Recent work on the foundations of classical EM demonstrates that the usually accepted form of the Lorenz force law is actually wrong, because it does not obey relativistic invariance, and should be replaced by a more complex Einstein-Laub formula [Phys. Rev. Lett. vol. 108, 193901 (2012)]. But is this claim credible or not?
A safe statement is that the text-book definition of the Lorentz force works strictly for the vacuum, but needs serious modifications in the presence of matter. The details are messy.
@Peter, the PRL paper is in the archives as well if you want to look at the equations. I read the paper carefully and the critique is well-justified.
Mansuripur’s bold claim of a paradox with the Lorentz law has generated some intense criticism. One critic, Daniel Vanzella, a physics professor at the University of Sao Paulo in Sao Carlos, Brazil, has submitted a comment to Physical Review Letters arguing that the Lorentz law is perfectly compatible with special relativity, and that Mansuripur has misunderstood relativistic mechanics. The only paradox, Vanzella says, is why the high-ranking journal accepted the paper in the first place.
http://phys.org/news/2012-05-classical-electrodynamics-law-incompatible-special.html
@Pankaj. Thanks for the info! Based on the news feature I would say that Vanzella is of course right in his comment about the covariant form of the force law; I thought that this was checked by Mansipur but the story indicates that this might not be the case. The story becomes more and more interesting!
Sir Dimitrov, can you give some link or reference for this publications, please
The Lorentz-force law for classical charged particles in vacuum follows from the basic Schwarzschild Lagrangian (which is Lorentz scalar density). It is therefore definitely correct and in agreement with special relativity. To claim otherwise is non-sense.
my 2 cents:
i) the Lorentz force is written down essentially already by Maxwell since 'On Physical Lines of Force';
ii) the expression
qE + qv x B
is not Lorentz invariant: the Lorentz factor is missing; both together are called 'Minkowski force' by Sommerfeld;
iii) important is not the transformation properties of the force alone, but of the equation of motion as a whole
iv) the Lorentz force can be derived thru purely mechanical reasoning -> it's not special to electromagnetism
v) Gsponer's cited paper looks quite interesting; his statement, that charge conservation is a consequence of the Maxwell equations (p. 1), is the opposite of the physically reasonable, however (cf also Mie's derivation of the inhomogeneous Maxwell eqs.)
The question now appears to have been resolved: Mansipur's argument does not hold water: http://news.sciencemag.org/sciencenow/2013/01/purported-relativity-paradox-res.html
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