Why does an Accelerating Charge Radiate - Solved or Unsolved?

[yoron]

I can see your thinking Antiphon. Potential energy right :)

To me it comes how to see kinetic energy. Naively expressed every object in the universe will have a different kinetic energy relative you, depending on your choice of 'system' to observe. And they have it with you simultaneously. So kinetic energy, to me that is :), reminds me more of defining a relation than a actual 'energy'. That relation will fall out naturally with an collision f.ex with any of those objects and will be unique for each case but as long as we don't have an actual interaction it's only a possible outcome.

And potential energy in this relation is the description of what kinetic energy we can expect from our defining a system, like pencil Earth and pencil rocket in the other case. From your own frame of reference your heartbeat will have the same beat, according to your wristwatch, in the rocket as well as on Earth. So in that frame everything will be 'as usual' according to you in a black box scenario counting on a uniformly accelerating motion by your rocket at f.ex one G. And until death by tidal forces or other, to the one inside that black box, 'unexplainable circumstances' that frame will be equivalent to Earth. And whatever potential energy that have been built up will only be a relation, observed by you being at rest relative Earth, as a real 'energy' but as defined from inside that black box as non-existant as there is no way for you to realize it in that frame except in a interaction, like f.ex a collision.

I'm not discussing CBR and what that can do relative your acceleration in a vacuum here :) btw. In reality you have all kinds of 'interactions' possible in a vacuum as describer by the Rindler observer (Rindler effect) But I'm just using a isolated example, like the original 'black box' used for the equivalence principle. Would you agree to how I see it or do you think I missed out on things here?

Yoron.

 

[Antiphon]

I agree with you for those parts of your post that I know about and will take your word for the rest.

There are some interesting papers about acceleration and quantum fields which you may like. Look for publications by Ulrich Gerlach at the Ohio State University.

 

[yoron]

Thanks Antiphon.

I don't know that much, all to little in fact. It's just that I'm trying to learn :)
As we all are I guess. I will definitely look up your suggestions.

Be cool.

 

[ynot]

I think Antiphon hit upon it. If you drop an electron in a gravitational field, and it speeds by you, you should feel radiation from the accelerating charge. Conversely, if you are accelerating past an electron, you should also experience radiation, being that in classical physics electromagnetism is based on relativistic motion. I understand that if you stand next to the LHC while charges are circling through it, that there is enough radiation to kill you in a relatively short time because of the accelerating charges (the centripetal force of the magnets forcing the charges to curve in a circle). If you were riding along with the protons, or mercury nuclei in some cases, you would not experience any radiation, right? So it's relative, an electon sitting on a chair next to you is experiencing the same acceleration as you, and there is no relative spatial motion to you, so it doesn't radiate to you.

The earliest model of the atom (electrons orbiting a nucleus), was ridiculed because classical physics predicted that the electron would radiate and spiral into the nucleus. Quantum physics allowed atoms to be by preventing infinitesimal energy changes in a potential field. So that is one place where uniform acceleration (including relative motion) does not cause a charge to radiate.

 

[yoron]

I liked the explanation(s) too, it's just that I'm unsure. If you accept the idea of equivalence then the question seems to become how far you can 'draw it'? As Antiphon saw it, as I understood it, the difference between the frames was that one frame was expending energy (rocket) and the other wasn't.

And expending energy for velocity have very strange effects for that frame relative others. It's only without any comparative evidence those frames are equivalent, looking out a window would destroy the equivalence f.ex. Is there any way to expend energy without begetting a radiation btw? I was thinking of using the sun instead but it falls on that it will radiate there, and the reason for that one was the question if it was the 'energy spent' or 'velocity' that would create the effect if so.

As for dropping an electron into a gravitational field?

That one gives me a headache :) Consider it empty on other particles, just you and that electron 'free falling' down some ? No 'static' EM fields around, just that electron. Would it then radiate? And then have a far observer at rest versus the gravitational field 'accelerating' you. Would they see the same?

Why?

But the explanation Antiphon presented was quite good.
And understandable, which is even better :)

 

[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.