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.

Status Report and a Hypothesis about Why the Electron g-factor is 2

After months of feeling stuck and confused, I have finally been making real progress towards getting my paper on the origin of the magnetic force revised so that I can re-submit to a journal.  I saw a different way of going about things, compared to how I was doing it previously, and it really seems to have paid off with new insights.

One new insight is that the force I've been investigating for the last 4 years, the anti-Coriolis force due to Thomas precession of the rest frame of a field-source charged particle as observed from an inertial frame, is not the known magnetic force.  The most obvious reason it cannot be the magnetic force is that it vanishes when there is no acceleration of the source particle, whereas the magnetic force needs only a translating, non-accelerating charge to set up a magnetic field that can act on a second translating charge.  A second problem is that the force (as described in my paper) has a mass ratio factor, of the ratio of the mass of the particle being acted on to that of the field-source particle, that is not seen in Maxwell-Lorentz electrodynamics.  However, due to the fact that most electrodynamical observations are based on electron currents interacting with other electron currents, so that the mass ratio factor would be unity,  I was ignoring this problem for the time being.  Happily, though, I now believe I have a new understanding of how the magnetic force can arise kinematically as a consequence of Thomas precession, and as an anti-Coriolis force, that does not have these difficulties. 

The way around these aforementioned difficulties is to recognize that even if the field-source particle is non-accelerating, because of assumed essentially infinite mass or other constraint (such as being confined to an electrically-neutral wire),  its rest frame will undergo Thomas precession from the point of view of a test particle that's being accelerated toward the field-source particle by Coulomb attraction.  A physicist-observer in the rest frame of the test particle will notice that although the source particle rest frame is rotating, there is apparently no Coriolis force acting on the test particle in the source particle rest frame, and so deduce that there must be an anti-Coriolis force acting on the test particle there.  In this case, however, the numerator mass factor needed in the anti-Coriolis force is cancelled by the denominator mass factor of the same particle acceleration that induces the Thomas precession of the source-particle rest frame.  This obtains a magnetic force that agrees with observation in not involving a mass ratio between the field-source and test particles, nor an acceleration of the source particle with respect to an inertial reference frame. 

I hope to be able to provide this description quantitatively fairly soon.  I will update the paper on arxiv as soon as possible.  I may even do a retraction that acknowleges the known problems of the current version and outlines the new approach and findings, in a week or so, prior to posting the full revision.  In the meantime, though, I want to mention the new idea I am having about how all of this might relate to the known (so-called) "non-classical" gyromagnetic ratio of the electron.  It is of course a well-established fact that the electron produces intrinsic magnetic moment very close to twice as effectively as expected from classical electrodynamics, given its intrinsic angular momentum and charge-to-mass ratio, and assuming it has no complex structure.  The idea is, this other force that I've been studying that is the anti-Coriolis force due to Thomas precession of a field-source rest frame when the field-source particle is accelerating under Coulomb attraction or repulsion to the test particle, and a relativistic-kinematics necessity just as is the magnetic force, will effectively double the magnetic field strength for an electron that is generating magnetic moment, at least for one model of the electron spin,.  (In the zitterbewegubg model, the electron spin is a consequence of a relativistic circularatory motion of the point charge electron, with radius of the motion equal to the electron Compton wavelength.)  Thus the g-factor of two is to be expected, at least according to this model, which I have found compelling for other reasons.

Why There Can Be No Rotational Inertial Forces in Thomas Precessing Reference Frames

There is a simple and compelling argument for why the Thomas precession (TP) does not give rise to rotational inertial forces such as the centrifugal, Coriolis, or Euler forces, for hypothetical observers or systems that are undergoing TP.  There can be no forces of rotational inertia in such reference frames because the rate if any of TP is entirely observer dependent.  An inertial frame observer sees  TP of a gyroscope only if the gyroscope is simultaneously translating and accelerating transversely (i.e., crosswise) to the relative translation.  The amount of TP, that is, its angular velocity or rate of precession, is then readily calculated as proportional to the vector cross product of the gyroscope's relative translational velocity and acceleration. Thus, because the TP is calculated by the external, inertial frame, observer and depends entirely on the relative translation and acceleration, it is not uniquely defined from the point of view of an observer co-moving with the gyroscope.  Other observers in inertial reference frames moving at different velocities relative to gyroscope observe a different rate of TP of the gyroscope.  Indeed, from the point of view of an observer moving with the gyroscope, there is no TP of the gyroscope at all, since the relative translation and acceleration both vanish.  Therefore the co-moving observer cannot experience rotational inertial effects such as the centrifugal or Coriolis pseudoforces.

It is a very short step from making this observation to understanding the origin of the magnetic force, and probably the strong and weak forces as well. 

A sign error in my arxiv paper

I just found a sign error in my latest arxiv version (v3) of my paper:http://arxiv.org/abs/1108.4343v3. The second sign from the right on Eq. (20) is wrong.  The gamma^2 factor in the denominator of the first term on the right of equation of Eq 21 has to move to the numerator. Also then the equation is an approximation but still good to order (v/c)^2, which is all it ever was good to, at best.

My philosophy is: finding errors is  always a good thing, especially when you can find them yourself.

Sorry for letting it slip through.

I was actually looking for an error, because things were not making sense as it was.  With this correction, and with what follows it but is unposted so far, I hope to be able to show soon that the magnetic force between two particles of equal mass can be derived exactly and generally from an assumption of no pseudoforces in Thomas-precessing particle rest frames. 

As version 3 of the paper correctly shows, the complete magnetic force is present in the anti-Coriolis force of the Thomas precession, but there are extra terms as well.  These originate because the velocity in a particle rest frame is relative to the particle, while the magnetic force is proportional to the (other) particle velocity in the inertial frame.  This leads to an additional vector triple product term (the last term in the right of Eq. (19)) which then can be split into a sum of two vector terms with dot-product factors (Eq. (20)).  One of them  contributes a gamma-squared factor (that now has to move to the numerator but can still be subsumed into the full relativistic electrodynamic description, I think)  and the other vanishes in the circular orbit case (only).  So, if the magnetic force is to result exactly with no leftover terms, something has to cancel that leftover term, or it must get subsumed somehow into the proper relativistic electrodynamic descrption of the electromagnetic two-body problem in an inertial frame.  This one I think will get cancelled by the anti-Euler force, in the case of non-circular motion.   I got a suitable term from the anti-Euler force, but it was the wrong sign to cancel, hence I was hunting for a sign error. 

I may be days away from having everything worked out and ready to get into shape for re-submission.  This will take at least a month but perhaps I can post something sooner in rough form if I get everything to work out, and then do a final clean-up prior to submission. 

No evidence of ethics in Romney's behavior

Mitt Romney says, he paid the legally-required amount of taxes, and we wouldn't want a president who paid more than the legal amount, would we?

Personally I'd be quite comfortable with a president who figured his taxes simply and without inventing heroic dodges to avoid paying his fair share, like whatever he did to accumulate tens of millions in his IRA, when the yearly contribution restrictions make it nearly impossible. 

Romney apparently believes only a fool would fail to exploit every loophole.  It does not even occur to him there are more noble ways of thinking.

This modus operandi is well evidenced in his business dealings as described here: http://www.bloomberg.com/news/2012-07-15/romney-s-bain-yielded-private-gains-socialized-losses.html . 

There is no trace of introspection or social concern in this man.  We certainly don't want him for our President.

New version of my paper explaining the origin of the magnetic force

Last week I posted a version of my paper linking the magnetic and strong forces with the Thomas precession on arxiv here.

The revision was needed to correct several errors and misunderstandings, as I previously described.

The new version doesn't attempt to extend the analysis, it just corrects the recognized errors and reflects my better current understanding.  It contains an Errata section identifying the corrections.

I'm still working on extending the analysis beyond the bound, circular orbit case.   Any case other than this must invoke an anti-Euler force as well as becoming generally more relativistic in nature.  The circular orbit case is greatly simplified by the fact that the force is perpendicular to the velocity, and so the relativistic gamma (or Lorentz) factor doesn't come much into play.  Also, the Euler force doesn't come into play since the angular velocity of the Thomas precession is constant.  So, relaxing the restriction to circular motion makes the analysis much more complicated, but it should also become much more persuasive if it all comes together in a consistent way, as I believe it must.

Also, I'm still uncertain whether an anti-Euler force implies the existence of hitherto unknown forces, or merely leads to previously-known forces such as the magnetic and weak forces.  As I  mentioned a couple of posts ago, it gives rise to force terms at order (v/c)^2 that are of course at the same order as the the magnetic force.  But, the full relativistic treatment of the classical two-body electromagnetic problem for (spinless) charged particles already has a lot of terms at this order that are not directly recognizable as magnetic force related terms.  So, the anti-Euler force terms could simply correspond to terms already present in inertial-frame electrodynamics.  Showing this to be the case will make the derivation quite persuasive, seems to me.  On the other hand, if there are new forces at the same order as the magnetic force, consistency with observations to date demands they would have to average to zero or be otherwise difficult to notice.  Perhaps if they were difficult to notice but gave a hint of where one might look for confirmation, that would be of interest.  However at the moment I'm optimistic that the anti-Euler force at order (v/c)^2 will simply be relatable to electrodynamics as it is already understood.  The anti-Euler effects at higher order in v/c however I think will have to correspond to either the weak or new forces.
   

I Haz Cites

One of them was expected and I posted about it previously (but see also here), but the other was completely unexpected.

Vladimir Hnizdo's paper, "Spin-orbit coupling and the conservation of angular momentum"  (http://arxiv.org/abs/1103.4092) has now been published in European Journal of Physics (subscription or payment required).  This paper cites two of my arxiv papers (0905.0927       and 0709.0319) and also acknowledges me as raising the issue the paper addresses.

The other citation is in a commissioned review article, "Resource Letter EM-1: Electromagnetic Momentum," (http://ajp.aapt.org/resource/1/ajpias/v80/i1/p7_s1) by David J. Griffiths, in American Journal of Physics.  (There is apparently no arxiv e-print but the references may be found here.  The citation of my paper is also noted here.) It appeared in January but I just found out about it last week.  My paper is cited as one of three examples of ongoing research related to "hidden" momentum.  My arxiv paper is in response to one of the other two articles, that was published in American Journal of Physics, that I commented on, and as I posted about previously, my comment was published in the journal, followed by a response by the original paper authors that seemed to negate my comment. Then, when I wrote a further response, it was rejected.

I don't mean to fault American Journal of Physics particularly for not publishing my paper that is now being cited by their own comissioned review article, as I understand they have many many submissions and as a pedagogical journal have to be averse to controversy.  However I am very pleased that this paper is being cited and by such a distinguished author.  It is especially nice because I had essentially given up on that paper and had no further plans to submit it anywhere, and yet it took a lot of time to do the work and write and I thought it obtained an interesting result.  Now it seems reasonable to think I was not the only one to find the results interesting (and in fairness, two of three of the referees were positive about it). 

I do hope and even expect that eventually I will be getting my work published in mainstream peer-reviewed journals, but until it is, getting cited in mainstream journals is a pretty good substitute.  If it was a choice to get published but not cited, versus not published but cited by such distinguished authors, I would have to choose the latter.