## Wednesday, September 24, 2014

### Correction

A few days ago I realized I'd overlooked a different way out of the problem that time-advanced magnetic fields want to reverse sign compared to retarded ones, and so causing magnetic effects to cancel out in the time-symmetric picture. The cancellation doesn't happen because the sign on the unit vector from the source to field point, that is crossed onto the electric field to obtain the magnetic field, also changes sign in going from retardation to advancement.  That is, in the retarded case we have B = n x E, but in the advanced case this becomes  B = -n x E.   The unit vector n here changes sign because it originates as the gradient of the retarded or advanced time, so the sign change that changes retardation to advancement applies directly to it.

This means the problem I've been working to overcome for the last eight or ten months does not even exist.  In particular, the cancellation of the strong magnetic force that I was getting in the time symmetric picture does not occur. So, it can account for preon binding (for charged preons, at least) just fine. What I have been saying recently, that Lorentz covariance requires magnetic forces be preserved in the time-symmetric picture, if there is one, is perfectly true, but it is also completely consistent with electrodynamics and time-symmetric electrodynamics under the usual assumption that the retarded and advanced solutions are summed rather than differenced.  Writing it up for publication forced me to realize this, because when I went through, as a simple demonstration of the problem, calculating the magnetic moment from a static current loop from the retarded potentials (see, e.g., Landau and Lifshitz  Eq. 66.2) I discovered that it absolutely does not change sign when going over to the advanced case.

Now, everything is better except the idea that the electron g factor of (about) 2 can be explained as the difference between retarded only and time symmetric electrodynamics.  I still think this is a very attractive idea, but the story isn't as compelling because it isn't true as I said that in the conventional time-symmetric picture the g factor would be zero, i.e., that the electron magnetic moment would vanish.  In the usual picture (attributable to Dirac 1938) the time symmetric field is the mean of the retarded and advanced fields, which leads to a g-factor of one.

Maybe I should give up my obsession with the electron g factor, now that I am routinely thinking of the electron as a composite particle.  If it has a positive charge part with opposite but smaller spin, doesn't that give a g factor larger than unity?  Maybe g factor two is easy to get in the preon model.  I am still used to thinking of an electron as a structureless object so this kind of thinking is not natural.  Maybe g-factor two is simply a confirmation that it's a composite particle.

Later I think I will look more at the g factor of a composite electron, but for right now I'm trying to complete something entirely new to put on arxiv and hopefully soon after submit to a journal.  Hopefully I will upload it to arxiv within a day or two.   Before that happens, I am also planning on revising my kinematics arxiv paper to remove the new section I just added a few weeks ago.  Probably I will do that later today.  I can't let it stay up there long knowing it is dead wrong.