From: mcirvin@husc8.harvard.edu (Mcirvin)
Newsgroups: sci.physics
Subject: Re: Did electric/magnetic symmetry "break"?
Date: 10 Sep 92 01:28:59 GMT
Article-I.D.: husc8.mcirvin.716088539
 <1992Sep7.214235.24769@galois.mit.edu> <1992Sep9.204019.17182@asl.dl.nec.com>

terry@aslws01.asl.dl.nec.com (Terry Bollinger) writes:

>Hi folks,

>In article <1992Sep7.214235.24769@galois.mit.edu>
>jbaez@riesz.mit.edu (John C. Baez) writes:

>> ... 2em/hbar must be a multiple of an integer.   Note that this condition
>> is PERFECTLY SYMMETRICAL BETWEEN MAGNETIC AND ELECTRIC CHARGES.

>(?) disappointing.  you have simply restated the original premise -- that
>photons are fully symmetrical between electric and magnetic vectors --
>only this time in caps.  This is non-enlightening.

Well, not exactly.  What John has stated in caps is that the Dirac
quantization condition behaves symmetrically with respect to the
two kinds of charges.  The size difference comes from the smallness
of alpha.  

>> This seeming asymmetry is
>> just an artifact of a particular system of units.

>No.

Here I agree with Terry; hbar and c are important in setting various
scales in nature, and this "artifact" is more than just a feature of
a system of units.  He gives the example of atomic sizes.  Another
example is the validity of perturbation-theoretic calculations.  The
essential fact is that alpha (which is defined independently of
systems of units, though it's only equal of e^2/4pi in one system)
is a couple orders of magnitude smaller than 1/2.  The asymmetry is
contained in that fact.

[description of "symmetry breaking" idea]

>   EM SYMMETRY FARFETCH: In the very, VERY early universe, the current
>   coupling value (alpha) had no real meaning.  Charges, if they could be
>   defined in a meaningful way at all, were of magnitude sqrt( 2em/hbar ),
>   and were completely symmetrical between the electric and magnetic
>   components. 

If you can define the charge, you can define alpha.  It's conceivable
that the value of alpha goes to 1/2 at very high energies.
(At one loop, I think it goes arbitrarily large at high energies,
but that means nothing since one-loop calculations are by definition
worthless at a large value of alpha.)  If alpha were 1/2, and 
magnetic monopoles furthermore existed, there wouldn't be any
asymmetry between the two except for the mass, which you'd also
have to postulate as equal at those energies (I don't know, maybe
this situation is at such high temperature that the Higgs VEV is
zero).  So I suppose the idea has some possible validity.

The problem is that I don't think it could be easily expressed
in terms of the way spontaneous symmetry breaking generally works.
What appears in the standard model (and GUT) Lagrangian coupled
to particles is not the field but the scalar and vector potentials.
Dirac's whole argument rests on the idea that you can only in
full generality express things in terms of these potentials if
you only have one kind of charge (which you might as well call
electric).  If you have two kinds of charge then you need to take
into account the singularity in the vector potential that results;
it's not a gauge-invariant thing but it has to go somewhere, and
charge quantization emerges from that.  To express the potentials
in such a way that electric and magnetic charge come in symmetrically
in the Lagrangian, my guess is that you'd have to somehow put in
more degrees of freedom: define a "dual potential" whose 4-curl
would be the dual field strength tensor, and then put in constraints
so that everything stays consistent, or some such thing.

It's potentially interesting enough to be worth studying.  The way
most of the theories that particle physicists play with today are
constructed, duality symmetry is pretty much ignored, since the
idea is that the 4-vector potential (in which duality symmetry is
not at all explicit) is the primary object in electromagnetism. 
The result is that electrically charged objects are handled in a
very ordinary manner, whereas magnetically charged objects, if
they're in the theory at all, appear in the form of exotic
topological defects resulting from continuous symmetry breaking.

If the 4-vector potential were replaced with a more complicated
sort of structure, a large part of the Standard Model would have
to be reconstructed, since you'd have to do the same thing for
the other electroweak gauge fields.  The modification would 
likewise propagate through any grand unified theory and infect
the gluons.  It might take a reformulation of the idea of a gauge
theory.

>BTW:  No, I do NOT consider the Mystery of Alpha, much talked about in
>song, dance, an folklore, to be quite the same question as whether a very
>early universe could have had a much simpler, more direct relationship
>between charge and hbar.  My question is whether a coherent mathematical
>structure could be built up in which the current alpha is not relevant,
>and is replaced by a much more direct relationship with hbar.  That does
>not necessarily mean that such a mathematical construct would "explain"
>the actual value of alpha.

It would, actually.  As I alluded to above, coupling constants like
the electric charge (and therefore alpha, which is just another way
of expressing it) change with the energy scale at which event happen.
At higher energies alpha gets bigger than 1/137.  Now, if you had a
theory in which alpha were equal to 1/2 at some scale (which is
really what you're describing) the theory could be used in conjunction
with what are called renormalization group techniques to "run" alpha
down to low energies.  The hope is that it would go to 1/137.  If
it did, that would be very impressive, since you'd then have an
explanation for the electron charge.  If it didn't, that would
falsify the theory.

I don't think anyone has yet tried to do something like this.
 
-- 
Matt McIrvin, Cambridge, Massachusetts, USA