# Do electrons radiate when in free fall?

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## Main Question or Discussion Point

So, I've been reading a whole bunch of different answers to this online. Some people say yes, some people say no. I'm totally confused...

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Dale
Mentor
How do you want to measure the radiation? Especially, with a detector that is also in free fall or with an accelerating detector

Well, supposedly there is a paradox here, where the free fall frame doesn't see the electron radiate, but the lab frame does. However, I just looked on wikipedia, and supposedly the paradox is resolved by using the equivalence principle.

Not to an observer falling with the charge. Here is a link to an article that addresses that question in depth: "Radiation from a Uniformly Accelerated Charge and the Equivalence Principle," Parrott, S.,

https://arxiv.org/abs/gr-qc/9303025

Dale
Mentor
Well, supposedly there is a paradox here, where the free fall frame doesn't see the electron radiate, but the lab frame does. However, I just looked on wikipedia, and supposedly the paradox is resolved by using the equivalence principle.
That didn’t address my specific question to you.

Demystifier
So, I've been reading a whole bunch of different answers to this online. Some people say yes, some people say no. I'm totally confused...
It depends on how "radiation" is defined. In principle, it is straightforward (but not necessarily easy) to calculate the EM field around the charge falling in a gravitational field. The debate is about should such EM field be called "radiation".

Staff Emeritus
2019 Award

Second, with a background that seemingly includes neither a classical treatment of radiation (a la Jackson) or of GR, I don't think it's possible for us to give a better answer. Any deeper answer requires more background. Certainly picking up bits and pieces here and there isn't going to do this. This topic in particular, because for some reason it attracts people whose background includes neither a classical treatment of radiation or of GR yet they feel qualified to chime in.

Matterwave
Gold Member
Not to an observer falling with the charge. Here is a link to an article that addresses that question in depth: "Radiation from a Uniformly Accelerated Charge and the Equivalence Principle," Parrott, S.,

https://arxiv.org/abs/gr-qc/9303025
This paper seems (to me) to be making quite a bold claim in that it would invalidate at least the strong equivalence principle.

From the abstract:
We argue that purely local experiments can distinguish a stationary charged particle in a static gravitational field from an accelerated particle in (gravity-free) Minkowski space. Some common arguments to the contrary are analyzed and found to rest on a misidentification of “energy”.
Unless I'm reading this wrong, this would say that you could in fact, using only local experiments and charged particles, tell the difference between a uniform gravitational field or being uniformly accelerated. In fact, I think this would invalidate the Einstein equivalence principle as well wouldn't it? I wonder how this reconciles with the commonly held view that the strong equivalence principle is respected by GR or that Einstein built GR on top of his equivalence principle.

The conclusions in this paper seem to also say that the equivalence principle does not hold for charged particles (emphasis mine):
Does Einstein’s Equivalence Principle hold for charged particles? We cannot definitively answer this because a mathematically precise statement of the “equivalence principle” seems elusive — most statements in the literature are not sufficiently definite to be susceptible of proof or disproof. However, we do conclude that most usual formulations seem not to hold in any direct and obvious way for charged particles.
This seems to be in direct contradiction to other conclusions on the subject, e.g. this paper: https://arxiv.org/abs/gr-qc/0006037v1 or the papers by Fritz Rohrlich and Thomas Fulton.

As an aside, looking at that paper, the original was written in 1993 (before the paper I cited above) but the final version was in 2002 (after the paper I cited above was published)...that's quite a long time to be editing one paper, is there a reason for that?

vanhees71
Gold Member
2019 Award
I think, another paper by Rohrlich, treating the free fall of a charge in a uniform gravitational field using GR, is more to the point than the Fulton-Rohrlich paper, which is about the radiation of a charge in hyperbolic motion. The latter of course radiates in the inertial frame since it's accelerated. The trouble to get this obvious result is in the mathematical details, because hyperbolic motion is unphysical in the sense that it assumes that the particle accerates ad inifinity and thus its speed reaches asymptoticially $c$.

The paper about the free fall using GR is

https://doi.org/10.1016/0003-4916(63)90051-4

About the question with the special relativistic problem of radiation of a uniformly accelerated particle, see the nice AJP article by Franklin and Griffiths (the E&M textbook Griffiths!):

https://doi.org/10.1119/1.4875195
https://doi.org/10.1119/1.4906577 (erratum)

I am not sure about the definition of radiation. Where can I find its mathematical formula in electromagnetic field?

vanhees71
Gold Member
2019 Award
See the papers I quoted in #9. In the meantime I've found a much clearer paper than the one by Franklin and Griffiths, who overcomplicate the quite complicated issue of the em. field from a charged particle in hyperbolic motion (even Born and Pauli were wrong about it!) more than necessary. Now I'd rather recommend the paper by Cross quoted in Franklin's and Griffiths's paper:

https://arxiv.org/abs/1409.1569

atyy
So, I've been reading a whole bunch of different answers to this online. Some people say yes, some people say no. I'm totally confused...
An electron cannot be in strict "free fall", because it interacts with its own electromagnetic field.

The motion of point particles in curved spacetime
Eric Poisson, Adam Pound, Ian Vega
https://arxiv.org/abs/1102.0529
"In this picture, the particle simply interacts with a free field (whose origin can be traced to the particle’s past), and the procedure of mass renormalization is sidestepped. In the scalar and electromagnetic cases, the picture of a particle interacting with a free radiation field removes any tension between the nongeodesic motion of the charge and the principle of equivalence"

vanhees71