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blutoski
27th July 2009, 09:18 AM
Title: "Einstein Wrong: A Documentary Film"

URL: http://www.einsteinwrong.com/main

Excerpt:Why is Einstein considered the genius of our time yet no one knows anything about him or his theory? Why don't we understand anything theoretical and astrophysicists say yet we give them billions of dollars to build experiments that don't better mankind?

Watch them as they take matters into their own hands and in the 100 year
celebration of Einstein's miracle year, find their own miracles along
the way.


blutoskitorial:
I can't help but notice that the production credits include people who have books promoting alternative physics in play. My impression is that this is half of a typical two-pronged sales strategy: invent a 'problem' and make sure you have a patent on the 'solution' (a la Wakefield).

technoextreme
27th July 2009, 09:23 AM
Uggg... I love how the FAQ completely botches up the concept that special relativity and general relativity are two separate concepts. And how the hell do you go about explaining away the .87 degree change in stars during a solar eclipse? And how the hell do you explain away special relativity when we can measure the time dilation? And I love how movie proponent is a supporter of a theory that we bloody dam well know is wrong. How the hell are you a supporter of autodynamics when the existence of the neutrino is true? I think I shall write an article about it on my blog. Yay blog.

wackyvorlon
27th July 2009, 11:11 AM
Of course, the Sudbury Neutrino Observatory is just a cover-up:) It would be very interesting to hear their explanation for the relativistic corrections that are required in order for GPS to work.

JHGRedekop
27th July 2009, 11:21 AM
I want to know where they get the idea that "no one knows anything about [Einstein] or his theory". There are few 20th century physicists as well biographied than Einstein, and even fewer theories as written about.

MattusMaximus
27th July 2009, 11:32 AM
Looks to me like the physics version of "Expelled" :rolleyes:

ben m
27th July 2009, 12:34 PM
Of course, the Sudbury Neutrino Observatory is just a cover-up:) It would be very interesting to hear their explanation for the relativistic corrections that are required in order for GPS to work.

GPS? They can't handle the math associated with a ball thrown from a moving car.

Wally
27th July 2009, 12:57 PM
GPS? They can't handle the math associated with a ball thrown from a moving car.

If Newtonian physics was good enough for Jesus, it's good enough for me!!!:duck:

Marduk
27th July 2009, 01:02 PM
If Newtonian physics was good enough for Jesus, it's good enough for me!!!:duck:

I thought he relied on Babylonian physics like the rest of the middle east
:D

lightfire22000
28th July 2009, 07:33 PM
I'm by no means a qualified theoretical physicist, and I can tell that this site is bogus.

jimtron
28th July 2009, 08:03 PM
I want to know where they get the idea that "no one knows anything about [Einstein] or his theory". There are few 20th century physicists as well biographied than Einstein, and even fewer theories as written about.

Yeah, check the Wikipedia article; nothing:
http://en.wikipedia.org/wiki/Albert_einstein

...oh wait, the page just finished loading...there are 141 footnotes.

Robster, FCD
28th July 2009, 08:06 PM
Looks to me like the physics version of "Expelled" :rolleyes:

Einstein caused the holocaust, and if kids learn physics, they will nuke the world. -- All delivered in a sleepy monotone.

linusrichard
28th July 2009, 08:30 PM
A non-scientific comment: it seems unlikely to me that a site that offered educated, substantive, scientific criticism of Einstein's theories would go under the name "einsteinwrong.com"

Maybe that's just me.

ETA: Ditto for the film.

Wowbagger
28th July 2009, 09:04 PM
Wow, this must be some really super, special, awesomely powerful theory... if the only way we can learn about it, is by watching this film! :rolleyes:

No paper citations, no summary of their replacement theories on the site, not even a mention of the new theory in the trailer! But, if she can bend fabric, and hug babies, it must be true!

vIQleS
28th July 2009, 09:35 PM
And plenty of Lord Privy Seals?

"The fabric [show image of some cloth] of the universe [image of milky way] is made up [image of some cosmetics]..."

Eggs Ackley
28th July 2009, 11:49 PM
I think the anti-relativists are almost certainly wrong, but there are or have been some very sophisticated ones, like Petr Beckmann and T. E. Phipps Jr. Beckmann was an electrical engineering professor and founded the anti-relativity journal Galilean Electrodynamics and wrote a very interesting book called Einstein Plus Two. Phipps is (I assume) the son of the T. E. Phipps who made (with Taylor) the first measurement of the magnetic moment of atomic hydrogen, published in 1927. This was an important measurement at the dawn of modern quantum theory. Phipps jr has a PhD in nuclear physics from Harvard (from a long time ago) so at least he's adequately credentialed. He has a couple of books out where he attempts to reformulate electrodynamics in an invariant rather than covariant fashion, which he traces back to Hertz.

One of Phipps' critiques of relativity is related to the effect known as the Thomas precession, which is demanded by Einsteinian relativity but is a very strange and paradoxical effect. The Thomas precession is the necessary rotation of a reference frame that is simultaneously translating and accelerating. I think the weirdness of it is not well appreciated by mainstream physics, but I give Phipps credit for noting it, and was quite surprised when I read his critique of it, because he was asking the same question I ask, which is, why doesn't it violate angular momentum conservation? He seems to in part have rejected relativity on this account. (I however have now accepted that mechanical angular momentum conservation is violated by Thomas precession.) Phipps argues there's no experimental evidence for it. However I think the magnetic force can be viewed as a consequence of it, as being the Coriolis force of the Thomas precession, and also certain features (at least) of quantum behavior, such as the precession of angular momentum even in the absence of an applied magnetic field, are simply a manifestation of Thomas precession. I think the Thomas precession may be the cause of quantum behavior, rather than quantum theory being itself fundamental. It turns out that quantum effects become important at exactly the same scale as the Thomas precession is significant. Perhaps quantum behavior is simply nature's way of conserving angular momentum in spite of the Thomas precession. If so, this would be the best proof of Einsteinian relativity, ever.

sol invictus
29th July 2009, 05:00 AM
One of Phipps' critiques of relativity is related to the effect known as the Thomas precession, which is demanded by Einsteinian relativity but is a very strange and paradoxical effect. The Thomas precession is the necessary rotation of a reference frame that is simultaneously translating and accelerating. I think the weirdness of it is not well appreciated by mainstream physics, but I give Phipps credit for noting it, and was quite surprised when I read his critique of it, because he was asking the same question I ask, which is, why doesn't it violate angular momentum conservation?

Why would it? If you calculate the angular momentum in a non-relativistic expansion I suppose Thomas precession would make a contribution to the total at second order, but why would it violate angular momentum conservation?


(I however have now accepted that mechanical angular momentum conservation is violated by Thomas precession.)

I'm not sure what you mean by "mechanical", but relativity certainly conserves angular momentum - that's extremely easy to prove.


Phipps argues there's no experimental evidence for it.

There's an very famous and important piece of evidence for it: the fine structure of hydrogen. I'd be willing to bet there's lots of other direct experimental evidence too.

I think the Thomas precession may be the cause of quantum behavior, rather than quantum theory being itself fundamental.

That doesn't make sense. Quantum mechanics involves a new constant of nature - Planck's constant. Thomas precession does not. For that simple reason alone, your idea is impossible.

Eggs Ackley
29th July 2009, 07:42 AM
Why would it? If you calculate the angular momentum in a non-relativistic expansion I suppose Thomas precession would make a contribution to the total at second order, but why would it violate angular momentum conservation?

Consider two superconducting coils loaded with currents, in space, a small one inside a big one, and unaligned, so that they mutually precess. The sum of the angular momentum in the two coils in this system, where there's no Thomas precession, is fixed, and so is the total magnetic moment. Now, the effect of Thomas precession is like reducing the rate of precession of one of the coils by half, without changing the rate of the other. Hence, the total angular momentum can no longer be stationary. The total angular momentum is precessing in the absence of an external torque.

I'm not sure what you mean by "mechanical", but relativity certainly conserves angular momentum - that's extremely easy to prove.

There is mechanical momentum and field momentum in this system. I think the total of both is probably conserved but I haven't been able to evaluate it explictly yet. I just started trying to and it is fairly complicated. However I appreciate that there is a proof that it must be conserved. I don't think that Noether's theorem has to be violated.

However, I recently realized much to my surprise that the mechanical angular momentum nonconservation does not lead to radiation, provided that the electron g-factor is the right value to compensate for the Thomas precession. Since the Thomas precession reduces the spin precession by (about) a half, the g-factor must be (about) 2 to preclude radiation. This is exactly what happens in quantum theory. My old Eisberg and Resnick textbook says the total angular momentum precesses (just "randomly") even in the absence of an externally-applied field, for nonzero l.

When you think about it you will realize that allowing a nonunity (i.e., nonclassical) g-factor will make it impossible to maintain the total angular momentum and total magnetic moment in alignment when the spin and orbit are moving. Only one of the angular momentum or magnetic moment can be stationary, not both. Present Thomas precession and spin with g =2, it's the magnetic moment that's fixed.


There's an very famous and important piece of evidence for it: the fine structure of hydrogen. I'd be willing to bet there's lots of other direct experimental evidence too.

It is Phipps who argues that bit, not me. I think he would consider that indirect evidence. He has tried to measure it directly using spinning disks or something.

About the fine structure argument, if you are a physicist (I'm not, I'm a EE) maybe you can tell me, does the Thomas precession enter explicitly into the fine structure calculation in the Dirac theory? Seems to me it doesn't. This is on my list of things to determine but it's more of a curiosity than a part of my hobby research project on this, which is purely semiclassical.


Also, the original argument by Thomas (1927) on this is flawed, as it is based on there being a "secular angular momentum that is conserved", which is not actually correct. I can explain (have explained already) how Thomas went wrong. It wasn't all his fault, as the effect of hidden momentum was not appreciated in 1927. But anyhow it is not clear what this does to his derivation of the spin-orbit coupling magnitude. I'm trying to work it all the way through but it gets very weird when then the spin and orbit angular momentum are not moving oppositely.

That doesn't make sense. Quantum mechanics involves a new constant of nature - Planck's constant. Thomas precession does not. For that simple reason alone, your idea is impossible.

Planck's constant can enter the dynamical equations alternatively due to it being associated empirically with the electron spin. This is not the same as how it enters in conventuional quantum theory. It seemed to me, no one had ever tried seriously to exploit this, as the existence of the spin was not known to Bohr or Sommeerfeld in the earliest quantum theory days, and then when it was discovered Heisenberg and Schroedinger were already doing well without it, and it could be incorporated in their theories fairly easily, and of course Dirac published his theory in about 1928 I think. So nobody ever has spent much time trying to make (relativistic) classical physics describe atoms with the knowledge of the spin, apparently except me.

Then I found out David Hestenes has also been saying the spin is the cause of quantum behavior since at least the 1970s.

sol invictus
29th July 2009, 08:32 AM
Consider two superconducting coils loaded with currents, in space, a small one inside a big one, and unaligned, so that they mutually precess. The sum of the angular momentum in the two coils in this system, where there's no Thomas precession, is fixed, and so is the total magnetic moment.

The total angular momentum will be conserved - including the angular momentum in the fields.

Now, the effect of Thomas precession is like reducing the rate of precession of one of the coils by half, without changing the rate of the other.

Hmmm - I'm not sure that's correct. But even if it is...

Hence, the total angular momentum can no longer be stationary.
Why not? You have to take into account all effects at this order (which is v^2/c^2). In particular, you have to solve for the fields carefully, and make sure you've accounted for all the angular momentum.


The total angular momentum is precessing in the absence of an external torque.

Nope - that's impossible.


There is mechanical momentum and field momentum in this system. I think the total of both is probably conserved but I haven't been able to evaluate it explictly yet. I just started trying to and it is fairly complicated. However I appreciate that there is a proof that it must be conserved. I don't think that Noether's theorem has to be violated.

I'm confused - that seems to contradict what you just asserted.

My old Eisberg and Resnick textbook says the total angular momentum precesses (just "randomly") even in the absence of an externally-applied field, for nonzero l.

I think you've misunderstood something. If you measure the angular momentum component along some axis, it's true the result you get is random (unless the system happened to be in an appropriate eigenstate). But the total angular momentum is conserved in all the usual senses which apply to quantum mechanics (its expectation value is independent of time, as is the result of any measurement of it if you begin in an eigenstate).


When you think about it you will realize that allowing a nonunity (i.e., nonclassical) g-factor will make it impossible to maintain the total angular momentum and total magnetic moment in alignment when the spin and orbit are moving. Only one of the angular momentum or magnetic moment can be stationary, not both. Present Thomas precession and spin with g =2, it's the magnetic moment that's fixed.

Again - the total angular momentum must be conserved. There's a mathematical proof which applies to the systems you're considering.


It is Phipps who argues that bit, not me. I think he would consider that indirect evidence. He has tried to measure it directly using spinning disks or something.

That's going to be quite difficult - the effect is order v^2/c^2.

About the fine structure argument, if you are a physicist (I'm not, I'm a EE) maybe you can tell me, does the Thomas precession enter explicitly into the fine structure calculation in the Dirac theory? Seems to me it doesn't.

If by "Dirac theory" you mean "quantum mechanics" - sure, it changes it by a factor of 2.

Also, the original argument by Thomas (1927) on this is flawed, as it is based on there being a "secular angular momentum that is conserved", which is not actually correct. I can explain (have explained already) how Thomas went wrong. It wasn't all his fault, as the effect of hidden momentum was not appreciated in 1927.

I don't understand what you mean here, but I haven't read Thomas' paper. The effect he discovered is certainly there, though - it's easy to see it must be from basic relativity arguments.


Planck's constant can enter the dynamical equations alternatively due to it being associated empirically with the electron spin. This is not the same as how it enters in conventuional quantum theory.

What do you mean, "conventional quantum theory"? In quantum theory as it's understood today, Planck's constant enters in precisely the same way always - it's a new constant of nature that determines the degree of quantization of various quantities, according to a specific and well-understood prescription.

It seemed to me, no one had ever tried seriously to exploit this, as the existence of the spin was not known to Bohr or Sommeerfeld in the earliest quantum theory days, and then when it was discovered Heisenberg and Schroedinger were already doing well without it, and it could be incorporated in their theories fairly easily, and of course Dirac published his theory in about 1928 I think.

That may be, but this isn't 1928.

So nobody ever has spent much time trying to make (relativistic) classical physics describe atoms with the knowledge of the spin, apparently except me.

As I said, such a program is totally impossible, because Planck's constant does not appear in classical physics.

Eggs Ackley
29th July 2009, 08:52 AM
Sory, no time right now to answer in detail, but in the early part of my post I am talking about the mechanical angular momentum, excluding the fields. If we were to halve the precession rate of one of the coils (and that is exactly what happens with Thomas precession to the spin), then we would see the total mechanical angular momentum precessing in the absence of an external torque. And no it's not impossible in electrodynamics if the field angular momentum is compensating.

It's not even controversial that this happens with linear momentum in classical ED. See Griffiths. I see no reason it can't happen to angular momentum as well.

Eggs Ackley
29th July 2009, 11:17 PM
The total angular momentum will be conserved - including the angular momentum in the fields.

Agreed, see various comments above and below.

Hmmm - I'm not sure that's correct. But even if it is...

It is correct. Even if it is, what? I don't know what you are getting at. Why don't you say what you mean explicitly? You seem to be dismissing a very important point, which is that halving the precession of one coil but not the other must cause the precession of the total mechanical angular in the absence of an external torque.



Why not? You have to take into account all effects at this order (which is v^2/c^2). In particular, you have to solve for the fields carefully, and make sure you've accounted for all the angular momentum.

I started just the other night trying to integrate the field angular momentum to see if it cancels the mechanical angular momentum nonconservation. It does not look very easy to evaluate so I may for the time being simply assume that it does.

Nope - that's impossible.

Agree if we are talking about field plus mechanical angular momentum. Are you then comfortable though with the idea that the mechanical angular momentum can be nonconserved, and furthermore nonradiative?

I'm confused - that seems to contradict what you just asserted.

See my comment above. My usage above where I talk about nonconservation of the total angular momentum while meaning only the mechanical part is the same as Thomas's usage of the total (secular) angular momentum. Ordinarily it's not necessary to distinguish between mechanical or mechanical plus field because either is conserved alone (neglecting radiative effects, which are smaller here). For example in my hypothetical system of the mutually-precessing coils (in the absence of Thomas precession) the total mechanical angular momentum alone is a constant of the motion. The fact that a system can exist where this is no longer true seems quite remarkable to me, and seems not to have been previously noted (although Muller came close in a paper, "Thomas Precession: Where Is the Torque?").

I think you've misunderstood something. If you measure the angular momentum component along some axis, it's true the result you get is random (unless the system happened to be in an appropriate eigenstate). But the total angular momentum is conserved in all the usual senses which apply to quantum mechanics (its expectation value is independent of time, as is the result of any measurement of it if you begin in an eigenstate).

I understand the intended meaning. What I am observing is that the quasiclassical system with intrinsic spin and Thomas precession behaves the same in the essential characteristics. It also has <J_x> = <J_y> = 0, and J_z = constant, where the z-axis is the "quantization axis". The claim to "randomness" in quantum theory has no observable consequences that distinguish it from the systematic precession of the total (mechanical) angular momentum that results simply from the Thomas precession.

Again - the total angular momentum must be conserved. There's a mathematical proof which applies to the systems you're considering.

Yes Noether's theorem I know and I already mentioned it in my previous post did you not read it? Again, I expect that the total angular momentum, that is, the sum of the field and mechanical angular momenta, is conserved. But really I think it is quuite surprising to be able to have an isolated system where the mechanical angular momentum is not conserved, and further that it also does not emit magnetic dipole radiation.

That's going to be quite difficult - the effect is order v^2/c^2.

I can't understand either why Phipps is surprised he can't measure the Thomas precession of a macroscopic mechanical system. The acceleration of an electron in a classical orbit is enormous compared to anything he could achieve. Still I give him credit for recognizing that the Thomas precession is paradoxical.

If by "Dirac theory" you mean "quantum mechanics" - sure, it changes it by a factor of 2.

Well, in nonrelativistic quantum mechanics the factor of a half is basically put in by hand based on Thomas's argument. When I looked at Dirac's treatment of it (in his textbook) I didn't see it being put in this way. I am under an impression the proper spin-orbit coupling emerges in a more elegant fashion and that the Thomas precession does not appear explicitly. But I have yet to study it very carefully so maybe I'm missing where the factor of two is simply inserted.

I don't understand what you mean here, but I haven't read Thomas' paper. The effect he discovered is certainly there, though - it's easy to see it must be from basic relativity arguments.

I don't deny the existence of Thomas's precession, and my analysis is based on his (or Jackson's equivalent) formula for it. Where Thomas went wrong is in his analysis that showed that the total secular angular momentum (by which he means the orbit-averaged total mechanical angular momentum of the spin and orbit) is a constant of the motion in spite of his "relativity precession". He didn't incorporate the "hidden momentum" of a magnetic dipole in an electric field. See Jackson for how to do this, but it does not appear until the newest (third) edition of Jackson.


What do you mean, "conventional quantum theory"? In quantum theory as it's understood today, Planck's constant enters in precisely the same way always - it's a new constant of nature that determines the degree of quantization of various quantities, according to a specific and well-understood prescription.

By conventional quantum theory I mean quantum theory as it's understood today. The nonconventional quantum theory would be the one I'm working on, where Planck's constant enters through the magnitude of the intrinsic spin and intrinsic magnetic moment. Also, there is the idea originated by C. K. Raju, that quantum behavior is a consequence when the effect of propagation delay is properly accounted for in electrodynamics. See here:

(url denied by system due to insufficient posts: search C K Raju on arxiv dot org, see "The electrodynamic 2-body problem and the origin of quantum mechanics" (was published in Foundations of Physics))

I think what i"m doing can coexist with the Raju's idea (which Michael Atiyah has co-opted as the "Atiyah Hypothesis"). De Luca has shown that accounting for delay and self-force runaway can explain the existence of spin itself, and the magnitude of it, and also resonant motions that don't radiate and exhibit orbital angular momentum quantization. See De Luca's 2006 Physical Review E paper.


That may be, but this isn't 1928.

....

As I said, such a program is totally impossible, because Planck's constant does not appear in classical physics.

You seem to missing my point here entirely. I said classical physics (and I mean including Einsteinian relativity - classical in the sense of no quantum assumption such as the uncertainty principle) with spin, that is, with incorporation of the empirical fact of the existence of the intrinsic spin and that it has a certain magnitude that happens to be h-bar by 2. So given that there is a property of particles of intrinsic spin and with it intrinsic magnetic moment, in classical physics there is a dynamics associated with this, and certainly the magnitude of the spin is involved in this dynamics, and it seems that working out the consequences of this has been overlooked for eighty years. Certain features of this dynamics look a lot like features of quantum mechanics that are generally thought to be entirely non-classical, such as precession of mechanical angular momentum in the absence of externally-applied magnetic field.

ben m
30th July 2009, 11:23 AM
You seem to missing my point here entirely. I said classical physics (and I mean including Einsteinian relativity - classical in the sense of no quantum assumption such as the uncertainty principle) with spin, that is, with incorporation of the empirical fact of the existence of the intrinsic spin and that it has a certain magnitude that happens to be h-bar by 2. So given that there is a property of particles of intrinsic spin and with it intrinsic magnetic moment, in classical physics there is a dynamics associated with this, and certainly the magnitude of the spin is involved in this dynamics, and it seems that working out the consequences of this has been overlooked for eighty years. Certain features of this dynamics look a lot like features of quantum mechanics that are generally thought to be entirely non-classical, such as precession of mechanical angular momentum in the absence of externally-applied magnetic field.

So you're just solving the classical equations-of-motion of a spinning top under a 1/r^2 force? And then you're setting the top's angular momentum to hbar/2 and the force to Ze^2 ?

That sounds reasonable enough, but isn't it precisely what Thomas did?

Eggs Ackley
30th July 2009, 12:46 PM
So you're just solving the classical equations-of-motion of a spinning top under a 1/r^2 force? And then you're setting the top's angular momentum to hbar/2 and the force to Ze^2 ?

That sounds reasonable enough, but isn't it precisely what Thomas did?


Well sort of but there are magnetic forces involved as well, and they are the crux. What I did initially is very similar to what Thomas did but different as I will describe momentarily. Then I found Thomas's paper online and was surprised to see that he had done essentially what I did (with the differences as will be described) and gotten basically exactly the opposite result. That shocked me and so I studied it very carefully to determing who went wrong and how. It turned out to not be me that did it wrong. I know I am not hardly the physicist that Thomas was but I got lucky certain ways and have 80 years of maturation of electrodynamics on my side. Also Thomas was probably under a lot of time pressure to get the answer published before anyone else, while I am under no pressure and can take a very circumspect approach. I have now gone through and done it the way Thomas did it, and shown how this should be modified according to the modern prescription per Jackson or Griffiths of accounting for the "hidden momentum" of a magnetic dipole in an electric field.

My initial analysis was to consider the torque on the electron orbit as being due to the magnetic force experienced by the (spinless and nonmagnetic) proton in traversing the electron's intrinsic magnetic field in the electron rest frame. The magnetic force on the proton is the "q*v cross B" force (Biot-Savarat force) of standard ED. So there is a torque on the proton orbit in the electron rest frame that transforms using the standard formula (per Goldstein, say) to a torque on the electron orbit. You have to average over an orbit which is where the term "secular" comes in in Thomas's usage.

I got the idea for doing this while looking at the spin-orbit interaction in my old senior-level atomic physics textbook, where the precession of the spin is calculated in the electron rest frame (the standard treatment at that level) and wondering why the precession of the proton orbit wasn't considered more directly. It seemed to me that it was a lot to expect without justification that the spin and orbit would precess around the total at the same rate independent of electron-proton separation. I didn't know then that this is based ultimately on Thomas's finding of 1927 that they do indeed.
I was already looking specifically for how the spin magnitude being h-bar by 2 could cause orbital angular momentum to be quantized as well (and knew nothing of the Thomas paper beyond that it derived Thomas precession), so I made a conjecture that total non-field angular momentum could only be conserved at certain radii. When I calculated the spin and orbit mutual (i.e., around each other not around the total) precession frequencies I found that they would equate only at the Bohr radius. This seemed a great success, and so I next calculated the total (non-field) angular momentum and its time-derivative and was shocked when I got that it was not a constant at any radius.

So I have had to spend all my spare time for the last two years trying to figure out the meaning of all of this.

About what Thomas did versus me, Thomas found the torque on the electron orbit also in the electron rest frame, but directly on the electron as basically the Stern-Gerlach force on the electron intrinsic magnetic moment, in the anisotropic magnetic field due to the proton charge orbting the electron in the electron rest frame. However unlike the way I did it where there is only one form ever proposed for the Biot-Savart force, there are a couple of different forms for the Stern-Gerlach "effective" (in Hnizdo's usage, see Jackson 3rd ed chapter 5 for cites) force that might be used, apparently even in Thomas's time. There was considerable research reported on this in the 60s-90s, culminating in the addition of the so-called hidden momentum into the equation of motion by Jackson in his 3rd edition and discssion of the hidden momentum is also in Griffiths. Thomas did his analysis initially simply assuming that the secular total angular momentum was a constant of the motion, and then he reported that he got the same result considering either of two forms of the equation of translational motion of the electron. He didn't provide the steps so I had to duplicate them myself. On one of the two forms he's right but on the other he made a mistake. He violated an assumption of his derivation. I wrote up a long paper on this which Physical Review E declined to send out for review, but I did get it onto the Cornell arxiv. Search for Llewellyn Thomas or hidden momentum in the title field and you will certainly turn it up. Also there is a working link at the end to Paul de Haas' Physis Project website where there is a scan of Thomas 1927 (which is where I got it from initially).