Surely if a charge particle radiates under electrical acceleration you also expect it to radiate under gravitational acceleration. Except that the former effect is much stronger and easier to observe.

Of course a stationary charge is not expected to radiate.

If it was moving and you stop it, the breaking radiation is well known.

No radiation in quantum situations.

Things are not that simple when we are discussing this subject! The question is an old one, and physicists as competent as Max Born and Wolfgang Pauli have studied it, and arrived at opposite conclusions!

That is what I think at any rate. Accelerated charged particles radiate, never mind what causes the acceleration(in clasical mechanics) If not current theory is incomprehensible.

Obviously we are not talking about the frame where the charged particle is at rest, but in a lab frame where you see the particle accelerate.

Thanks for your contributions so far. Since I posted the question, I came to realize that it is very important to consider the reference frame you are in when observing the charge, either in free fall or blocked by it. It is actually a well-known real "problem" (in the meaning of theoretical/calculational challenge) in physics, and it is non-trivial to tackle.

I agree with J.A. Souza that things are not at all trivial. I came across several papers, some of them stating that there be no radiation, some stating that there is! What needs to be borne in mind though is in any case what reference frame the observer is: is he freely falling or static (= blocked by free fall).

A good starting point for further research seems to be this: Article Radiation from a Charge Supported in a Gravitational Field

with some further references.

Juan Weisz : no, accelerated charges to not radiate at any rate. This is what the strong equivalence principle says. Vacuum electrodynamics is not valid in the presence of gravitation without modification. The same applies to any classical field theory. The mathematical way to implement this in a semiclassical way (only !) is via the relativistic correspondence principle to substitute partial derivatives by covariant derivatives. As a consequence, you should end up with exactly this result, albeit I am still missing some down-to-earth calculations. Hence my question!

I would like to understand, therefore, how to tackle this problem from a quantitative point of view: my concrete questions being:

- what is the radiation power of an elementary charge at rest on Earth's ground measured by an observer equally at rest on Earth's ground? And what does a freely falling observer measure?

- how is the back-reaction upon spacetime (curvature) to be considered calculationally?

Oliver, I misunderstand the first statement, sentence. If you simply say

accelerated charges do not radiate, you must be wrong. at least in the cases where such effect is known.

If you get to very strong gravitational fields I admit you dont

radiate because the radiation does not leave a black hole, but no one sais that the charges are not radiating, only that the radiation cannot get out.

With what result should I end up with?

Exactly what is the equivalent principle argument in the case of radiation?

Regards, Juan

Dear Juan, the point is: under all well-known circumstances, lab situations etc., accelerations caused by collisions, synchrotons, etc. are vastly bigger than gravitational "accelerations", approximately by a typical factor of 10^20, than accelerations caused by free fall. This is why under "normal" circumstances it is practically impossible to measure any effect which would be caused by gravitation, and this is why the Larmor formula works well in all practical situations.

The gedanken experiment I am envisioning is a freely falling charged particle where no other accelerating effects are in place (otherwise it would not be freely falling anyway!).

For this reason, the topic under discussion if mostly a theoretical, albeit fundamental question.

And it is not a question to be answered by relativity, in my opinion, because the (strong) equivalence principle should be completely sufficient for calculating the effect, via the correspondence principle. However, when we regard the back reaction of any emitted radiation upon the spacetime metric, then relativity must be considered!

This exciting, apparent paradox was resolved almost 5 decades ago. The resolution hinges on the basic notions of (a) radiation, which is EM amplitude falling as 1/r at very large radial distance r from the source, and (b) local inertial frames. Equivalence principle states that it is always possible to choose a sufficiently small enough frame for a sufficiently short duration in which the space-time geometry is locally flat (i.e. a limited size frame that falls freely in a arbitrary gravitational field). So, as argued by Dr. Oliver Tennert, it is true that in a freely falling frame the charge is not accelerating, BUT this is true only for a limited duration, as such a locally inertial frame cannot be very large in space and time when real gravity is present. On the other hand, radiation is flow of energy across surfaces that are at very very large distances. Hence, detailed calculations reveal that for big frames at such large distances, the aforementioned electric charge does accelerate and thereby does radiate EM waves.

Dear Patrick,

thanks for your reply. Could you point me to some relevant papers showing concrete calculations?

Best regards

Oliver

Please see http://inspirehep.net/record/44837/files/vol1p3-20_0

Also, a recent review: Article Electrodynamics of Radiating Charges

Thank you very much! I will take my time to read this. In any case, these seem to be serious and well-esteemed authors.

You are welcome. Yes, DeWitts were great theoretical physicists.

Das Gupta has it right. For a good discussion see the section on caveats regarding the equivalence principle in Wolfgang Rindler's "Relativity: Special, General, and Cosmological". Basically, the accepted solution to the paradox is that the electromagnetic field of the charge extends beyond your local inertial frame as Das Gupta pointed out. However, there are those who think the equivalent principle itself should be shelved. Rindler explains how these critics argue that there is never an exactly uniform gravitational field. With sufficiently accurate instruments you could always measure tidal forces. Rindler seems to argue that the EP is OK because it holds in the limit as the LIF shrinks toward a point. (Let me just say that Rindler was one of my profs at UTD and is a prince of a guy as well as a renowned researcher.)

Thanks for all your replies! I am now reading the paper by de Witt/de Witt-Morette. I think this answers my question, but the calculation is lengthy indeed. As I already mentioned, the exposition in Rindler's book actually was too short and superficial in my opinion, and it would have been great if he had given some citations...but anyway, I am satisfied now.

Best regards

Oliver

On this occasion, a serious discussion arose between Ginzburg and Logunov in the journal Phys. Usp. I have Russian copies that are free.

https://ufn.ru/ufn96/ufn96_1/Russian/r961d.pdf

https://ufn.ru/ufn95/ufn95_2/Russian/r952e.pdf

English citation: Ginzburg V L, Eroshenko Yu N “Once again about the equivalence principle” Phys. Usp. 38 195–201 (1995);

I deal with another aspect of the equivalence principle.

Preprint J. Bell's Relativistic Paradox and Equivalence Principle

and further

Book article

Rudolf Peierls Surprises in Theoretical Physics