# EM wave near field propagating faster than light?

DoobleD
Sources : paper here and http://www.quora.com/What-is-the-phase-of-the-EM-waves [Broken] (fifth paragraph).

This is beyond my knowledge so I am not looking for an explanation of the phenomenon. But I thought nothing could go faster than light so I am very surprised.

Are there exceptions to the speed of light as a maximum limit?

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## Answers and Replies

Science Advisor
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There are no exceptions. The ##c > c_0## in the article is the group speed.
As a student I had to solve this problem:

Imagine a bar moving in the vertical direction with a speed 90% of the speed of light. It is at an angle ##\alpha## with the horizontal where ##\tan \alpha = 0.5##.
The bar passes another bar that is horizontal and at rest. With what speed does the crossing point of the two bars move in the x direction ?

(The answer is 1.8 c. But that doesn't mean things can move faster than light).​

Science Advisor
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There's no limit for the phase velocity. Only the speed of the wave front must be ##\leq c##, and that's always the case, as proven by Sommerfeld in 1907. There are two famous papers by Sommerfeld and Brillouin somwhat later (but they are in German). You find a good discussion of this issue in the textbook by Jackson, Classical Electrodynamics, even with the citation of an experimental observation of the Sommerfeld and Brillouin precursers.

BTW, it's better to give an explicit link to an abstract on the arxiv:

http://arxiv.org/abs/physics/0001063

I haven't read the paper, but note that it is not published in a peer-reviewed journal, and it's typed in Word. Thus, you have to read the paper with great sceptical care ;-)).

DoobleD
Imagine a bar moving in the vertical direction with a speed 90% of the speed of light. It is at an angle ##\alpha## with the horizontal where ##\tan \alpha = 0.5##.
The bar passes another bar that is horizontal and at rest. With what speed does the crossing point of the two bars move in the x direction ?

(The answer is 1.8 c. But that doesn't mean things can move faster than light).​

Hm I have the feeling this problem requires special relativity, which I haven't really learned yet. I have briefly read about the Lorentz transform and some if it consequences though, so I might be able to understand the solution to this problem, if you can show it to me. If that's not too much to ask!

There's no limit for the phase velocity. Only the speed of the wave front must be ##\leq c##, and that's always the case, as proven by Sommerfeld in 1907. There are two famous papers by Sommerfeld and Brillouin somwhat later (but they are in German). You find a good discussion of this issue in the textbook by Jackson, Classical Electrodynamics, even with the citation of an experimental observation of the Sommerfeld and Brillouin precursers.

BTW, it's better to give an explicit link to an abstract on the arxiv:

http://arxiv.org/abs/physics/0001063

I haven't read the paper, but note that it is not published in a peer-reviewed journal, and it's typed in Word. Thus, you have to read the paper with great sceptical care ;-)).

The paper is a bit above my knowledge. I really need to learn about complex numbers...

Anyway both of your answer make me remember something I heard : that nothing can move through space faster than light, but space itself, distance between two points for instance, can grow faster than light.

Is this somehow like the phase? I mean, the phase angle is a kind of distance I guess, a shift.

Does the light speed limit is only for physical "things" (matter, energy, ...) moving?

Science Advisor
There is a paper from LANL about superluminal polarization currents that are generated by phasing several RF generator on a curved dielectric. They built several types of technology demonstrators where the pattern of electric polarization is superluminal.
http://laacg.lanl.gov/superluminal/pubs/DRsummary.pdf

Some impressive engineering in designing systems to create electromagnetic "Shock waves".

Science Advisor
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Without having read the above linked report, it's for sure saying on p. 6 that nothing violates Maxwell's equation or (consequently) Special Relativity. So the question is, which speed the authors refer to. As I said above, many "speeds" can exceed the speed of light in vacuo without violation any relativistic laws, among them the phase or group velocities of electromagnetic waves. The only velocity which has to obey the speed limit is the speed of the wave front, and that all proper retarded solutions of the Maxwell equations automatical obey this speed limit. Besides Jackson's treathment in his textbook I can also recommend Sommerfeld's treatment in vol. 4 (optics) of his "Lectures on Theoretical Physics".

nsaspook
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Dear DD,

Hm I have the feeling this problem requires special relativity, which I haven't really learned yet. I have briefly read about the Lorentz transform and some if it consequences though, so I might be able to understand the solution to this problem, if you can show it to me. If that's not too much to ask!
The crux is that it doesn't. Such a crossing point is not a material thing but an imagined, geometric observation. So ##v'= v / \tan\alpha = 0.9 c /0.5##.

The superluminal articles are way above your head (and mine). Concentrate on understanding the Lorentz transformation for very simple cases. It's already dazzling enough. Next step would be electromagnetism. Then the combination of the two with retarded potentials and such. Long way to go.

DoobleD
The crux is that it doesn't. Such a crossing point is not a material thing but an imagined, geometric observation. So v′=v/tanα=0.9c/0.5v'= v / \tan\alpha = 0.9 c /0.5.

I'm sorry I don't get it. Could you show me the setup of the problem? I have tried several possibilities (2 below) but I must set it wrong.

Long way to go.

Aha, yep. And then if I get there, I'll still have in front of me some minor things to learn like quantum mechanics, general relativity, quantum field theory, string theory and so on, with all the required maths to learn as well, of course. :D

Have a look at my (unfinished) writeup about SRT:

http://fias.uni-frankfurt.de/~hees/pf-faq/srt.pdf

Thank you, I stored the link for when I'll start SR.

Science Advisor
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I'm sorry I don't get it. Could you show me the setup of the problem? I have tried several possibilities (2 below) but I must set it wrong.

and your right picture was just a few nanoseconds too late

DoobleD
View attachment 88164

and your right picture was just a few nanoseconds too late

Damn when you look at the drawing it is obvious! Thank you very much. Indeed the crossing point is moving faster than light then. Geometry can change faster than c, good thing to remember.

BTW at 0.9c isn't there some relativistic effect that affect the solution? Length contraction of the moving bar? Hm, well that doesn't seem to affect the speed of the crossing point. So no relativistic effect here? Just being curious.