A correction, and resolution of a problem

In the current version of my paper on arxiv, http://arxiv.org/abs/1108.4343v5, as well as version 4, I argue that the strength of atomic (at least) spin-orbit coupling should be doubled compared to what is predicted according to Maxwellian electromagnetism, and apart from the electron g-factor being about twice the classically expected value.  This caused me to suspect that the doubling of the g-factor could be a mistaken interpretation of the increased strength of the magnetic interaction expected when both interacting particles are free to accelerate. However, as I observe in version 5, the g-factor being closer to one than two is directly contradicted by highly precise "g-minus" two experiments that measure the electron (and also muon) g-factor to sufficient precision to measure the g-factor anomaly (that is, the small deviation predicted by quantum electrodynamics of the  g-factor from the Dirac value of exacctly 2).   Because these experiments utilize strong magnetic fields generated by electron currents in neutral wires, there is no doubing of the magnetic field strength expected according to the mechanism of my paper.

The resolution to this problem is that I was simply not paying attention to what my own theory is saying.  In hydrogen or other atoms, the nucleus is much heavier than the elecron and so the acceleration of the nucleus is much smaller than the acceleration of electron, and the additional magnetic interaction strength is reduced accordingly.  I had been thinking of the situation as seen from the electron rest frame, where the proton (in hydrogen, say) is relatively accelerating with the  same acceleration as that of the electron seen from an inertial frame, and thinking that this would cause a doubling, but on further reflection it is now clear (and should have been obvious) to me that the proton acceleration seen from the electron rest frame is only just how the usual magnetic field arises and can't cause a doubling.  In order for an actual doubling to occur, it would be necessary that the proton acceleration as seen from inertial frames be of the same magnitude as the electron acceleration seen from inertial frames. 

I don't know why it took so long for this to become obvious to me but a couple of days ago it did and now I feel foolish.

I'll be updating my paper on arxiv to cover this and some other items including what I have already posted about regarding what is the expected form of the anti-centrifugal force of the Thomas precession.  It will probably be within a couple of weeks.

In the meantime, I can mention that based on this proper understanding, it is possible to say what should be the expected effect on the spin-orbit coupling strength due to the effect of both interaction particles being free to accelerate. In positronium, the spin-orbit coupling strength should indeed be doubled compared to that expected according to pure Maxwellian electromagnetics.  I haven't done any research yet into whether anyone has ever tried to measure the spin-orbit coupling strength in positronium, but I suspect it would be difficult. In hydrogen, on the other hand, there will be an additional magnetic interaction strength equal to the ratio of the electron to the proton masses.  This is about one part in 1836 (if memory serves) and so it might be within the realm of possibility for measurement.   

An online discussion I'm having about my model of the magnetic force

It's here, but I re-opened it recently after a hiatus, since I recently figured a lot of things out I didn't previously understand, starting here.

I am "Eggs Ackley" there.  (Eggs Ackley is a cartoon character by R.  Crumb.)

A better demonstration of the similarity of the anticentrifugal force to the strong magnetic force

The current version of my paper ( 1108.4343v5 ), like previous versions 2-4, has a section that attempts to characterize the anticentrifugal force of the Thomas precession in the highly relativistic limit, and to show that it can, like the strong force, overcome Coulomb repulsion as needed to bind quarks into nucleons.  At the time it was written, over a year ago, and until just a couple of weeks ago, I was thinking that the anticentrifugal force was not present in Maxwell-Lorentz electrodynamics, and said or implied as much in the earlier versions.  I didn't elaborate on this much, but I was thinking that the Maxwell fields didn't contain the strong force, and so although I stated or implied the Lorentz force was incomplete, I didn't expect that strong force could be added to electrodynamics by a modification of the Lorentz force law without an accompanying modification of the electromagnetic field.  Now of course I think this was a mistaken belief, and that the strong force is already apparently present in Maxwell-Lorentz electrodynamics as the magnetic force between highly relativistic mutually-Coulomb-accelerating charges.  This has resulted in an explicit form (if only approximate so far, due to my neglect so far of retardation effects, which cannot be considered insignificant here) of the strong magnetic force, which can be compared with my earlier characterization.  This comparison has forced me to realize the previous characterization is at best confusing and less than clear.

The problem of my initial characterization of the anticentrifugal force, which is in section V of the version at the link above, is that it obtains a force law that is inversely proportional to only the first power of the interparticle separation.  The Coulomb repulsion of course is inversely proportional to the square of the separation, so in order to overcome it, the anticentrifugal force should be inverse to a higher power of separation than two.  The strong magnetic force obtained in section VI is inverse to the third power of separtion, and so meets this expectation.  On the other hand, when I equated the anticentrifugal force magnitude with that of Coulomb repulsion, I got essentially the same formula that I got by equating the Coulomb repulsion with the strong magnetic force (and immediately declared success).  Naturally when I examined this situation further I was perplexed and at least a little disturbed by it.  I'm still in the process of sorting this out, but I think there's probably a straightforward explanation, that there's a hidden dependence on separation in the assumption of near light-like particle velocities, that can contribute additional inverse dependence on separation.  However, while looking into this, I realized there's an easier and I think more straightforward way to see the direct correspondence between the anticentrifugal force and the strong magnetic force.  I put this into a new draft version of my paper, but I don't want to do another update on arxiv just yet, pending addressing the issue of retardation, so I think I will copy it in here instead, for now.

 

The above equation  (303), derived as the anticentrifugal force, is essentially the same as Eq. (34) of my version 5 at the link above, that is derived from the Lienard-Wiechert potentials, if the test and source particles are of equal mass, apart from some gamma factors that still need to be sorted out carefully.   This shows more explicitly than the current arxiv version how the strong magnetic force is the embodiment of the anticentrifugal force of the Thomas precession.



A. O. Barut

I want to mention that A. O. Barut argued that the strong force was plausibly related to or derivable from the magnetic force.  I have had this report for some time: Stable Particles as Building Blocks of Matter

Abstract:  Only absolutely stable indestructible particles can be truly elementary. A simple theory of matter based on the three constituents, proton, electron and neutrino (and their antiparticles), bound together by the ordinary magnetic forces is presented, which allows us to give an intuitive picture of all processes of high-energy physics, including strong and weak interactions, and make quantitative predictions.


Here is another I haven't downloaded exceptt for the free preview:

Derivation of strong and weak forces from magnetic interactions in quantum electrodynamics (QED)


Abstract: The principles of magnetic interactions between stable particles are outlined and a simple theory of matter is discussed based on absolutely stable particles proton, electron and neutrino as constituents. Experimental tests are proposed.

The Magnetic Force as the Strong Force

It's been over a year since I proposed that the anticentrifugal force of the Thomas precession might be identified with the strong force.  But, I thought it was something that would have to be added to electrodynamics, not already part of it.  Last week though I started thinking seriously that it needed to be in electrodynamics already, if the latter is truly Lorentz covariant, so over the weekend I looked for it and tentatively I seem to have found it.  At least, neglecting propagation delay effects (which cannot be considered insignificant so addressing them is a next step) I can show how the magnetic force between two charged particles can become attractive independent of the relative polarties of the particles  and so potentially overcome electrostatic repulsion between like charges.  When I solved for the particle separation where this would happen, I got the same result as for the anticentrifugal force.  This is in section VI of the new version of my paper, which is now publicly viewable here: http://arxiv.org/abs/1108.4343v5 .


This has developed quite abruptly and somewhat unexpectedly.  If it's meaningful, I should be able to find the anti-Euler force and another magnetic-like anti-Coriolis force for an accelerating field-source particle, so I will be looking for those.  I've looked previously for physically significant atomic-scale effects of the acceleration fields, though, with no success.  This time I'll be trying more persistently.

A little more about the electron g factor

I spent a little bit of time reading about the electron "g minus 2" experiments that are referred to in Jackson's Chapter 11, that are based on the BMT or Thomas's equation of motion for the spin.  These do appear to contradict my hypothesis that the electron g-factor being (approximately) 2 is a misunderstanding due to a failure to recognize that the magnetic interaction strength doubles when it is between two equal-mass free particles, compared to that given by Maxwell-Lorentz electrodynamics.  When I make my next revision to my paper I will at least mention this fact.  I may decide to de-emphasize the hypothesis that the doublling of the magnetic interaction strength can explain the electron non-unity g-factor, by removing mention of it from the abstract.

When I finish obtaining the main thrust of the paper, I will look into the matter further.  The problem here is (and I already mention this in the revision I posted on arxiv in January), that if it doesn't account for doubling the g-factor compared to classical expectations, the doubling I found would be an additional and unneeded factor of two. 

If this had been known in 1926 then there would have been no motivation for postulating the electron must have a non-unity g-factor, but now that the g-factor has been measured as being close to 2, it must be reconciled with the doubling of the magnetic interaction strength by other considerations.  There is almost room for such a reconcilation, since Bucher has shown that we should not expect the classical analog of the atomic L=1 quantum state to be a circular orbit.  This means that the Sommerfeld explanation of the anomalous fine structure could be accounting for the extra factor of two.  However, this would also require invoking the Thomas explanation for the (spin-orbit coupling) anomaly, which I believe is not correct.

I just want to register some awareness of the issue.  Right now I am focused on getting the fully relativistic version of my paper finished and reposted on arxiv, and then submitted to a journal.  It is coming along pretty well and perhaps I will be able to repost it within a month or so, or even less.

New Version of My Paper is Posted

It's uploaded but won't be publicly viewable until midnight Wednesday (23 Jan), at the earliest.  I'll try to either resist any immediate revisions or get them in before the point when it will delay the process.   When the link goes to version 4, with a 2013 date, that will be it.

http://arxiv.org/abs/1108.4343


I had hoped to have more relativity in this version, but I'm having to hold off on the more rigorous argument, for the moment.  I hope it will come along fairly quickly, and then I will do an arxiv update again and submit to a journal.  I don't plan to submit this one.  Apart from it probably needing a lot of writing improvements, I have at least one major section in work to add, that I hope will make the entire thing much more convincing.

The specific argument that the magnetic force is the anti-Coriolis force predicted for the lab frame by the test-particle rest frame obserever, who sees the lab frame Thomas precessing relative to the source particle rest frame (where the interaction is purely Coulombic) , is only a couple of days old at this point.  Previous arguments have always resulted in additional cross-product terms that I tried to subsume into the relativistic electrodynamics, with limited if any success.  This new argument yields explicitly just the magnetic force.  I also used to think (and say) that the anti-Euler force had to be part of the magnetic force, and was involved in the hypothesized subsumation of the extra terms.  That now seems unrealistic, and instead I now think the anti-Euler force part at order v^2/c^2 is a new force.  I guess that generally the anti-Euler force at higher order in v/c corresponds to the weak force, but I think that the piece at order v^2/c^2 may be overlooked until now.  The form of it is explicitly provided in this new version.