Thursday, May 03, 2012

Is Lorentz Force Law Incompatible with Special Relativity?

This paper has been getting quite a bit of brouhaha among physicists, but not with the General Public since most probably don't get the big deal or understand what a "Lorentz force law" is. Of course, among physics students and physicists, the Lorentz force law is one of the first things we learn in intro physics classes. So it would be astounding that a textbook principle is shown to violate Special Relativity right in front of us. But does it?

The paper is to appear in PRL (if it hasn't already), but you can find the preprint here. Adrian Cho at Science covered it last week in the News and Analysis section. It highlights the status so far where people think there's something wrong with the analysis, but no one can figure out where.

“If it's true, it's astonishing,” says Stephen Barnett, a theorist at the University of Strathclyde in Glasgow, U.K. “I suspect there is something subtle going on here” that doesn't contradict relativity. But Rodney Loudon, a theorist retired from the University of Essex in the United Kingdom, says, “As far as I can tell, [the analysis] is right."
I tell ya, even now, classical E&M can still spring a few surprises! I love it!


Edit (5/8/2012): As one can imagine, there are already responses to this paper. One just appeared on arXiv today:

I'm sure we'll hear a lot more.

Edit (5/24/2012): More rebuttals against this paper, and this time, it comes from someone who should know what he is taking about:

I believe this effectively solves the "paradox" in the original paper.


Peter said...

The article may present "incontrovertible theoretical evidence of the incompatibility of the
Lorentz law with the fundamental tenets of special relativity", but the evidence certainly isn't transparent. I can't believe that a PRL referee would recommend acceptance without requiring it to be presented in a manifestly covariant form. The vector notation has its place, but not when arguing about fine details of Lorentz covariance or otherwise of some piece of mathematics.

Doug Natelson said...

So, I've just read the paper. It seems like this its roots in the fact that "bound current loops" are really an unphysical model for magnetization. I would argue that bound current loops are unphysical on the level of classical E&M because a charge actually moving in a loop should radiate, and a system with some static magnetization M does not do so. What do you think?

altertoby said...

As Peter I assume, that the contradiction in the paper is based on notational problems.

The Maxwells equations as well as the Lorentz force are covariant entities. So a change in the reference frame should have no impact on the physics. Maybe he forgot, that the angular momentum is a second-rank tensor in SR and so a spacial contribution to the 3D-angular momentum could be created just be changing the reference frame.