# Does a linearly accelerated charge radiate?

Does a linearly accelerated charge radiate? And if yes, is the electromagnetic waves emitted detectable from both its non-inertial frame and from other observing inertial frame? And If yes, doesn't this contradict with Einstein Equivalence principle?

• Are you asking about linear acceleration with arbitrary time dependence? Or uniform acceleration? – G. Smith Sep 24 '20 at 17:42
• @G.Smith: The mention of EEP makes me certain that OP is interested in constant acceleration. – A.V.S. Sep 24 '20 at 20:28
• Then the OP should say so. The question is unclear because linear acceleration has nothing to do with the Equivalence Principle. – G. Smith Sep 24 '20 at 22:03

Does [a] linearly accelerated charge radiate?

"It depends". Accelerating relative to whom?

Is the electromagnetic waves emitted detectable from both its non-inertial frame and from other observing inertial frame

No.

Doesn't this contradict with Einstein Equivalence principle

This is indeed an apparent paradox in GR.

The solution to the paradox is to accept and acknowledge that radiation has no absolute meaning. Which is the reason of the "it depends" to the first question. The emission and detection of radiation depends both on the motion of the source (radiation field) and on that of the observer.

An inertial observer, stationary with respect to the accelerating charge, will indeed detect the radiation.

But a comoving observer, to whom the charge is at rest, will not detect any radiation. Simple reason being that yes, in their frame the charge is not accelerating. The mathematical reason is that, when you put this in Rindler coordinates, the charge and its field are enclosed in a horizon.

• Are you talking about uniform acceleration? Linear acceleration includes 1D simple harmonic motion, which certainly radiates. – G. Smith Sep 24 '20 at 17:47
• @G.Smith Yes uniform acceleration, like a graviational field. – SuperCiocia Sep 24 '20 at 17:47
• OK, but the OP didn’t ask about that. They may have intended to, though. – G. Smith Sep 24 '20 at 17:48
• @G.Smith Ok sorry, it seemed to me they were asking about the typical paradox of whether a free-falling charge emits radiation as seen by a free-falling observer. – SuperCiocia Sep 24 '20 at 17:49
• I suspect you’re right. I suggest editing your answer to say that you are assuming uniform acceleration. – G. Smith Sep 24 '20 at 17:50