einsteinwrong.com

[ben m]

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]

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).

 

[Darwin123]

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.

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.

I am not sure whether I would call Phipps sophisticated. It depends on what you call sophisticated. He certainly knows how to expand a false hypothesis. He doesn’t know Newtonian physics well enough to recognize that there analogous effects that have nothing to do with Einstein’s relativity. By ignoring these analogous situations, Phipps lies by omission.

I started a Phipps thread elsewhere on this site (The Thomas E. Phipps, Jr. cult). However, let me address some of what you just said. The Thomas Precession does not violate the conservation of TOTAL angular momentum.

Eggs: ‘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?’

This is a run on sentence. I hope you don’t mind as I break it down into parts.

There are many scientists who have examined the conundrums of Thomas Precession. Phipps has not acknowledged this other work. I commend Phipps for having done an experiment to examine a prediction made by only one theorist who has examined the problem. The theorist, Weinstein, predicted what would happen with a solid disk that was spinning and accelerated. Phipps has experimentally shown that Weinstein was wrong. However, Phipps claims that he showed a failure in Einstein’s relativity. He has ignored all the theoretical work that has gone into showing that the total angular momentum is conserved.

The total angular momentum includes both the angular momentum of the disk and whatever object applies an external force to the disk. There has to be an object, which can be another body or a field, which applies an external force to the disk. Otherwise, the disk would not accelerate. The total angular momentum is conserved.


The angular momentum of the disk alone is not conserved. Angular momentum of the other object alone is not conserved. Angular momentum is transferred from the disk to whatever object is applying the external force. The other object applies an external torque to the disk. The disk applies an external torque to the other object.

The reason that this is not obvious is because the dynamics are usually ‘hidden’ in the associated diagram. Only the spinning object is shown with an arrow labelled ‘acceleration’, often pointing in the direction of the object. However, the disk would not accelerate unless there was some object interacting with the particles in the disk. An extended object has to be made of smaller particles (atoms?). In order for the disk to maintain its shape, the external force on one particle has to be different from the external force on a particle that is on the other side of the disk. So there is a torque on the disk. Because of the conservation of angular momentum, there has to be a torque equal in magnitude and opposite in direction to the torque on the disk. However, the precession of the other object is usually not shown.

Consider the plasma of a cyclotron accelerator. By plasma, I mean the particles that move in a circle. The plasma forms a disk that is precessing at the frequency of the Thomas Precession. That synchrotron radiation emitted shows a component with a frequency equal to the Thomas Precession frequency. However, every cyclotron accelerator has a magnet that makes the plasma move in circles. Theoretically, the magnet is also precessing in an opposite direction. However, the magnet is huge and heavy. Therefore, it is impossible to measure the precession of the magnet. BTW: Phipps ignores cyclotron accelerators.

Here is a link and quote.


http://iopscience.iop.org/0143-0807/35/6/065027;jsessionid=2B060714B2499A4666F2B520313AC541.c3
‘As no torque is applied in the rest frame of the gyroscope, it appears that the principle of conservation of angular momentum is violated. In this paper, we show that in fact the Thomas precession of the gyroscope is accompanied by a torque emerging due to the Lorentz transformation of the force acting on segments of the gyroscope. ‘

The best analogous case that I can think of is the regular top in Newtonian physics. When you spin a top, it precesses. The angular momentum of the top alone is not conserved. Direction of the axis of spin is constantly changing, showing that angular momentum is changing. According to Newtonian physics, the total momentum is conserved. How is that possible?

The earth is applying two external forces to the top. The center of mass of the top is being pulled down by gravity. That is external force 1. The contact force of the ground is pushing up against the bottom tip of the top. That is external force 2. If the top maintains its shape, the two forces can’t be equal.

Therefore, the earth applies a torque to the top. So the angular momentum of the top is constantly changing. However, the top is also applying a torque to the earth. Therefore, the angular momentum of the earth is changing. The changes in angular momentum of top and earth cancel each other out.

This is an analogy. This is not the same. However, people seldom claim that angular momentum is not conserved when a top is spun. If Phipps was a self consistent idiot, then he would ask where the angular momentum went in the common top.

The reason that Phipps didn’t see a precession in his shaving head experiment was because there are giant internal forces in the disk he used. In order for the Thomas precession to work, the internal forces in the disk have to be negligible. However, that point is worth another thread.

Quantum mechanics is not necessary to observe the Thomas Precession. The Thomas Precession has been observed in the plasma of particles that orbit in a cyclotron accelerator. Although the particles are small, the orbits in the cyclotron are huge. So quantum mechanics is not necessary to analyze this system. Only special relativity is required for cyclotron accelerators.

Let me also point out that Phipps NEVER shows a force diagram. I don't think he understands Newtonian physics. However, that is only a conjecture !-)

 

[fuelair]

Looks to me like the physics version of "Expelled"

i.e. pile'o'feces on video.

 

[fuelair]

I am not sure whether I would call Phipps sophisticated. It depends on what you call sophisticated. He certainly knows how to expand a false hypothesis. He doesn’t know Newtonian physics well enough to recognize that there analogous effects that have nothing to do with Einstein’s relativity. By ignoring these analogous situations, Phipps lies by omission.

I started a Phipps thread elsewhere on this site (The Thomas E. Phipps, Jr. cult). However, let me address some of what you just said. The Thomas Precession does not violate the conservation of TOTAL angular momentum.

Eggs: ‘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?’

This is a run on sentence. I hope you don’t mind as I break it down into parts.

There are many scientists who have examined the conundrums of Thomas Precession. Phipps has not acknowledged this other work. I commend Phipps for having done an experiment to examine a prediction made by only one theorist who has examined the problem. The theorist, Weinstein, predicted what would happen with a solid disk that was spinning and accelerated. Phipps has experimentally shown that Weinstein was wrong. However, Phipps claims that he showed a failure in Einstein’s relativity. He has ignored all the theoretical work that has gone into showing that the total angular momentum is conserved.

The total angular momentum includes both the angular momentum of the disk and whatever object applies an external force to the disk. There has to be an object, which can be another body or a field, which applies an external force to the disk. Otherwise, the disk would not accelerate. The total angular momentum is conserved.


The angular momentum of the disk alone is not conserved. Angular momentum of the other object alone is not conserved. Angular momentum is transferred from the disk to whatever object is applying the external force. The other object applies an external torque to the disk. The disk applies an external torque to the other object.

The reason that this is not obvious is because the dynamics are usually ‘hidden’ in the associated diagram. Only the spinning object is shown with an arrow labelled ‘acceleration’, often pointing in the direction of the object. However, the disk would not accelerate unless there was some object interacting with the particles in the disk. An extended object has to be made of smaller particles (atoms?). In order for the disk to maintain its shape, the external force on one particle has to be different from the external force on a particle that is on the other side of the disk. So there is a torque on the disk. Because of the conservation of angular momentum, there has to be a torque equal in magnitude and opposite in direction to the torque on the disk. However, the precession of the other object is usually not shown.

Consider the plasma of a cyclotron accelerator. By plasma, I mean the particles that move in a circle. The plasma forms a disk that is precessing at the frequency of the Thomas Precession. That synchrotron radiation emitted shows a component with a frequency equal to the Thomas Precession frequency. However, every cyclotron accelerator has a magnet that makes the plasma move in circles. Theoretically, the magnet is also precessing in an opposite direction. However, the magnet is huge and heavy. Therefore, it is impossible to measure the precession of the magnet. BTW: Phipps ignores cyclotron accelerators.

Here is a link and quote.


http://iopscience.iop.org/0143-0807/35/6/065027;jsessionid=2B060714B2499A4666F2B520313AC541.c3
‘As no torque is applied in the rest frame of the gyroscope, it appears that the principle of conservation of angular momentum is violated. In this paper, we show that in fact the Thomas precession of the gyroscope is accompanied by a torque emerging due to the Lorentz transformation of the force acting on segments of the gyroscope. ‘

The best analogous case that I can think of is the regular top in Newtonian physics. When you spin a top, it precesses. The angular momentum of the top alone is not conserved. Direction of the axis of spin is constantly changing, showing that angular momentum is changing. According to Newtonian physics, the total momentum is conserved. How is that possible?

The earth is applying two external forces to the top. The center of mass of the top is being pulled down by gravity. That is external force 1. The contact force of the ground is pushing up against the bottom tip of the top. That is external force 2. If the top maintains its shape, the two forces can’t be equal.

Therefore, the earth applies a torque to the top. So the angular momentum of the top is constantly changing. However, the top is also applying a torque to the earth. Therefore, the angular momentum of the earth is changing. The changes in angular momentum of top and earth cancel each other out.

This is an analogy. This is not the same. However, people seldom claim that angular momentum is not conserved when a top is spun. If Phipps was a self consistent idiot, then he would ask where the angular momentum went in the common top.

The reason that Phipps didn’t see a precession in his shaving head experiment was because there are giant internal forces in the disk he used. In order for the Thomas precession to work, the internal forces in the disk have to be negligible. However, that point is worth another thread.

Quantum mechanics is not necessary to observe the Thomas Precession. The Thomas Precession has been observed in the plasma of particles that orbit in a cyclotron accelerator. Although the particles are small, the orbits in the cyclotron are huge. So quantum mechanics is not necessary to analyze this system. Only special relativity is required for cyclotron accelerators.

Let me also point out that Phipps NEVER shows a force diagram. I don't think he understands Newtonian physics. However, that is only a conjecture !-)

But a correct and accurate one.

 

[Darwin123]

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

If this was all true, then wouldn't it prove the validity of Einsteinian physics ?-)

 

[Darwin123]

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.

Let me summarize. The cause of the Thomas precession is whatever object is applying an external force to the spinning disk. This object can be a body or a field. The total angular momentum is conserved because this object is precessing in the opposite direction. The other object is usually too massive for detection of the precession.

So what is so hard ?-)

There is a scientist, J.D. Jackson, who wrote maybe the best textbook on electrodynamics theory in the world. So far as I can tell, he made only one mistake in the entire textbook. He says that the Thomas Precession effect is entirely 'kinematic'. Other physicist working on the problem emphasize that the Thomas precision effect is intrinsically dynamic. While I respect J.D. Jackson for writing the best textbook in the world, I have to draw the line with respect to the Thomas Precession.

Jackson made one major goof. Phipps has manufactured goofs on a production scale.

Furthermore, internal forces within the disk dampen the Thomas procession. By internal forces, I mean forces that come from interactions between pairs of particles that comprise the disk.

This is one reason why Phipps did not see precession in that shaving head of his. The elastic forces between atoms in the steel of the shaving head prevented the Thomas Precession from taking place.

I commend Phipps on this particular experiment, though. The shaving head experiment was the only experiment of Phipps which I think demonstrated a valid point about physics. Phipps showed that internal forces dampen the Thomas Precession, as predicted by Newburgh. If you are still interested, buy Newburgh's book. Or try to find copies of his articles, at least.

 

[Eggs Ackley]

Darwin123, thanks for replying to my old comments, and my magic merry-go-round post, which I do intend to respond to as well. It's funny, I was reading along not realizing this was an old thread, and then was surprised to find my old comments.

First, I want to say, I no longer think Thomas precession violates conservation of angular momentum, strictly. I think the apparent non-conservation is a consequence of treating intrinsic angular momentum (i.e., spin) as a fundamental rather than an emergent property of elementary particles. We have a proof that classical electrodynamics conserves angular momentum, but classical electrodynamics doesn't include fundamental entities with intrinsic angular momentum and intrinsic magnetic momentum, just point charges with mass, so saying angular momentum is not conserved in the quasi-classical treatment isn't violating any real fundamental principle. (It's worth noting that Thomas's proof of angular momentum conservation was only valid in an average sense, over the course of an orbit, anyhow. This is not strict angular momentum conservation, either.)

Second, my finding of apparent angular momentum non-conservation in the quasi-classical analysis of atomic spin-orbit coupling was not based on anything Phipps said or wrote. I'd never heard of the guy when I found it. I just happened to come across later that he'd said something similar and felt obligated to acknowledge it.

I have three different papers posted an arxiv about it. (I think only one of them cites Phipps.) It's true that none of them have been published in a peer-reviewed journal, but some mainstream electrodynamicists have looked at them and nobody has shown clearly that I made a mistake. Hnizdo wrote a response that was published in European journal of physics, but he did an alternative analysis using Lagrangian mechanics, rather than showing where I went wrong. (I really appreciate what Hnizdo did, and that he responded to me, but I think it's worth pointing out and at least a little amusing that most of what I did used techniques I learned from Vladimir Hnizdo's papers in American Journal of Physics from the 90s.)

Here is my paper that attempts to explain why Thomas's finding that angular momentum can be conserved in spite of his "relativity precession" is invalidated by the modern concept of "hidden" momentum: http://arxiv.org/abs/0905.0927

Here is Hnizdo's paper about it (and notice that the acknowledgement credits me with raising the issue): http://arxiv.org/abs/1103.4092

 

[Eggs Ackley]

Let me summarize. The cause of the Thomas precession is whatever object is applying an external force to the spinning disk. This object can be a body or a field. The total angular momentum is conserved because this object is precessing in the opposite direction. The other object is usually too massive for detection of the precession.

Yes, but with Thomas precession present and for a g=2 electron the precession of its spin is half of what it has to be to conserve total angular momentum.

Alternatively, if the total angular momentum were conserved in the presence of Thomas precession, then it would not be conserved in the absence of Thomas precession. It is very easy to show this.

 

[Darwin123]

Yes, but with Thomas precession present and for a g=2 electron the precession of its spin is half of what it has to be to conserve total angular momentum.

Alternatively, if the total angular momentum were conserved in the presence of Thomas precession, then it would not be conserved in the absence of Thomas precession. It is very easy to show this.

You misunderstand me. The total angular momentum is conserved because the spinning body (electron or disk) is interacting with another body. The total angular momentum includes the angular momentum of the other object which is causing the spinning body to accelerate.

In other words, angular momentum is not conserved by the electron alone. The electron can not be a closed system. If it was a closed system, then it could not accelerate. Angular momentum is conserved in the closed system containing the electron and whatever else the electron is interacting with.

We are talking about several types of spinning objects. We have been discussing electrons, cyclotron particles and steel shaving heads. These spinning bodies have been accelerated by electric fields, magnetic fields and air pressure. Relativistic constraints apply to fields, electric, magnetic and pressure. So the same argument applies to all these fields.

Therefore, let us refer to the spinning body as a 'gyroscope'. Let us refer to the external field as a 'relativistic lever'. The relativistic lever applies a torque to the gyroscope.

Angular momentum is conserved in the closed system of ‘gyroscope’ and ‘force field’. The gyroscope can be an electron, a plasma confined by a magnetic field, or a quark confined by a gluon field. Angular momentum is not conserved in the gyroscope alone.

Angular momentum is not conserved in the gyroscope alone. The gyroscope is being acted on by an external force. If it wasn’t being acted on by an external force, then it wouldn’t accelerate. The particles in the gyroscope are also being acted on by a centripetal force. Again, the centripetal force has to come from a body outside the gyroscope. If there was no centripetal force, then the gyroscope could not keep its shape.

Thus, there are forces on the gyroscope. The dynamics are important. The dynamics are ‘hidden’ by the kinematics. You took account of the dynamics when you decided which frames are inertial. Once you decide which frame is inertial, kinematic equations can be used with no trouble. None the less, the dynamics are fundamental to the problem.

Look up ‘relativistic right angle lever’. That is another conundrum which is often interpreted as a ‘paradox’.It turns out that the right angle conundrum precisely resolves the Thomas precession conundrum. There is a torque exerted by the object a on the spinning body. So there is a transfer of angular momentum between them.

The following was an undergraduate term paper. I recommend you read it. It is a pretty good explanation of what physically happens in the Thomas precession. In this fine essay, the spinning disk is called a ‘gyroscope’.


http://physics.unm.edu/Courses/Finley/p495/TermPapers/relangmom.pdf
‘Since the centripetal force on the rotating gyroscope acts at the centroid, it creates no torque in this frame, and the 2πγ total rotation is simply the result of length contraction. However, in the lab frame, some parts of the gyroscope will be seen to be rotating faster than others, resulting in an asymmetric distribution of mass and shifting the centroid off-axis. Nevertheless, the centripetal force still acts at the centroid, wherever it is, and it is this torque (centripetal force × displacement of ⃗rC from ⃗rP C ) that rotates the gyroscope in the lab frame’


As in many conundrums in vernal relativity, the physical process is objective while the explanation is subjective. All frames see motion associated with the Thomas precession. In the frame of the gyroscope center of mass, it is explained as a rolling length contraction. However, in the lab frame it is a rotation that varies over the gyroscope.

This also explains why Phipps did not detect a Thomas precession in his shaving head experiment. In order for the disk to precess, some parts of the ‘gryroscope’ has to rotate faster than other parts of gyroscope. The elastic forces that held the steel shaving head together forced the rate of rotation to be the same throughout the gyroscope. The rotation rate couldn’t vary in the lab frame. So there was no Thomas precession.


In order to see a Thomas precession, one needs a disk which allows different parts of itself to rotate at different rates. Shaving disks don’t do this. Toroidal cyclotron plasmas do. The Thomas precession has been observed in cyclotron plasmas.

Newburgh wriote an entire book on the subject. However, it is behind a paywall. If you want your research to be more credible than Phipps, you may want to invest in this article. Here is a citation.

http://link.springer.com/article/10.1007/BF02905258
R. G. Newburgh, ’Thomas precession and extended structures’ Lettere al Nuovo Cimento
30 Settembre 1972, Volume 5, Issue 5, pp 387-388.
‘Now the Thomas precession is derived by considering the group properties of suc- ... (13) relating the Thomas precession to the relativistic right-angled lever.’
You should find out a little about the relativistic right angled lever problem. So sorry. Another paywall citation!

Aranoff, More on the Right-Angled Lever at Equilibrium in Special Relativity 
Am. J. Phys. 41, 1108 (1973); http://dx.doi.org/10.1119/1.1987485 BUY: $30, rent $4.00

Here are two articles which are not behind a paywall. See the following link.

http://www.analysis-knowledge.com/Physics/Equilibrium in Special Relativity.pdf
S. Arnoff, ‘Equilibrium in Special Relativity’ Il Nuovo Cimento 10, (1972)
S. Arnoff, ‘The Thomas Precession in special relativity.


Okay, I gave you some citations where the author examines the Thomas precession conundrum closely. According to what you told me, you haven't seen these articles before. So now you can't say no one showed you possible resolutions to the conundrum. I don't guarantee all these authors are completely correct. However, you can now criticize these articles yourself without referring to Phipps. I am confident that you could do a better job than Phipps!-)

 

[Darwin123]

Agreed, see various comments above and below.



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.

Correction: The TOTAL angular momentum does not precess. The clampsthat hold the coils still also have angular momentum. How could one half the precession of one coil without clamping that coil down? Whatever the coil is clamped to will absorb or supply 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.

Fields include the stress field of the clamp.

Don't just draw the coils. Draw the clamps on the coils. Draw a force diagram of the coils and clamps. Include ALL real forces, elastic and electromagnetic. Then tell us what happens to the TOTAL angular momentum.

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 non radiative?


Sure. Are you comfortable with the fact that a non radiative electromagnetic field can have angular momentum? Are you comfortable with the fact that a stress field in an elastic material can also hold angular momentum?

I will quite now. I haven't really looked at your two could example. It would be unfair to press too hard until I have looked them over. However, I suggest that you read the articles that I cited before you respond further.

While your read these articles, keep in mind that only the total angular momentum need to be conserved. The angular momentum may be contained by more objects than you are taking into account.

 

[Darwin123]

Yes, but with Thomas precession present and for a g=2 electron the precession of its spin is half of what it has to be to conserve total angular momentum.

Lets go through some atomic spectroscopy. Although the conservation of angular momentum doesn't require quantum mechanics, the election rules in atomic spectroscopy have classical analogues. The laws of atomic spectroscopy are more widely know than either the Thomas precession or the relativistic right angle lever. From your posts, I get the impression that you have been exposed to atomic spectroscopy.

The g-factor was first introduced in the spin-orbit coupling interaction of electrons in an atom. This is where the g-factor turned out to be 1/2 rather than 1 as expected without relativity. You brought up the fact that the g-factor of 1/2 is a consequence of the Thomas precession. The orbit-orbit coupling factor is 1 rather than 1/2.

It turns out that the total angular momentum of an electron in an atoms is a 'good' quantum number. However, neither the electron spin nor the orbital angular momentum is a good quantum number.

The classical analog to this spectroscopy rule is this. The total angular momentum of an electron is conserved in the atom at all times. However, both the spin angular momentum and the orbital angular momentum are changing so fast that neither can be accurately measured. This means that the orbital angular momentum is being transferred back and forth between the spin and the orbit. The motion of the electron in orbit around the atom is exerting a torque on the intrinsic spin of the electron.

Both the orbital angular momentum and the spin orbital momentum in the atom are precessing. This is how lots of physical chemistry textbooks illustrate it. Each of these precessing vectors can be said to undergo a Thomas precession. The total angular momentum is not precessing. The total angular momentum is not affected by the Thomas precession.

A conservation rule valid a total is not the same as a conservation rule valid for separate components. The conservation of spin angular momentum as a vector quantity could only be valid if the electron spin is a closed system. It is not.

Even though the electron in the atom is not radiating energy, the total angular momentum is conserved. This is an example of angular momentum being conserved in a non radiative system. This is a consequence of quantum mechanics. However, classical system radiate energy. Still, the total angular momentum is conserved.

The important thing to realize is that the electron in the atom is not a closed system. The electron in the atom is strongly interacting with the electromagnetic field of the nucleus. Hence, angular momentum can be transferred to the electron to the electromagnetic field and back. The electron is traveling in a curved path, or what would be a curved path in a Newtonian world., solely because of the nucleus. Hence, the orbital angular momentum of the electron is not conserved. However, the atom is a closed system. Hence, the total angular momentum of the atom is conserved.

Your mistake is thinking that the gyroscope that undergoes a Thomas precession is a closed system. It can't be a closed system because it is undergoing acceleration. In order for there to be acceleration, there has to be an external force. The external force is mutually exclusive of a closed system.

Alternatively, if the total angular momentum were conserved in the presence of Thomas precession, then it would not be conserved in the absence of Thomas precession. It is very easy to show this.

The total angular momentum is conserved in the presence of the Thomas precession. However, the angular momentum of the gyroscope alone is not conserved because the rest of the system exerts an external torque on the gyroscope.

You had possibly read an article that showed you that the synchrotron radiation from the plasma of a cyclotron helps to conserve angular momentum even though the plasma is undergoing a Thomas precession. The reason is that the synchrotron radiation itself has nonzero angular momentum. So the change in angular momentum of the orbiting particles in a cyclotron is mostly taken up by the synchrotron radiation. So in this case, the electromagnetic radiation balances the total angular momentum. That portion of angular momentum lost or gained by the orbiting particles is gained or lost by the electromagnetic radiation.

According to classical electrodynamics, all electric charges that are accelerating due to any force emits electromagnetic radiation. Therefore, if an extended body is electrically charged and spinning, then the emission of electromagnetic radiation is unavoidable. This isn't always true for atoms since motion is not in a classical scale. The electron has an intrinsic spin, for instance. However, quantum mechanics shows that even in this case total angular momentum is conserved.

You have asked whether we could accept that a body could rotate 'nonradiatively'. I said 'yes'. I was thinking only of electromagnetic radiation. However, there are other ways to emit energy.

Consider a gyroscope that is not electrically charged. Suppose that it is merely spinning in an air tunnel, such as is the case with Phipps shaving head. Suppose that the gyroscope has a great deal of flexibility, so that it could bend back and forth with great amplitude. The spinning of the earth applies a centripetal acceleration to the gyroscope. How could angular momentum be conserved in this case?

If the gyroscope is not electrically charged, then it could not emit electromagnetic radiation. A static electric field or a static magnetic field could not accelerate it. Hence, it would superficially seem to be a different system then the cyclotron. However, now we come to stress field.

The neutral gyroscope could emit pressure waves. It could give off sound. In the inertial frame of the center of mass, the gyroscope would be bending and flexing. Hence it would give off sound waves. Both energy and angular momentum would be carried off by sound waves.

I do not accept the possibility of non radiative precession, if radiative includes any form of wave. The gyroscope can emit waves that carry off the angular momentum. The form of the wave would vary with the force that is causing the acceleration. However, the Thomas precession would still be observed in the gyroscope.

The problem with Phipps shaving head is that it was not flexible. The internal forces would keep in semi-rigid, which would inhibit the Thomas precession.


In any case, you can't treat the spinning disk as a closed system. There is always something causing the disk to accelerate. This something will always emit something that applies a torque to the disk.

One can not ignore the rest of the system when you have Thomas precession. You can't ignore the synchrotron radiation in a cyclotron because accelerating electric charges always emit electromagnetic radiation. You can't ignore the magnetic field in an atom because orbiting electric charges always emit a magnetic field. You can not ignore the stress field when you are looking at a neutral disk because something has to hold the disk in position. However, you can assume that the TOTAL angular momentum is always conserved.

 

[Darwin123]

Yes, but with Thomas precession present and for a g=2 electron the precession of its spin is half of what it has to be to conserve total angular momentum.

The other half of the angular momentum goes from the spin component to the orbital component of momentum. In atomic physics, the spin and the orbit precess in opposite directions.



The spin orbit interaction causes the z-direction component of the spin (m_s) to flip. However, the z-component of orbital angular momentum (m_l) also flips. So the z-component of the total angular momentum (m_j) does not flip.

Suppose that you had an electrically charged coil in orbit around a heavy body of opposite charge. There would be two components of electric current: the electric current corresponding to the charge that is circulating in the coil and the electric current corresponding to the electric charge orbiting. The orbit and the coil would precess in opposite directions. This is caused by the delay in propagation.

The moving coil creates a magnetic field due to its center of mass motion. However, the magnetic field created by the spin is delayed. The magnetic field caused by the spin causes the orbit to precess. The magnetic field caused by the center of mass motion causes the spin to precess.

The torques in this case are caused by the magnetic field. You can't have one component of a system have a Thomas precession without another component having a Thomas precess in the exact opposite direction.