Charges in gravitational fields

[hellfire]

Accelerated charges emit radiation. Due to the equivalence principle there is no difference between an accelerated frame and a frame inside a gravitational field. But we do not experience any radiation from charges inside the gravitational field of earth. Why?

 

[DW]

Accelerated charges emit radiation. Due to the equivalence principle there is no difference between an accelerated frame and a frame inside a gravitational field. But we do not experience any radiation from charges inside the gravitational field of earth. Why?

This is discussed at
http://www.geocities.com/zcphysicsms/chap7.htm#BM7_2

 

[hellfire]

Ok, I went through that chapter. My understanding: the charge at rest on Earth does not radiate because of the global static behaviour of the field lines according Larmor's effect. This does not contradict the equivalence principle because it aplies only for local experiments and no global frame is definable in this case. Is this correct?

 

[DW]

Ok, I went through that chapter. My understanding: the charge at rest on Earth does not radiate because of the global static behaviour of the field lines according Larmor's effect. This does not contradict the equivalence principle because it aplies only for local experiments and no global frame is definable in this case. Is this correct?

There are global frames. Its just that none of the global frames for this case are globally inertial. But otherwise, yes. The experiment is intrinsically non local, so a statement about local equivalence does not apply.

 

[outandbeyond2004]

Let's just try to get away from gravitational fields for now and consider these 4 cases:

(1) The charged particle is at rest in an inertial frame of reference, and you are also.
(2) The charged particle is accelerating ("feels" an acceleration), but you are at rest in an inertial rf.
(3) The charged particle is at rest in a irf, but you "feel" an acceleration.
(4) The charged particle feels an acceleration and you do also.

(1) - no radiation.
(2) - radiation
(3) - radiation
(4) - depends. If you are always at rest wrt the particle = NO radiation. Otherwise, radiation.

Now, let's get back to Earth. Does the gravitational field of Earth change anything? Not really. It still depends on the relative acceleration, although that may become problematic to calculate in odd-ball cases I guess. The fact is, even if both the charged particle and you follow geodesics (essentially case 1 above), there may nevertheless be relative acceleration between you and the particle ("tidal effect"). I suppose then there should be some radiation.

The subject of energy and power may not be well thought out yet in GR, unfortunately.

 

[hellfire]

Now I am confused. Do you claim that the radiation emitted by accelerated charges is an observer-dependent phenomenon? If yes, it seams to me that this is in contradiction with the reference DW gave us.

As far as I understood, there the norm of the four-acceleration is used in the Larmor formula, which makes the radiated power invariant (refer to eq. 7.2.3).

So, what kind of acceleration is the one to be used in the Larmor formula? Furthermore, what is the validity of this formula?

Regards.

 

[DW]

Now I am confused. Do you claim that the radiation emitted by accelerated charges is an observer-dependent phenomenon? If yes, it seams to me that this is in contradiction with the reference DW gave us.

As far as I understood, there the norm of the four-acceleration is used in the Larmor formula, which makes the radiated power invariant (refer to eq. 7.2.3).

So, what kind of acceleration is the one to be used in the Larmor formula? Furthermore, what is the validity of this formula?

Regards.

Some people do claim this and they are wrong. They are usually mixing Larmor radiation which is known to exist with Unrah radiation. Larmor radiation is a far field effect and as such is frame invariant. Unrah radiation is hypothetical and yet to have any experiment to support a belief that it even exists. In the link I gave the "a" is coordinate acceleration with respect to a globally inertial frame. The A is the four-vector acceleration and those tensor equations with g_mu_nu in them are relativistically correct for any spacetime for which a global inertial frame exists whether you are using that frame or not.