Charged particle at relativistic velocity

1. Jul 24, 2008

Privalov

Imagine a charged particle moving in vacuum with relativistic velocity. It emits electromagnetic wave with some known energy. This energy can be detected and used somewhere else. I guess this energy should come from particle’s kinetic energy, thus particle should slowly decelerate over time.

However, General Relativity states all inertial points of view are identical. If an observer moves near the particle with the same constant speed, he will believe particle stays still and emits no energy. From his point of view, particle should not decelerate.

Will the particle decelerate, after all?

I came up with the following assumption to resolve this paradox: if radio detector exists somewhere nearby, moving electrons n it’s antenna will attract to the moving particle by electromagnetic force, so particle will decelerate. If there is no radio detector nearby, particle will keep its speed.

However, then comes the next question: electromagnetic wave is a photon. Photon can be seen as a particle. Logically, it can not exist for some observers and does not exist for another observer.

2. Jul 24, 2008

George Jones

Staff Emeritus
A charged particle moving at constant velocity with respect to any inertial frame doesn't radiate.

3. Jul 24, 2008

cesiumfrog

That's going a bit far for the GR forum, do you deny a charged moon would radiate?

On topic, a charge with constant velocity will certainly cause a stationary observer to experience a changing electromagnetic field, and hence induce acceleration of charges in a stationary antenna (i.e., radiation of energy). Presumably there will also be a Lenz back-reaction such that it requires work to hold the charged particle at constant velocity.

4. Jul 25, 2008

Privalov

OK, so my guess was right. Now, can photon exist in some inertial frame of reference and do not exist in another? Is photon the same thing, as electromagnetic wave?

Quote: "According to Maxwell's equations, a time-varying electric field generates a magnetic field and vice versa."
http://en.wikipedia.org/wiki/Electromagnetic_waves

5. Jul 25, 2008

Staff Emeritus
A moon doesn't have constant velocity. It may have constant speed, but not velocity.

Yes, but when you add these other charges, you change the problem from the OP's single charge in vacuum. Different problem, different answer.

6. Jul 25, 2008

MeJennifer

Since we are discussing special and general relativity here I think you should explain why you think that the moon's velocity is not constant.

7. Jul 26, 2008

HallsofIvy

Staff Emeritus
Because it is not going in a straight line at constant speed, for God's sake!

8. Jul 26, 2008

MeJennifer

You seem to be talking about Newtonian mechanics not general relativity.

9. Jul 26, 2008