# Textbook Electrodynamics May Contradict Relativity

According to "physics today" www.physicstoday.org/daily_edition/science_and_the_media/em_science_em_magazine_news_report_textbook_electrodynamics_may_contradict_relativity [Broken] the paper "Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation" http://arxiv.org/abs/1205.0096 was admitted for publication in PRL.
I see a thread was locked recently adducing lack of publication, is it enough that the abstract of the article appears in PRL as admitted to comment it here?

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PAllen
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Seems fine to open this for discussion now:

Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation

Masud Mansuripur

Phys. Rev. Lett. 108, 193901 (2012) – Published May 7, 2012

Physics Monkey
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Seems interesting, but one thing I would note already is the distinction between the macroscopic Lorentz force and the microscopic Lorentz force. As far as I can tell, the article is concerned primarily with some coarse grained version of the Lorentz force law and not the law as it might be applied to structureless point charges (realizing that this is in itself an idealization). I find it weird that despite using the macroscopic laws the paper proceeds to consider very microscopic looking situations.

Also, the microscopic Lorentz force for point particles follows from a manifestly Lorentz invariant action, so that can't be an issue. Corrections due to finite size etc. can be organized in terms of higher derivative operators that couple to the charge.

Personally, I can't understand the mere existence of such papers.
The whole electrodynamics can be reduced to a simple variational principle.
The Lagrangian density, including particles, fields and their interaction is covariant.
It is well defined on a microscopic level: based on charged particles.
How could one then derive something that might in any way contradict SR ???
How could there even be any ambiguity about the force law applicable in electrodynamics ???
At most there could be technical difficulties.

Why does the author refer to "L. Landau, E. Lifgarbagez, Electrodynamics of Continuous Media, Pergamon, New York, 1960" as a basis to discuss the "pillars of elecrodynamics"?
Obviously the "Classical theory of fields" by the same authors should be the reference of choice, as it is more fundamental?
The "pillars of electrodynamics" are based on charged particles, not on copper wires, plasmas or supraconductors.

Reading quickly through section 2 of the arXiv article linked to in #1, seems to me Mansuripur has made an elementary mistake in assuming a net torque acting on the 'point' magnetic dipole m0 as seen in the unprimed frame, where both charge q and m0 are moving at uniform colinear speed. The electric forces owing to the action of charge q on the relativistically transformed magnetic current loop 'electric dipole charges' surely do not form a couple at all - the E field eminating from q continues to radiate in straight lines with q the origin there. Hence there is just a net lateral electric force exactly cancelled by the magnetic forces acting on that loop current. Everything balances out the same in both frames - zero forces and torques. So imo the supposed Lorentz force law inadequacy is non-existent.

Despite that, while in certain situations hidden momentum occurs and is real enough, I'm not convinced it rescues energy-momentum conservation in all situations. Have an interesting example in mind but not going to use it to hijack this thread.

It is rather surprising that noone noticed before that torque, the set up as presented in figure 1 looks quite simple.

It is rather surprising that noone noticed before that torque, the set up as presented in figure 1 looks quite simple.
Well I must admit that on closer inspection, an exact treatment does get involved owing to higher order field gradient effects re current loop force/torque. The system though is steady state with no net time changing field momentum contribution to consider. Therefore given the magnetic dipole can be taken as just a collection of steadily circulating point charges q (plus equal number of opposite sign static lattice charges), there can ultimately only be the sum of 'primitive' q(E + vxB) Lorentz forces at work - in either frame. Plus I suppose one must have non-electromagnetic mechanical restraining forces for loop current stability - but the sum of such can never act other than to transmit the net lorentz forces at work. So if Mansuripur's calculations can be believed, the point charge Lorentz force law is invalid. Strange how no particle accelerator data has indicated that to date!

Why does the author refer to "L. Landau, E. Lifgarbagez, Electrodynamics of Continuous Media, Pergamon, New York, 1960" as a basis to discuss the "pillars of elecrodynamics"?
Obviously the "Classical theory of fields" by the same authors should be the reference of choice, as it is more fundamental?
The "pillars of electrodynamics" are based on charged particles, not on copper wires, plasmas or supraconductors.
I haven't read the paper yet but it does sound interesting based on the abstract. "Classical theory of fields" is a far simpler work and deals more or less with issues that are more readily assimilable in SR. "Electrodynamics of Continuous Media" is just as fundamental, if not more. SR, outside of Minkowski's electrodynamics considers c as primal. Of necessity, the electrodynamics of continuous media deals very heavily with the components of c, namely $\epsilon_0$ and $\mu_0$ in a vacuum and $\epsilon$ and $\mu$ as scalars or tensors for determining the electrodynamics in media.

The situation in the Mansuripur paper is very similar to the old "Trouton-Noble paradox" from a 100 years ago. http://arxiv.org/abs/physics/0606176 see also:http://arxiv.org/abs/1205.1502

It seems the way to solve the paradox has to do with using 4D instead of 3D quantities.
Anyway, is torque usually considered a 3D or a 4D quantity? I've always seen it treated as 3D.

Physics Monkey
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Not surprisingly there are a rapidly growing number of comments e.g. http://arxiv.org/abs/1205.1502

What really surprises me is that prl actually published the paper with the word incontrovertible in the abstract and given the general tone of the work. What is the point of that? Clearly the paper will be controverted (almost certainly successfully). It seems fine (even good) to me to try out new puzzles e.g. like analyzing perpetual motion machines, but why all the grandstanding and hoopla? It embarrasses me as a physicist.

The resolution given in the arXiv counter claim article linked in #9, #10 at http://arxiv.org/abs/1205.1502 replaces Mansuripur's single charge q with a uniform E, and that then fails to account for the action on the magnetic moment of the highly non-uniform magnetic field produced by q in the unprimed frame. An article that tackles the problem preserving the original geometry [but on closer reading still does not fully consider the magnetic action of q on m0] and clearly setting out the role of hidden momentum there and with another example can be found here: www.physics.princeton.edu/~mcdonald/examples/mansuripur.ps

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Meir Achuz
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Meir Achuz
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M has a string of nonsense papers with spurious effects, but this is the first time he fooled, and embarrassed PRL.

M has a string of nonsense papers with spurious effects, but this is the first time he fooled, and embarrassed PRL.
Yes the whole thing looks pretty embarrassing both for him and PRL, a quick look at papers about this "torque paradox" shows that this is nothing new, something similar at least in general concept if maybe not in all the details has been discussed by several authors (among them none other than Jackson) and apparently satisfactory solutions have been given, see for instance http://arxiv.org/abs/physics/0505013.
I certainly can't understand why Mansuripur doesn't give any reference to this previous work and why this was welcome as breaking news (for instance in Science mag.) and "incontrovertible" when it is such an old and beaten issue.

I think, if Hendrik Antoon Lorentz would be the Division Associate Editor of PRL, Mansuripur's Letter could not have been published.

The paradox was resolved quickly by Kirk Mcdonald (search mcdonald mansuripur).

The basic reasoning mistake was that one must consider all the effects to a given order in v/c. As KM shows, there must be some mechanical momentum in the system, since it is, initially, at rest. It is easy to see that there's linear momentum in the electromagnetic field (since it is a point-like magnetic dipole, it makes no difference if the electric field is homogeneous or not), and one sees from $\vec S = \vec E \times \vec B$, the Poyinting vector. This mechanical momentum is the so-called "hidden momentum" (which stems from the fact that the momentum of a charge carrier is $\gamma m v$, not $mv$) gives a correction that perfectly accounts for the momentum in the EM field. As the dipole moves away from the observer, it's angular momentum increases, since $\vec L = \vec r \times \vec p$, and $\vec r = \vec v t$. Finally, since torque is the rate of change of angular momentum, there must be a torque on the charges. That's all.

Seems to be another variant of the Trouton-Noble paradox (or right-angle lever paradox). There are already plenty solutions, such as

http://en.wikipedia.org/wiki/Trouton–Noble_experiment

*Additional momentum by the Laue current (Laue, Teukolsky etc.)
*Replacing 3D with 4D quantities (Rohrlich, Cavalleri etc.)
*Different directions of force and acceleration (Epstein, Franklin).