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For an accelerated charge to radiate, must an electromagnetic field be the source of the force?

Would it radiate if accelerated by a gravitational field?

John McAndrew
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5 Answers5

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Your question is somewhat abstruse, but here's what I think you're asking:

Put a charged particle in a uniform external magnetic field. The particle will move in a circular orbit, but since it's accelerating, it will radiate and its orbit will decay.

Now remove the magnetic field. Grab the charge and forcibly swing it around in the same circle as before by some other, unknown means. Does it still radiate in the same way as before?

The answer is yes because Maxwell's equations are linear. Therefore we can analyze any situation in classical electromagnetism by superposition.

Mark Eichenlaub
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    So a charge would radiate if accelerated by a gravitational field? – John McAndrew Mar 16 '11 at 16:41
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    @John McVirgo Yes – Mark Eichenlaub Mar 16 '11 at 16:42
  • nope, the gravitational field is the exception - radiating in free fall would violate equivalence principle – lurscher Mar 16 '11 at 17:09
  • @lurscher Good point. – Mark Eichenlaub Mar 16 '11 at 17:15
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    But then radiation of gravitational waves is also ruled out with the equivalence principle, isn't it? ;-) – Vladimir Kalitvianski Mar 16 '11 at 20:48
  • @lurscher, would be nice if you could give an answer with your point in it, so I can mark it as the correct one if others agree. – John McAndrew Mar 17 '11 at 00:40
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    @Vladimir, exactly! point-like masses in free-fall will not radiate gravitational waves; only extended objects with non-zero quadrupole moments will, please see my answer – lurscher Mar 17 '11 at 15:20
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    @lurscher: no. Bryce De-Witt wrote the paper on this--falling charges actually should radiate. Also, point-like objects DO radiate gravitational waves, a charge current has a quadrupole moment. The equivalence principle only works inasmuch as you can ignore the gravitational field of test particles. – Zo the Relativist Mar 17 '11 at 22:47
  • @jerry the answers so far don't answer my question, or are vague, so could you post an answer? – John McAndrew Mar 18 '11 at 23:02
  • @John: could you clarify your question a bit? I'm not 100% sure what you are asking, so it would be hard for me to be more clear than the existing answers. Are you asking about whether or not gravitational accelerations can cause charged particles to radiate? – Zo the Relativist Mar 18 '11 at 23:54
  • @Jerry Schirmer, yes that is what I asked in my question. It seems that your answers would be: 1. for a charge to radiate, an electromagnetic field doesn't have to be the source of the force causing the acceleration, the charge only needs to be accelerated. 2. Therefore charges do radiate when accelerated by gravity. Mention of Bryce De-Witt's paper showing that falling charges should radiate would be useful.Did Bryce De-Witt also take into account that the observers are in the Earth's gravitational field and so are equivalently accelerated? – John McAndrew Mar 19 '11 at 02:36
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    @lurscher: The principle of equivalence does not have that conclusion, since radiation is not a local effect. Charge that is accelerating (with respect to some distant observer) will radiate even though locally you can transform to a freely falling frame. In that frame the local electric and magnetic field generated will be that of an inertially moving charge, but that statement only applies locally. Radiation has to do with the behavior of those fields asymptotically, far away from the source, and specifically with how much energy flux (=radiation) they involve. –  Mar 19 '11 at 21:02
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The radiation, if considered classically, is independent for the reason Mark Eichenlaub gives. But considered quantum mechanically, it is not independent.

In short, photons are bosons. So the presence of radiation of a particular polarization and frequency will increase the probability of the particle radiating that polarization and frequency.

This is a topic I'd not seen before. I'll look around and see if I can find a reference to the effect.

An accelerated electron produces "synchrotron radiation". An example of the electromagnetic field altering the emission of such radiation would be "stimulated synchrotron emission". Stimulated emission was described by Einstein and is the physics behind lasers. An example paper combining these ideas:
Phys. Rev. Lett. 66, 2312–2315 (1991), J. L. Hirshfield and G. S. Park, Electron-beam cooling by stimulated synchrotron emission and absorption
http://prl.aps.org/abstract/PRL/v66/i18/p2312_1

Carl Brannen
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  • Since stimulated emission is by an E&M field, maybe the above should be excluded. However, I think I've answered the question under the usual definition of "accelerated" as opposed to "electromagnetic field". Hmmmm. Maybe the original question is a little loose. – Carl Brannen Mar 16 '11 at 06:27
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I suspect that two charged objects orbiting one another due to gravitational attraction would radiate, but I can't support that assertion with a citation.

The question of whether or not a charge radiates when it is uniformly accelerated by gravity is an open question; read the link for an excellent discussion of why.

EDIT:
The link I posted isn't inspiring trust, so I searched for peer-reviewed work. I found two relevant papers:
Physical interpretation of the Schott energy of an accelerating point charge and the question of whether a uniformly accelerating charge radiates
The significance of the Schott energy for energy-momentum conservation of a radiating charge obeying the Lorentz–Abraham–Dirac equation

I'm not qualified to comment on the quality of the papers, but both attack the question 'does a falling charge radiate', implying an open question. I didn't find any experimental work on the subject.

This brings up a topic better suited for meta-discussion: I would like to see even more external citations in the answers here. I would also like to see more answers clearly indicate their logical foundation. Is your answer based on...
- Original research?
- Predicted by peer-reviewed theory but unverified?
- Indirectly experimentally verified?
- Directly experimentally verified?
Don't make us guess!

Andrew
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  • I think this is the most germane answer; use gravity to cause the acceleration. Maybe there's a reference in rotating charged black holes. – Carl Brannen Mar 17 '11 at 00:35
  • what about Lurscher's point that a charge in free fall in a gravitational field doesn't radiate? – John McAndrew Mar 17 '11 at 21:14
  • How could this possibly be an open question? – Peter Shor Mar 17 '11 at 21:23
  • The link I included discusses the equivalence principle. Perhaps the link I included is not a reputable source? It does cite Feynman's lectures, which may be more reputable. If this is not an open question, I'd love to see a reference to the experiment that settled the issue. – Andrew Mar 17 '11 at 21:44
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    @Andrew: indeed, the link seems to be quite strange. It mixes lots of theories together in a weird manner and discusses irrelevant topics like self-interaction in classical theory while for the most part it omits the most relevant theory, QED (or anything quantum for that matter except for incorrect Feynman-Wheeler absorber theory). I would take that reference with a bit more than a grain of salt. – Marek Mar 17 '11 at 23:16
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    Orbiting bodies emit gravitational radiation (there was a Nobel prize given for verifying this). It would be very strange if charged orbiting bodies didn't emit electromagnetic radiation as well. – Peter Shor Mar 18 '11 at 11:20
  • @Peter Shor I agree! But without a citation, I didn't feel comfortable asserting this as fact. – Andrew Mar 18 '11 at 21:54
  • The calculation of radiation from circular orbits that @Peter is suggesting is standard in UG course in electrodynamics, and nothing in the calculation refers to the way the orbit is supported - the charge can orbit a massive object or being hauled by a pickup truck or being pushed by a million small fairies, it would not make a difference to that calculation. As for the confusion to do with the principle of equivalence, see my comment to @Mark's answer. –  Mar 19 '11 at 21:20
  • @Moshe I couldn't agree more, regarding radiation from circular orbits. However, I suspect all experimental verification of this fact has used electromagnetic forces, which is explicitly not what the question is asking about. I trust the theory, but I would still love to see an experimental citation that observes radiation from circular orbits caused by gravity. I also suspect this citation does not exist. I think we should work to cleanly distinguish between accepted (but unverified) theoretical predictions, and direct experimental observations. – Andrew Mar 20 '11 at 13:33
  • @Andrew, your question has no mention of experimental verification, which is why all the answers are about the theoretical predictions. Also, the main point of having a theory is making more predictions than experimental tests. You can only know finite number of facts by direct tests, theory which is consistent with all direct tests also tells you infinitely many other facts. Kind of pointless if you only believe in direct tests, in which case you don't need any theory. –  Mar 20 '11 at 16:49
  • @Moshe It sounds to me like we're in perfect agreement. I don't think either one of us "only believes in direct tests". If you would like to discuss this further, I've started a discussion on meta. – Andrew Mar 20 '11 at 17:29
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If you mean an external EMF, the answer is "The radiation is determined with an external filed". The charge acceleration is proportional to the external field, and a single accelerated charge radiates.

If you mean the radiated field influence on the charge motion and subsequent radiation, the answer is "No" because the radiation is only expressed via external field. There is no need to invoke the proper field here.

In QM radiation of hard single photons happens discontinuously in time so QM is somewhat different.

Vladimir Kalitvianski
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According to the equivalence principle, a point-like charge in free fall will not radiate EM waves, because its movement its locally equivalent to any other inertial frame.

point-like masses will also not radiate gravitational waves in free-fall by the same reason; gravitational wave emission is a function of the third time derivative of the quadrupole mass moment; this basically means that only extended, non-symmetric masses will give such radiation (being extended means that significant parts of the mass will NOT be in a inertial free-fall frame)

Edit: The only other macroscopic force outside gravity (and the force that is not a force called exclusion principle) is the electromagnetic field. I don't think we have any evidence how accelerated charges radiate in other non-EM forces (i.e: weak and strong) but theoretically acceleration induced on hypotethical macroscopic fields of such should produce the same effect

lurscher
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  • OK, the particle equations of motion do not say whether it radiates or not. How about field equations? What the Maxwell equations say in GR? What is the source of EMW in GR, not acceleration? – Vladimir Kalitvianski Mar 17 '11 at 15:28
  • classically, i think EM waves are also emitted as the third-derivative of position, but i forgot where i saw that (I think it was a quote from Dirac, but i've never seen the derivation) – lurscher Mar 17 '11 at 15:33
  • Let's forget about particle equations of motion and look at the EM field equations. What they say in case of GR? – Vladimir Kalitvianski Mar 17 '11 at 15:59
  • i don't know, what do they say? – lurscher Mar 17 '11 at 16:00
  • In CE the field solutions are explicitly written via particle motion. In case of acceleration there are "propagating" solutions caused with the charge acceleration. The Maxwell equations in GR are modified somehow but they exist anyway. I do not know how their propagating solutions arise in GR either. – Vladimir Kalitvianski Mar 17 '11 at 16:26
  • @Lurscher, could you add an edit to answer the first question as a yes, and the second as a no? The rest of your answer explains your reasoning clearly. – John McAndrew Mar 17 '11 at 21:12
  • @John, about the first statement, i don't know if that is true - it probably it is not; however we don't have any other macroscopic non-EM fields to test that experimentally. I don't know what the theory says on quark-gluon plasmas for extended QCD fields – lurscher Mar 17 '11 at 21:20
  • @Lurscher I think an observer on Earth would observe a charge in free fall as radiating Unruh radiation because his frame would be equivalent to an accelerated frame – John McAndrew Mar 17 '11 at 21:21
  • i think Unruh is only about the radiation from vacuum – lurscher Mar 17 '11 at 21:25