Another argument that time-advanced fields cause opposite forces

I put an update of my paper on Researchgate that has a couple of changes compared to the arxiv v14 version from a couple of days ago.

The most important bit is an additional argument for why the sign of the Lorentz force must invert when an advanced EM field acts on a charge, as viewed in the ordinary forward-time reference frame. The argument in v14 is based on Wheeler-Feynman absorber theory, and is slightly complicated.  A more direct argument based on essentially the same equations is that when two charges are interacting electromagnetically, the interacting part of the retarded field of one charge is the interacting part of the advanced field of  the other charge.  If the field is regarded as retarded, then standard Maxwell-Lorentz electrodynamics applies and so everything is completely defined about the retarded description of the interaction. Also, the form of the advanced field is completely determined in standard theory.  Since the retarded or advanced descriptions are really two different descriptions of the same interaction, they need to be consistent. The result I obtained is that the Lorentz force must be sign inverted in the advanced interaction if the two descriptions are to agree.

I am now planning on using the stuff in section II of the linked paper to make a new, shorter, paper and submit it maybe to a Physical Review journal, maybe as a comment on Schild's paper that seems to have assumed the usual Lorentz force for the advanced force.  (This is necessary if the Coulomb force is to be preserved in a time-symmetric interaction, but in my paper, the magnetic interaction substitutes for Coulomb binding, and so a Coulomb force is redundant for atom formation.) 

I also fixed a couple of inconsequential errors.  Equation (29) of arxiv v14 is correct on the third line but the first two were not exactly right.  It was a copy of another similar equation that didn't get fully edited for v14.  It's Equation (30) in the today (28 June) version.

The other change is to Eq. (48) of v14 (Eq (50) of June 28) and onward, where I hadn't yet gotten around to accounting for the sign change on the advanced part of the time-symmetric magnetic interaction.  It doesn't make any significant difference, though, as adding or subtracting two sinusoids is only ultimately a phase difference.