Why does an Accelerating Charge Radiate - Solved or Unsolved?

[0xDEADBEEF]

The problem is solved http://en.wikipedia.org/wiki/Liénard–Wiechert_potential
Look for $$\vec{ \dot{\beta}}$$ that is the acceleration leading to the 1/r term typical for radiation. There is even a covariant formulation of electrodynamics that works in GRT. Maybe ask in the relativity forum, but this problem is solved and there is no question about the radiation except for intuitive insights into the formulas. Feynman simply tried to say that it is not as simple as people tend to tell you.

 

[Antiphon]

The problem is solved http://en.wikipedia.org/wiki/Liénard–Wiechert_potential
Look for $$\vec{ \dot{\beta}}$$ that is the acceleration leading to the 1/r term typical for radiation. There is even a covariant formulation of electrodynamics that works in GRT. Maybe ask in the relativity forum, but this problem is solved and there is no question about the radiation except for intuitive insights into the formulas. Feynman simply tried to say that it is not as simple as people tend to tell you.

Thanks for the reference 0xDEADBEEF. The acceleration term of course is what gave life to part of this thread in terms of the equivalence principle. Why doesn't a charge sitting still in a gravity field radiate when (by the referenced equation) a charge in a "speeding up" elevator would? That seems to *violate* the equivalence principle.

To sum it all up, it is possible for the radiation from accelerated charges to show up as something other than radiation if the frames are chosen correctly. Common sense says that radition in one frame looks like radiation in any frame but it seems this is not the case. This has probably been the (historical) origin of the controversy.

Edit: Apparently someone has done the analysis on this in 2006 (a year after the thread started.) It's good to know the
thinking was correct. If they get a Nobel prize I want my cut.

http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000074000002000154000001&idtype=cvips&gifs=yes&ref=no

 

[yoron]

Citing your link DB.

"Liénard-Wiechert potentials describe the classical electromagnetic effect of a moving electric point charge in terms of a vector potential and a scalar potential. Built directly from Maxwell's equations, these potentials describe the complete, relativistically correct, time-varying electromagnetic field for a point charge in arbitrary motion"

In my definition above, how do you get to a "time-varying electromagnetic field for a point charge in arbitrary motion" ? I'm not sure how to see a gravitational 'acceleration' at all. To you falling there just is a weightlessness, isn't there? Similar to a uniform motion in that you can have all kinds of speed as measured by an 'far observer' at rest with the gravitational field you're 'falling into' but still from your frame being unable to differ between those?

Just like different 'uniform motions' won't be measurable inside a black box scenario either. Also you won't have any external 'EM field' as observed by that 'free falling' electron, well, as I defined it above?

Anyone heard about "Schott energy, which seems to have no physical limit and can go infinitely negative in value." http://www.hep.princeton.edu/~mcdonald/examples/EM/eriksen_ap_297_243_02.pdf

Just to bring this to a new, even more refined, level of confusion, well, to me that is :)

 

[0xDEADBEEF]

In my definition above, how do you get to a "time-varying electromagnetic field for a point charge in arbitrary motion" ? I'm not sure how to see a gravitational 'acceleration' at all. To you falling there just is a weightlessness, isn't there? Similar to a uniform motion in that you can have all kinds of speed as measured by an 'far observer' at rest with the gravitational field you're 'falling into' but still from your frame being unable to differ between those?

It is all in the math. If you want to find the answer, you have to use the covariant formulation of the theory and derive the Lienard-Wiechert type potential in a curved space time metric. Then you know, but as I said that's a question more appropriate for the relativism subforum.

 

[GRDixon]

Are the questions

a) why does an accelerating charge radiate

and

b) why does an uniformly accelerating charge not radiate

satisfactorily answered and accepted by the physics community?

or are there still some unresolved inconsistencies in theory regarding this?

I read two articles related to this:

http://www.mathpages.com/home/kmath528/kmath528.htm

http://citebase.eprints.org/cgi-bin/fulltext?format=application/pdf&identifier=oai%3AarXiv.org%3Agr-qc%2F9303025

which got me thinking. Is this an unsolved thing?

Any takers? I am not sure whether this belongs to quantum physics or classical physics?

The accelerating charge (e.g. an oscillating charge) radiates because the surface integral of its Poynting vector, integrated over a cycle time, is nonzero. (The Poynting vector is constructed from the charge's E and B fields, as calculated/computed using Maxwell's equations.) Griffiths, "Introduction to Electrodynamics," provides the E and B field solutions for a point charge moving in any prescribed way.

BTW, to my knowledge it is a charge subject to a constant driving force that does not radiate, and not a charge moving with a uniform acceleration. Given a constant driving force, the charge's acceleration asymptotically approaches zero as its speed approaches c.