# Why does an Accelerating Charge Radiate - Solved or Unsolved?

1. Mar 3, 2005

### controlfreak

Are the questions

a) why does an accelerating charge radiate

and

b) why does an uniformly accelarating 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 [Broken]

which got me thinking. Is this an unsolved thing?

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

Last edited by a moderator: May 1, 2017
2. Mar 3, 2005

### ZapperZ

Staff Emeritus
Eh? Isn't (b) a subset of (a)? You are contradicting yourself.

Zz.

3. Mar 3, 2005

### controlfreak

and also:

Please explain why an uniformly accelerating charge doesnt radiate in order to uphold "conservation of energy" (or whatever you mean by that)?

The two questions where to distinguish the cases : an non uniformly accelerating charge and uniformly accelating charge, but also to illustrate that the uniform accelaration as an exception case to the theory which proclaims accelarating charges radiate. The contradiction in my question was intentional. I am glad that it struck a note and produced the desired effect

4. Mar 3, 2005

### ZapperZ

Staff Emeritus
Do you think "uniformly accelerating charge" is not included in "accelerating charge"? I said earlier that "uniformly accelerating charge" is a SUBSET of "accelerating charge". From basic mechanics, this should have been obvious.

And also from basic mechanics: an object moving with a constant velocity requires NO WORK to be done on it. An object moving with an acceleration (be it uniform, non-uniform, etc, etc..) requires that work be done on it. Since you said that you already have an "M.S", I would leave the rest for you to check up in either Griffith or Jackson to figure out where the work done on a charged particle would go to.

Zz.

5. Mar 3, 2005

### controlfreak

I am not saying that "uniformly accelerating charge" is not included in the concept of an "accelerating charge". I agree the former is a subset of latter, I only said that, I intentionally made a contradiction (mistake) in my statement to highlight the discrepancy with respect to the fact that the theory for a set doesnt hold good for a subset.I see you have missed that subtelity in my questioning. Anyway that is besides the main question.So let is not argue on this. I give it to you.

I am well aware of radiation fields, Larmor Formula and derivation (supposed) of abraham-lorentz formula for the radiation reaction force (possibly self force of a point charge) from conservation of energy.But abraham-lorentz formula has some implications/classical inconsistencies which are listed by grifiths which you can very well read from that book.

Anyway leaving that, what I dont understand is the fact that why then should an "uniformly accelarting charge" not emit radiation (as shown in experiments)? The theory given in grifiths doesnt preclude it.

What theory explains this discrepancy or exception?

Last edited: Mar 3, 2005
6. Mar 3, 2005

### ZapperZ

Staff Emeritus
What experiment has shown that uniformly accelerating charge does NOT emit radiation? If this is true, why the hell is there so much shielding around all those synchrotrons and cyclotrons?

Zz.

7. Mar 3, 2005

### controlfreak

Quoting from an article:
http://www.mathpages.com/home/kmath528/kmath528.htm

In Feynman's "Lectures on Gravitation" he says "we have inherited a prejudice that an accelerating charge should radiate", and then he goes on to argue that the usual formula giving the power radiated by an accelerating charge as proportional to the square of the acceleration "has led us astray" because it applies only to cyclic or bounded motions.The radiation reaction force (and therefore the radiated power) is proportional to the third derivative of position, so if the particle is undergoing constant acceleration it does not radiate.

This claim of feynman has been rubbished by other people.

Richard Becker says:

"Absurd results are obtained if [feynman's eqn] is applied to other forms of motion, such as the retardation of a free electron in a constant opposing field. In this case only the second derivative would be different from zero, and [feynman's eqn] would therefore predict no radiation damping at all.

The above derivation of the radiation damping is unsatisfactory, because it is not at all clear how the emitted spherical wave influences the electron's motion. In order to gain a closer understanding of the nature of this "self-reaction" it is necessary to compute the resultant force on all electron volume elements... Types of motion [such as that of the free electron] can only be treated in the light of a more precise knowledge of the structure of the electron...
"

My question is that has the physics community reached a conculsion on this debate??

Last edited: Mar 3, 2005
8. Mar 3, 2005

### ZapperZ

Staff Emeritus
Correct me if I'm wrong, but you DID SAY "... as shown in experiments...", didn't you? None of what you talk about above has anything remotely connected to any experimental observation, no?

Zz.

9. Mar 3, 2005

### controlfreak

I supposed that there were experiments which proved that the uniform accelarted charges doent radiate considering the fact that a lot of work in theory has been done exactly to prove that. I assumed that nobody tries to prove opposite of experimental result.

Anyway that (experimental results or not) is besides my actual question as I have to search more of the internet for that.

BUT There is still exists a confusion in the physics world that whether a uniformly accelerated charge radiates or not.

"all accelarating charges radiate" is a debatable issue when considering the uniformly accelerated charge. The evidence of this debates is all over. I have already provided 3 articles which contain further references on this specific debate.

My question is that whether this debate is over and have we reached a consistent non debatable theory?

10. Mar 3, 2005

### ZapperZ

Staff Emeritus
Then you will pardon me if I, as an experimentalist, will WAIT till you can produce some.

Zz.

11. Mar 3, 2005

### Andrew Mason

The question can be posed on several different levels:

1. Does a charge radiate when it is accelerated by means of an electromagnetic force?

The answer is most certainly YES. This is what Zapperz is referring to when he talks about synchrotron radiation. Very high speed electrons radiate enormous quantities of EM radiation when subjected to magnetic forces. These magnetic forces can be uniform (as in bending magnets) or non-uniform (as in 'wiggler' or undulator magnets).

2. Does a charge radiate because it is experiencing acceleration?

The answer to this is not so clear. If it radiated em energy because of the acceleration, one would predict that a charge accelerating due to a gravitational field would radiate. But it doesn't. Nor does a charge at 'rest' in a gravitational field whose weight is opposed by an equal and opposite electrical force (as in the Millikan experiment) radiate (according to Einstein's General Theory of Relativity, this is equivalent to an electron uniformly accelerating in the absence of gravity).

3. Is the radiation caused by acceleration but only non-uniform acceleration?

The answer to this is also not clear. It appears that all non-uniformly acclerating charges do radiate. But if the answer is 'yes', then one would expect that all uniform acceleration - whether produced by gravity or electromagnetic force - would not cause the charge to radiate. But this is not the case - as Zapperz will tell you from working with electrons in a synchrotron uniformly accelerated as they pass a bending magnet.

The contention that an electron radiates when accelerated is based on a theory that the electron interacts with its own field when accelerated. It is, as far as I can tell, unproven and still controversial. Feynman appears to have taken different positions on that. He may have ended up believing that it all depends on how you want to look at it, suggesting that there may be more than one 'correct' equivalent explanations.

I would highly recommend that you read Feynman's Nobel Lecutre to get a sense of his thinking on this most interesting subject (at least in 1965):
http://nobelprize.org/physics/laureates/1965/feynman-lecture.html

If we could find a particle that possessed charge but no mass, we might be able to answer this question. But it appears that charge and mass cannot be separated.

In any event, to answer your question: this appears to be still an open question in physics (but one for which there may not be a 'correct' answer).

AM

12. Mar 4, 2005

### controlfreak

Thanks a lot AM for that comprehensive and lucid answer, especially the way you have linked the presence of radiation to the means of acceleration (gravity/EM).

Question:
Are we very sure that the electron doesnt radiate due to graviational field or could it be just that the raditation is very less that one is not able to detect it?

13. Mar 4, 2005

### Andrew Mason

Good point. Experimental evidence shows that a charge does not radiate when accelerating in a gravitational field but it is very difficult to measure because the amount radiation (ie. for the equivalent electrical force) is very small.

If it did radiate, General Relativity would go out the window. GR says that a mass in free fall in a locally uniform gravitational field (ie. gravitational force on all parts of the mass is same - no tidal forces) is equivalent to an electron in uniform motion in the absence of gravity.

The evidence, to me, indicates that it is the interaction of the electrical/magnetic force with the field of the charge that causes radiation. Since the charge also has mass, the charge accelerates as well. But the acceleration is not the cause of the radiation.

AM

14. Mar 18, 2005

### Antiphon

A charge at rest in a gravitational field is accelerated (assume uniformly)
yet does not radiate. Therefore (by equivalence) a charge at rest in a
uniformly accelerating reference frame does not radiate *in that frame*.

Thus if you suppose you are next to a charge in an elevator that is
undergoing uniform 1 G acceleration, it will not appear to emit radiation
to *you*.

But an observer in a nearby non-accelerated frame will measure the
presence of both electric and magnetic fields changing as a function
of time. Time-changing fields (in free space) will result in radiation.
There IS radiation coming from the accelerating charge which can be observed in other frames. The energy for this radiation comes from the mechanical source which is accelerating the charge, it's prime mover.

The observer in the elevator sees no radiation, but *does* measure
an anisotropic field in the elevator *and through all of space*.
That is, the static electric Coulomb field at the top of the elevator
is different than at the bottom. There is a time-static spatial potential
energy variation in this Coulomb field that has an equivalent mass which
takes work by the elevator's prime mover to accelerate.

If you transform this time-static spatial variation of the Coulomb field
back into the uniformly moving reference frame, you will recover the

Last edited: Mar 18, 2005
15. Mar 18, 2005

### Andrew Mason

There is, of course, no such thing as a mechanical force. There is only eletromagnetic force and gravity (nuclear interactions do not apply). So are you saying that it must be the electromagnetic interaction that provides the energy for this radiation?

AM

16. Mar 21, 2005

### Antiphon

There are two (equivalence-based) situations. The uniformly accelerated
reference frame (man next to charge in elevator going up at 1 G) and the
uniform gravitational field (charge sitting still in lab on "earth").

In the uniform gravitational field the charge does not radiate, period.

In the uniformly accelerated case, the charge *does* radiate but not
to the observer in the accelerated frame. It only radiates to other observers.

is radiaitaing away in the second case is *work* done by whatever is
accelerating the charge. It doesn't matter what the source of this energy
is. You may assume it is a chemical rocket engine.

Lest anyone conclude that this violates the equivalence principle, rest
assured it does not, any more than the fact that a mass in a uniformly
accelerated frame gains kinetic energy while a mass in a gravitational field
does not. The equivalence princile says that it is impossible to distinquish
a difference between the two by doing expeiments *in those two frames.*

17. Mar 21, 2005

### Andrew Mason

This is still somewhat controversial. I have never been able to understand how the radiation could be inaccessible to the co-accelerating observer. It is not as if the em wave from the charge does not pass through the 'co-accelerating' observer. How does the radiation escape detection? This paper seems to conclude that the co-accelerating observer exception theory is not correct, if I understand the abstract correctly.

You seem to be saying that the force supporting the charge at rest in a gravitational field is doing work. But I don't see any distance that the supporting force acts over.

AM

18. Mar 22, 2005

### Antiphon

[I cannot acess the link below for some reason.]

In the accelerating frame, there is no radiation but there is a distortion of
the usual Coulomb field through all space as seen by the accelerating
observer. So it is seen by the accelerating observer- just not *as*

Regarding the force, the work is supplied by the motor to the charge, not
by the charge's support. The observer in the elevator sees no work being
done on the charge (as you say, no distance).

19. Mar 22, 2005

### Andrew Mason

It appears that the link to the actual paper is a transient one. You can find the paper by clicking the link and searching for "ashok k. singal".

Thanks for this explanation. I am not sure I understand it though. I am having trouble understanding how there could be a time dependent field in the inertial rest frame and a static field in the co-accelerating frame (ie. stationary observer in gravitational field at the same location as the charge) but it may just be my general ineptness in this area, particularly in tensor analysis.

AM

20. Mar 23, 2005