Equivalence principle implies uniformly accelerated charge doesn't radiate?

[mfb]

Don't we have direct evidence of orbiting charges radiating from black hole X-Ray radiation? The metric is the same, so I don't see why it should be much different on Earth's orbit, other than in magnitude, of course.

This is thermal radiation. Gravity just helps to compress and heat stuff, it does not generate the radiation itself.

 

[Andrew Mason]

Yes, there is a real difference. I'm not sure about the electric dipole specifically, but as a rule of thumb one cannot naively apply the equivalence principle to charged particle trajectories. For example, one might be inclined to think about a "free falling" charge - but generally a charge cannot be free falling because it is acted on by the field it produces.

Does that mean that a charge in free-fall will always have a non-symmetric electric field - right down to the smallest distances? That seems to be something that is testable. It seems also to violate the principle of equivalence because it shrinks the meaning of 'local' to an arbitrarily small region.

I think the dipole is important because one could always create an electric dipole by separating + and - charges in a neutral body. Many molecules (eg. water) have an electric dipole moment. If a dipole in free-fall radiates, then a great deal of matter in freefall must radiate. Mind you, there is likely a quantum mechanical threshold for radiation for an electric dipole ie. quantum harmonic oscillator.

AM

 

[atyy]

Does that mean that a charge in free-fall will always have a non-symmetric electric field - right down to the smallest distances? That seems to be something that is testable. It seems also to violate the principle of equivalence because it shrinks the meaning of 'local' to an arbitrarily small region.

Yes, in principle the EP applies only to an arbitrarily small region - a point, and even then only as long as one does not look at spacetime curvature.

I think the dipole is important because one could always create an electric dipole by separating + and - charges in a neutral body. Many molecules (eg. water) have an electric dipole moment. If a dipole in free-fall radiates, then a great deal of matter in freefall must radiate. Mind you, there is likely a quantum mechanical threshold for radiation for an electric dipole ie. quantum harmonic oscillator.

I don't know the quantitative answer, but here's my guess. Let's first ignore gravity and the equivalence principle, and do classical electrodynamics in flat spacetime. If we put water in a car and accelerate it, we generally do not detect radiation, so water can be treated as effectively neutral and classical at our level of experimental accuracy, ie. we don't worry about water violating classical electrodynamics even though we don't detect radiation when we accelerate it. For this reason, at the same level of accuracy for which water in a car is considered neutral, we also don't expect to detect any violation of the equivalence principle when water is accelerated by a gravitational field.

But at some level, one might think the non-neutrality of water at small scales does come into play. I don't know the answer for what one might expect then. For example, is it a limiting factor in our ability to do extremely precise equivalence principle tests?

 

[Andrew Mason]

I don't know the quantitative answer, but here's my guess. Let's first ignore gravity and the equivalence principle, and do classical electrodynamics in flat spacetime. If we put water in a car and accelerate it, we generally do not detect radiation, so water can be treated as effectively neutral and classical at our level of experimental accuracy, ie. we don't worry about water violating classical electrodynamics even though we don't detect radiation when we accelerate it. For this reason, at the same level of accuracy for which water in a car is considered neutral, we also don't expect to detect any violation of the equivalence principle when water is accelerated by a gravitational field.

I think you would have to reduce the water temperature to close to absolute 0 as well. Otherwise the thermal radiation would predominate. So it would be a pretty difficult thing to test.

AM