Purported Relativity Paradox Resolved

sciencehabit writes "A purported conflict between the century-old theory of classical electrodynamics and Einstein's theory of special relativity doesn't exist, a chorus of physicists says. Last April, an electrical engineer claimed that the equation that determines the force exerted on an electrically charged particle by electric and magnetic fields — the Lorentz force law — clashes with relativity, the theory that centers on how observers moving at a constant speed relative to one another will view the same events. To prove it, he concocted a simple 'thought experiment' in which the Lorentz force law seemed to lead to a paradox. Now, four physicists independently say that they have resolved the paradox."

Comments

Summary of Resolution Ceremony

[CodeBuster]

The four physicists waived their hands over the box containing Schrödinger's cat while repeating, "omine, omine, omine" before walking away without looking inside and thus the conjecture was false and the paradox is resolved.

Re:It's good to see that .....

[Anonymous Coward]

Science is alive and well in at least the Physics community. Whilst I won't even pretend to understand General Relativity, the questioning of it and discussion about those questions is the true essence of science.

Sigh. General Relativity was not even at question here. Perhaps commenting on Slashdot should require a minimum amount of knowing what one is talking about. AAAHAHAHAHAHAHAHAHHAHAHAHA. Sigh.

At any rate, electrical engineers tend to view parts of Special Relativity in isolation. That makes them easier to handle and "visualize" in some respects, but much harder to deal with interactions. Minkovsky vectors and tensors are what theoretical physicists use instead, grouping several codependent field parts into one entity that can then be transformed as a whole.

So the physicists will most likely just have employed a better mathematical toolbox for resolving the "paradox". I've not actually read the original Einstein papers, but I would not be much surprised if his equations were closer to what Electrical Engineers get to deal with than what Theoretical Physicists do. Shaking out all that tensor stuff is more or less elegant wrapup work.

That sort of approach was, however, at the core of General Relativity, and mastering it took quite a bit more time for Einstein. I seem to remember that he discussed the underpinnings with Hilbert, and Hilbert came up with the general equations independently within something like a week, but retracted his papers out of respect for Einstein doing all the visionary groundwork as well as shouldering the math (though being quite slower at it than well-versed mathematicians).

Re:Dark matter

[buchner.johannes]

So, hidden momentum and dark matter... What other concept will we invent to explain we dont know anything?

Dark matter is not an invented concept, it is a name for something we observe. Galaxies just rotate faster than from what is there in normal matter. So something is going on, and this something is called "dark matter", just because it does not produce/interact with light but behaves like a mass.

Now in what way you explain this (new physical laws, new elementary particles) is still an open question. But it's there and needs to be addressed. Dark matter is just the name of the problem.

It's not a paradox

[mocm]

if you forget part of the energy-momentum tensor when you transform your coordinates from a stationary into a moving frame of reference.
Special relativity really cannot "clash" with the Lorentz force law, because it is based on the Lorentz invariance of Maxwell's equations. I think a "paradox" like this keeps coming up ever so often in discussions of special relativity, form people who don't understand it. I just don't see how PRL can accept such a paper.
I admit it would make a nice problem for a physics test, but not much more.

Re:It's good to see that .....

[bill_mcgonigle]

And it's a healthy sign that some random guy can say, "look Special Relativity seems to be broken," and nobody starts screaming about golden idols or anything, but rather four smart guys kindly consider what he has to say and show him where he went wrong. Everybody learns something, egos remain intact, and nobody starts swinging guns. Science FTW.