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.

I have submitted a corrected replacement for arXiv:0619.04446v13

As I mentioned in my previous post, https://arxiv.org/abs/1609.04446v13 has a fatal sign error in Section IIB that seems to negate the assertion of the paper that time-advanced electromagnetic fields cause forces that are of opposite sign to the Lorentz force in retarded fields.  However, I believe I have recovered the original assertion in spite of the sign error, and have uploaded a new version that explains how.  The new version won't post on arxiv until Tuesday morning, but I placed the arxiv submittal pdf on Academia https://www.academia.edu/36766974/Spin-Spin_Coupling_as_the_Origin_of_Atomic_Binding_revised_23_June_2019_arXiv_v14_ and ResearchGate. 

So, v13 had a sign error that caused a result that electrodynamics must be anti-symmetric under sign inversion rather than symmetric as is widely (correctly) believed.  (The new version, which will be v14 when it appears, has a corrected section IIB which obtains the correct result.)  After going through the corrections, and thinking about it for a couple of days, I realized that symmetry under time inversion is not the applicable condition to apply to the question of what is the sign of the Lorentz for a forward-time observer of a charge in an advanced EM field. Time-symmetry means that the Lorentz force is invariant to inversion of the time coordinate, but this only says the the retarded force in the forward time frame has to be identical with the advanced force in the time-reversed frame.  It doesn't say what the time-advanced force has to be in the forward-time frame, and nobody knows what the retarded force is in the time-reversed frame.  But, the sign of the advanced force in the forward time frame can be got at by looking at the phase of an advanced wave returning to an oscillating charge from a charge re-radiating due to the retarded field of the oscillating charge. Wheeler and Feynman first recognized that if the outgoing retarded wave is absorbed, then the advanced wave will cause an opposing force that can be equated with the radiation damping force.  What I did was consider a non-absorbing charge (with no damping applied) and show that it will create the opposing force if the Lorentz force is assumed for the advanced interaction.  This is a contradiction with known physics, so the advanced wave must cause a force that is opposite the retarded Lorentz force.

When this link https://arxiv.org/abs/1609.04446 says v14 it will be the revised version, but that won't be until at least Tuesday morning GMT. 

I am withdrawing arxiv:1609.04446v13

There is a sign error that invalidates section IIB of my paper https://arxiv.org/abs/1609.04446v13, "Spin-Spin Coupling as the Origin of Atomic Binding," and so it is retracted. The previous version, https://arxiv.org/abs/1609.04446v12, "Spin-Spin Interaction as Quantum Phase Measurement and the Mechanism of Atom Formation," did not have this section or problem and so still stands.

I noticed the error for the first time a couple of hours ago.

It will be a little while until I replace v13 with a new version that corrects the error.  I'm going to first spend some time trying to recover the claim of v13 that the Lorentz force must change sign in going from retarded to advanced electrodynamic forces. I am still convinced this has to be the case. It is the lesson of Bohm's theory. I have a line of reasoning which may provide a compelling argument in (I hope) fairly short order.  If it doesn't work out within a few weeks I will make a new version that formally retracts section IIB of v13 without replacing it with a new argument.

New Versions of Three of My Papers

In December I realized I didn't fully describe the zitterbewegung phase of the moving test particle in my Foundations of Physics paper that was published in 2016.  I treated it as pure time dilation, simply dividing time by the Lorentz factor, when I should have done it as a Lorentz transformation, which changes the division to a multiplication and adds an additional term that involves the position and momentum.  So I have made a revision and placed it on arxiv here.

The correction did not negate the conclusions of the paper as published, but it greatly improved the outcome of follow-on work I'd been doing. With the proper treatment of the test zitter particle phase, I was able to obtain for the first time that one factor of the modulation of the radial Coulomb-like magnetic force between zitter particles with aligned spins satisfies a partial differential equation that is quite similar to the time-independent Schroedinger equation.  Essentially, it differs only by factors of four on the potential energy and the energy eigenvalue.  These factors originate in the electron being a spin-half particle, and so it is something of a mystery how de Broglie's reasoning based on the photon led to a correct result. I was actually expecting the energy to be off by a factor of two based on the photon-electron spin difference and on my analysis of the photon as a composite particle, which gives the energy-frequency relation of half the usual. (I have also recently updated that paper, although it turned out to not be directly affected, see here.)

I was very happy to have finally gotten my follow-on to the FOOP paper to arrive at something close to the desired result, but also frustrated that it wasn't as I anticipated.  I spent several weeks staring at it and trying to find a mistake or way around it, but was getting nowhere.  Then, I happened to get an email from a journal requesting submissions that I was not familiar with, so I looked at their latest issue (which is open access) and saw a paper by Osiak that seemed interesting, so I downloaded it. Osiak derives (in part) that the mass-energy equivalency is properly E = mc^2/2 rather than E=mc^2 as  currently accepted.  His argument seemed plausible enough, and since the de Broglie and zitterbewegung frequencies both originate from the equivalency and the spin magnitude, I decided to try using it in my analysis instead of the usual.  It only took a little while to get that the Coulomb-like magnetic force modulation factor satisfies the time-independent Schroedinger equation based on the Osiak form. 

My updated follow-on to the FOOP paper that uses the corrected zitterbewegung phase for a moving particle and has two subsections (IV. d and e) using the Osiak mass-energy equivalency is here:     https://arxiv.org/abs/1609.04446v12.