That was the paper I thought Jack
was referring to. You two can help repair my memory, perhaps. (I
just had a crash and had to fix my Mac's memory, and it is much
younger than I am.)

Leigh