Accelerating Charged Particle: Does it Fall Slower?

[cragar]

So I was doing a problem in Griffiths and it talked about an electron in free-fall towards earth.
And it would radiate. So does a falling charged object fall slower than an uncharged object.
Because some of its Gravitational potential energy goes into radiation and not all kinetic energy.

 

[Antiphon]

It doesn't radiate until it hits the earth.

 

[jfy4]

When a particle is in free fall, it is just following the space-time curvature. This comes from

$$\nabla\mathbf{u}=0$$

where $$\nabla$$ is the covariant derivative. That is, the particle cannot "feel" acceleration. So no, it does not radiate.

 

[cragar]

Then why does Griffiths say : "An electron is released from rest and falls under the influence of gravity. In the first centimeter, what fraction of the potential energy lost is radiated away? " Maybe I left out the fact that it started from rest.

 

[Antiphon]

Sounds like a trick question.

You can do a thought experiment to show this.

Imagine a metal box in free fall above the earth. In the box is a scientist and a large charge. If the radiative hypothesis were true, the box would feel a retarding force. As a result the scientist would feel a small amount of gravity, thus violating the equivalence principle.

 

[Naty1]

Is this a valid perspective:

Relativity does not view free fall as acceleration...Is this exactly the same as post #5??

 

[jtbell]

And it would radiate.

So no, it does not radiate.

This turns out to be a surprisingly tricky question which has stirred up controversy even among the professionals. There have been a number of threads about this on PF, for example:

https://www.physicsforums.com/showthread.php?t=160533

 

[Antiphon]

Is this a valid perspective:

Relativity does not view free fall as acceleration...Is this exactly the same as post #5??

I would put it like this; in GR, freefall is locally identical to no acceleration (and no gravity). Observers far away can tell the difference, but not the local observer.

I there's a lot of good discussion about this topic here. 5 years ago I posted about this explaining how a coaccelerating observer sees the static field of a charge while observers in inertial frames see radiation. There was also a paper published on this about 2 years ago. If you search for "Antiphon" and "uniformly accelerating charge" it should come up.

 

[cragar]

Interesting thanks for your answers.

 

[cosmik debris]

Yes, as JT says this is not an easy question to answer. Consider and electron stationary on a bench in a lab on the Earth's surface. According to General Relativity it is being accelerated, does it radiate? Feynman has an interesting perspective on this problem, as do many others.

 

[cragar]

Yes, as JT says this is not an easy question to answer. Consider and electron stationary on a bench in a lab on the Earth's surface. According to General Relativity it is being accelerated, does it radiate? Feynman has an interesting perspective on this problem, as do many others.

What does Feynman say about it .

 

[cosmik debris]

What does Feynman say about it .

I wouldn't start there, his explanations are pretty complicated. Read the thread that JT recommended first, to get a perspective on the problem.

 

[cragar]

already read it

 

[cosmik debris]

already read it

OK good, now try this: http://http://www.mathpages.com/home/kmath528/kmath528.htm"

 

[cragar]

That link didn't work for me.

 

[cosmik debris]

That link didn't work for me.

I pasted an extra http bit at the front, it should be pretty obvious what it is meant to be.

 

[cragar]

Thanks i didn't look that close at it .