My colleague and co-moderator Peter Enders over at SPF asked for some clarifications on the 1984 paper. You can read his queries, and my reply, over at:

http://groups.google.com/group/sci.physics.foundations/browse_frm/thread/d6676287ecd56235/73757d374d47b064#73757d374d47b064.

I have tried to summarize what I now see the main points of this paper to be, 23 years later. You may view this 2007 summary, which is only three pages long, at the link below:

A 2007 Update of the 1984 Paper

Jay.

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Okay, I’m beginning to understand this a little better. The point is that it is the potentials that break the duality between electric and magnetic fields. In QED, the photon potential is the important object, not the fields, so to me this is another way of saying that quantum mechanics breaks the duality between electricity and magnetism. Which is another way of saying that electric charge is a quantum number, but magnetic charge is not.

I’ve been having fun on WordPress. I’m maybe 2 blog posts away from completing my blog derivation of the neutrino mass equation. In QED, you usually end up with infinities when you compute corrections to the bare photon propagator. However, it turns out that there is a simplified version of QED that is exact to all orders of perturbation theory. One simply reduces the quantum states to qubits. When one wishes to describe a preon structure for point particles, this is a very natural thing to do. And it is effective because it allows you to exactly describe bound states. (And I like it cause it avoids all infinities.) When you work in this sort of QED / QFT, all the nasty calculus you’ve been suffering with (I suppose) becomes nasty algebra I’ve been suffering with.

Comment by carlbrannen — July 28, 2007 @ 12:06 pm |

Carl, you said “The point is that it is the potentials that break the duality between electric and magnetic fields. In QED, the photon potential is the important object, not the fields, so to me this is another way of saying that quantum mechanics breaks the duality between electricity and magnetism.” That is exactly so.

In the past day or so since writing this, I have started to think very carefully about how to formulate quantum field theory without a vector potential. Equation (9) for the electric source current, in the 2007 update above, is independent of the potential; it is the zeroing of the magnetic charge which requires the potential. Stated differently, the potential serves, at bottom, to zero the magnetic charge and break the duality symmetry, as you have observed. The electric charge is unaffected. Which raises the question:

Can one break the duality symmetry WITHOUT using a potential, such that the magnetic charge is still driven to zero? If so (and I have some ideas based on my prior work at http://arxiv.org/abs/hep-ph/0508257), then one may be able to arrive at all of the usual results of quantum field theory, but without ever writing down a potential A^u. This may then circumvent the redundancy inherent in the potential, and all the gauge fixing and other stuff that one needs to do when one does use a potential.

Jay.

Comment by Jay R. Yablon — July 28, 2007 @ 6:25 pm |

Jay,

After a gap of a few days, I now realize what is going on around here, as far as the way I look at things. At the foundational level, I don’t think that there are any potentials. To me, a potential is a convenient method to approximate a complicated interaction. The complicated interaction comes from some sort of gauge boson exchange.

So for the difference between magnetic and electric potentials, I would look to the QFT of the interaction, that is, QED.

Since I look at things from a QFT and elementary particle vantage point, there is a bunch of things that happen in E&M that don’t bother me very much. This includes not just the classical E&M potential stuff, but also the QM potential paradoxes, like the Aharonov-Bohm effect. To me, the A-B effect is just the result of taking a huge number of photon exchanges in a QFT, approximating them with a classical magnetic field, and then being surprised when the approximation is not exact.

Carl

Comment by carlbrannen — August 1, 2007 @ 5:00 am |

Hi again Carl,

Before I head out for a vacation week, I wanted to post some further thoughts about this, which are, indeed, to develop QED using only the field strength tensor F^uv, without relying on a potential A^u. This is contained in the file below:

https://jayryablon.files.wordpress.com/2007/08/qed-without-potentials.pdf

I would appreciate your thoughts, and those of anyone else who is interested, about this line of inquiry.

Have a good week!

Jay

Comment by Jay R. Yablon — August 5, 2007 @ 6:07 am |

Perhaps we agree that the problem with physics theories that involve gauges is that there is only one reality, so there should only be one description of it. The alternate gauges are fakes. Only one of them can be correct, at most.

Perhaps your logic for avoiding gauges is different. If you agree with this, then you have a bit of a problem because you can say the exact same thing about the preferred reference frames of relativity. (And I do.)

This was what dragged me back into physics. A few years ago I realized that I could rewrite the special theory of relativity onto a modified geometry and get all the usual results but with all matter traveling at speed c. I thought it was brilliant and original, but there were a bunch of people already working on it.

Anyway, getting back to gauges, if you agree that the reference frames of SR are a sort of gauge choice, (and there is a wonderful paper by the Cambridge geometry group deriving GR from a gauge principle), then this says that the gauge principles need to be written in a geometric language similar to special relativity.

Following up this train of logic, you might consider what happens to the electric and magnetic fields when one performs a change to a new reference frame. This shows that the electric and magnetic fields themselves are already subject to a choice that looks very much like a gauge choice.

Comment by carlbrannen — August 5, 2007 @ 9:11 am |