Paradox: Electron Radiates in a Gravitational Field

[stevendaryl]

Those three posts don't answer the question, at all. There is no reason, a priori, to believe that it takes the same amount of energy to accelerate a charged particle in an electromagnetic field as it does to accelerate an uncharged particle of the same mass. You can't compute the energy by simply knowing the mass and the final velocity.

When a charged particle is at rest in some frame, then I suppose that the mass of the particle already takes into account the electromagnetic energy. But is that true when the particle is accelerating, as well?

 

[Demystifier]

If it turns out that the energy required to accelerate a particle from rest to velocity $\vec{v}$ is independent of whether it's charged, that's a pretty remarkable thing. I'm pretty sure it's not true, in general.

I agree with that. That's similar to the fact that a car moving with given acceleration spends more fuel when the car's lights are turned on.

 

[stevendaryl]

I agree with that. That's similar to the fact that a car moving with given acceleration spends more fuel when the car's lights are turned on.

So it isn't obviously true that the energy required to transport a cargo of mass $M$ on board a Rindler rocket is independent of whether the cargo is charged.

But presumably, if the same rocket is hovering above a black hole, the energy required is independent of whether the cargo is charged.

 

[Demystifier]

But presumably, if the same rocket is hovering above a black hole, the energy required is independent of whether the cargo is charged.

I think that it isn't independent.

 

[Dale]

You cannot add together forces that belong to different categories.

Sure you can. You just need to make sure that the categories are mutually exclusive and collectively exhaustive.

 

[Demystifier]

Sure you can. You just need to make sure that the categories are mutually exclusive and collectively exhaustive.

But in this case they are not mutually exclusive because the rocket force has an electromagnetic origin.

 

[Dale]

But in this case they are not mutually exclusive because the rocket force has an electromagnetic origin.

Ok, so make that point instead. Adding forces of different categories is fine. Double counting is not.

 

[Demystifier]

Ok, so make that point instead. Adding forces of different categories is fine. Double counting is not.

Technically, you are right. But when you add forces from different categories, then there is a great risk of double counting or some other type of confusion. So in practice, it's better to avoid it.

 

[stevendaryl]

But in this case they are not mutually exclusive because the rocket force has an electromagnetic origin.

But the whole point I was making is that the force supplied by the rocket need not be the same for a charged versus uncharged cargo, because the charged cargo is moving through an electromagnetic field, while the uncharged cargo is not.

@PeterDonis wrote

Saying that it takes more force to keep a charged particle of mass M at rest in the same spaceship as an uncharged particle of mass M seems like saying that two objects following the same worldline can have different proper accelerations, which is impossible.

It's certainly true that the total force must be the same (by definition), but it doesn't follow that the force that the rocket must exert on the particle is the same, since the rocket is not the only thing exerting forces on the particle.

Certainly if you weigh a ping-pong ball on a scale in the presence of an electric field, the measured weight will be different if the ball has a charge on it.

 

[Rap]

I think of Einsteins elevator experiment. A guy and an electron in a box, all three are members of the same inertial system. If you accelerate the box, the guy and the electron drop to the floor, floor pushes back, and they are accelerated. If you put the box in a gravitational field, again the guy and the electron drop to the floor, floor pushes back to counter the force of gravity, and they are at rest. The principle of equivalence says that no experiment inside the box can detect the difference. If an electron is being pushed up by the floor in a gravitational field by whatever apparatus, and the guy in the box says it does not radiate, then the electron in the accelerated box being pushed up by the floor by the same apparatus will be deemed to be not radiating by the guy being accelerated along with that electron.