Sunday, August 10, 2014

Why the electron g-factor is 2

Today I realized (I think) that if electrodynamics is time-symmetric, and if the magnetic force does not flip its sign for the advanced magnetic forces compared to retarded magnetic forces, then this will naturally double the strength of the magnetic forces at scales where the retarded and advanced interactions are experienced close to in phase.  So the electron magnetic field, if produced by moving charge, will be twice what it would be for retarded only forces.  So perhaps the electron g-factor being (about) 2 can be taken as confirmation that electrodynamics is time-symmetric.

After mulling it over for a while today, I decided to do a quick update to my arxiv paper to include this observation. I added a new section V that consists of 3 paragraphs with no equations. It will post tomorrow (as v8) if I don't change it further and reset the clock.  (I also corrected Eq. (8), which did not affect any subsequent results.  It may become relevant in the next update (v9) however.  I have a lot of material towards a new version beyond v7/v8, but it was inconclusive until the new ideas of the last few weeks, which tentatively seem to be panning out nicely.  I have only been working on it again for the last few days, though.  Prior to that I was unusually tied up for several weeks with my engineering job on a hot project.)

Another thing I want to mention, that I was being coy about in my last post, is how it might be possible to have electrical velocity fields invert sign between retardation and advancement, and still have apparent electrostatic forces between (apparently) stationary charges.  The way it might possible is if what we take as electrostatic electric fields and forces are actually time averages of  electric acceleration fields.  Martin Rivas (citation will be in the new posted version, and is in some of the earlier versions already) has already shown how if the electron is modeled as a circulating point charge moving at the speed of light (and it will still be true for asymptotically close to the speed of light), then the time-averaged acceleration field is Coulomb-like by several Compton radii away (when the radius of the circular motion is the Compton wavelength).  Also, for the ultra-relativistic charge, the velocity field collapses to a point and so doesn't contribute to the average Coulomb-like field.

I spent today trying to modify Rivas' calculation to see if I can get a similar result in spite of switching the sign of the advanced forces.  It seems intuitively that it couldn't but I am encouraged, as far as I got today. It doesn't make it vanish identically, as my intuition predicts it should have.  This is a very preliminary observation, so maybe it will fall apart, but it shouldn't take long to get an answer one way or the other.  I have another reason to be optimistic, though, because I also tried yesterday adding sign-reversed (compared to the usual) advanced fields into my attempted derivation of anti-Euler forces from the velocity magnetic field terms, and now it does seem to be emerging.  I have spent six long months trying to get this with no prior success, so it seems very encouraging. This is also only a preliminary observation that could evaporate.  I still have a lot of work to do before I can have something to submit to a journal, but I feel like I'm making serious progress again finally, after months of getting nowhere fast.