On 3/20/2019 1:59 PM, John Clark wrote:
On Wed, Mar 20, 2019 at 3:06 PM 'Brent Meeker' t
<everything-list@googlegroups.com
<mailto:everything-list@googlegroups.com>> wrote:
>> If you were in a elevator with a charged particle
accelerating due to gravity
> You mean the elevator is stationary relative to the Earth and the
charged particle is accelerating, i.e. falling, due to gravity?
Or do you mean both the elevator, you, and the particle are in
free fall?
If the elevation is stationary sitting on the surface of the Earth
then it is not accelerating, nor is it in a inertial frame because a
force from the ground is being applied.
OK. But that doesn't clarify what you meant by, "you were in a elevator
with a charged particle accelerating due to gravity."
The "paradox" is that if the elevator is sitting still on the surface of
the Earth and you, in the elevator, drop a charged particle, then, as it
falls, standard electrodynamics says it will radiate and you can detect
the radiation (does it fall slower or faster because it radiates?). But
the EP says this should be the same being in the elevator accelerated by
a rocket; in which case when you release the particle you and the
elevator continue to accelerate and the particle doesn't, so there
should be no radiation observed.
>> or due to a rocket in deep space you would not observe any
electromagnetic radiation, although if the elevator were made
of glass an outside observer who was not accelerating would.
> But in that case the observer in the elevator would see the
particle mysteriously lose energy without radiating.
I'm not sure I know what you mean. If you're accelerating side by side
with a electron by exactly the same amount how could you observe the
electron lose energy?
A good question, but if the outside observer (who is either inertial or
stationary, I'm not sure which) sees radiation then the energy must come
from the gravitational potential of the falling (and accelerating)
charged particle.
How would that loss of energy manifest itself to you? It's true that
depending on the reference frame a electric field can look like a
magnetic field and vice versa,
That's true even for uniform motion in SR. No acceleration required.
but it makes no difference if the acceleration is caused by a rocket
or a gravitational field, you can't use that effect to tell the 2
situations apart.
John K Clark
This paper concludes that a charged particle which is uniformly
accelerated in gravitational field does radiate, but this radiation
cannot be detected by an observer who is moving with the particle
because the radiation will be beyond an event horizon relative to the
observer.
The radiation of a uniformly accelerated charge is beyond the horizon: A
simple
derivation
Camila de Almeida & Alberto Saa
By exploring some elementary consequences of the covariance of Maxwell’s
equations under general
coordinate transformations, we show that even though inertial observers
can detect electromagnetic
radiation emitted from a uniformly accelerated charge, comoving
observers will see only a static
electric field. This analysis can add insight into one of the most
celebrated paradoxes of the last
century.
arXiv:physics/0506049v5
So if a charged particle is stationary in a gravitational field, as on
the surface of the Earth, it is accelerated in spacetime (non-geodesic
motion) and radiates, but this is not observable by someone at rest
relative to it because of the Rindler horizon.
This paper discusses the result, the impossibility of empirical tests,
and compares the question of radiation by EM accelerated particles.
arXiv:1509.08757v3
Both of those papers consider uniform gravity fields and uniform
accelerations. They reference this paper, which considers general motions.
arXiv:physics/9710036v1
Brent
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