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[quote="thray"]Jay,

I think this is profound.

"It is intriguing to see that the non-linear relativistic effects emerging from what is
effectively the recursive relationship Aσ = φ0 (uσ ± (q / m) Aσ ), see (9.1), appear to be connected
with the anomalous magnetic moment. This raises the question for future study, whether the anomalous magnetic moments might be precisely understood, to all orders, as simply being the non-linear consequence of relativistic motion combined with strong electromagnetic interactions."

Nonlinear feedback may have the power to subsume quantum dynamics across scales, leading to metastability.

Best regards,
Tom[/quote]

Thanks Tom. I have been working for the last couple of weeks on the geodesic deviation and the tidal forces to establish that I have handling the spacetime curvature correctly i relation to the EM time dilation. The paper is still in progress and has grown to 25 sections and over 100 pages. I do plan to post another interim draft in the near future so my friends here at SPF can keep track of how things are developing and be the first to see these results. Jay

[quote="mok-kong shen"]I am not a physicist but engineer. In engineering non-linearity is ubiquitous and linearity is an idealization to simplify computations, e.g. the Hookes's Law. Years ago I asked in sci.physics whether Maxwell's equations should similarly take in non-linear terms but did't get responses of the genre I had expected.[/quote]
Yes, mok-kong, it is noteworthy that for electrodynamics only the linear weak field effects are known but the non-linear effects of extremely strong fields are not known. I am intending to change that state of affairs with this paper. Jay

Jay,

I think this is profound.

"It is intriguing to see that the non-linear relativistic effects emerging from what is
effectively the recursive relationship Aσ = φ0 (uσ ± (q / m) Aσ ), see (9.1), appear to be connected
with the anomalous magnetic moment. This raises the question for future study, whether the anomalous magnetic moments might be precisely understood, to all orders, as simply being the non-linear consequence of relativistic motion combined with strong electromagnetic interactions."

Nonlinear feedback may have the power to subsume quantum dynamics across scales, leading to metastability.

Best regards,
Tom

I am not a physicist but engineer. In engineering non-linearity is ubiquitous and linearity is an idealization to simplify computations, e.g. the Hookes's Law. Years ago I asked in sci.physics whether Maxwell's equations should similarly take in non-linear terms but did't get responses of the genre I had expected.

I woke up in the middle of the night yesterday, realizing that the section 8 I wrote yesterday introduced non-linear features into the electromagnetic interaction. So I got up, went to the computer for an hour, did the calculations, and realized that these interactions seem to account for the anomalous magnetic moments, and may provide a way to understand these to all orders out to infinity. I just added this as a new section 9, at the link below:

https://jayryablon.files.wordpress.com/2016/01/lorentz-force-geodesics-2-5-spf2.pdf

Jay

I just added a new section 8 tonight, and posted an updated draft at:

https://jayryablon.files.wordpress.com/2016/01/lorentz-force-geodesics-2-5-spf.pdf

This new section 8 completes the formal theoretical development (aside from my adding Kaluza-Klein more as an information item than part of the theory). It is important because it further details the mechanics of how I am properly fitting all of the details together, and answers some further comments that E. Weinberg sent me privately not as part of the review of the paper that once you have a gauge field, only the canonical velocity [tex]\pi^\mu=mu^\mu[/tex] is equal to mass times velocity, and not the usual [tex]p^\mu=mu^\mu[/tex]. He is wrong about this, as is everyone else who has been doing it this way for decades, which is why nobody could ever derive the Lorentz force in four dimensions from a variation until now.

Using Einstein's adage about pulling the covers over one's head only to expose one's feet, section 8 completes the proof that even though I am pulling up the covers to include the Lorentz force by using [tex]p^\mu=mu^\mu[/tex] even when there are gauge fields and charges, I am not exposing my feet by there being something somewhere else that becomes empirically wrong as a result.

You may think of section 8 as the special theory of relativity for electrodynamics, in the sense that it deals with all of the motions consistently with the variational derivation of the Lorentz force and consistently with all else that is known.

Jay

Dear friends:

I have made very substantial progress with the paper I spoke about at http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=242#p6221, and have posted a preview draft for my SPF friends at:

https://jayryablon.files.wordpress.com/2016/01/lorentz-force-geodesics-2-4-spf.pdf

You may recall that at http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=239#p6198 I reported the January 7 rejection by PRD, which I repeat here:

[quote="PRD"]The spacetime metric should not depend on the nature of the test particles moving within the spacetime. Because various types of particles have both different electric charges and different charge to mass ratios, the metric you propose in Eq. (2.1) would have to depend on the particular type of test particle whose geodesic was being determined, and could not be a property of the background spacetime and electromagnetic fields.

If instead you want to view this simply as an algorithm for obtaining the equations of motion of a test particle, then the manuscript should be directed to a journal of mathematical physics.[/quote]

This rejection is thoroughly addressed in section 7 of this draft at https://jayryablon.files.wordpress.com/2016/01/lorentz-force-geodesics-2-4-spf.pdf.

Best to all,

Jay