Contradiction in Abraham-Lorentz Force?

[Ozgen Eren]

Hey guys,

This is my fist post and I am curious enough about this to get a new account. Go on wikipedia for the formula and derivation of the abraham lorentz force: http://en.wikipedia.org/wiki/Abraham–Lorentz_force

Anyway my question is as follows:

Lets consider a charge that I am pulling with a constant force F.
Then obviously by F = ma it has a constant acceleration.
Thus it is radiating some energy.
But according to Abraham-Lorentz force there is no recoil force on the particle, so I spend no energy for radiation.

Because if this was the case I would just take a charge, pull it with a constant acceleration, harvest all the radiating energy, and then absorb the kinetic energy I just applied, and do it again and again. It would be my pretty little infinite energy source. Doesnt that imply any harmonic motion spreads infinite energy?

What is wrong, is it the formula or is it my reasoning?

 

[Vagn]

Hey guys,

This is my fist post and I am curious enough about this to get a new account. Go on wikipedia for the formula and derivation of the abraham lorentz force: http://en.wikipedia.org/wiki/Abraham–Lorentz_force

Anyway my question is as follows:

Lets consider a charge that I am pulling with a constant force F.
Then obviously by F = ma it has a constant acceleration.
Thus it is radiating some energy.
But according to Abraham-Lorentz force there is no recoil force on the particle, so I spend no energy for radiation.

Because if this was the case I would just take a charge, pull it with a constant acceleration, harvest all the radiating energy, and then absorb the kinetic energy I just applied, and do it again and again. It would be my pretty little infinite energy source. Doesnt that imply any harmonic motion spreads infinite energy?

What is wrong, is it the formula or is it my reasoning?

How are you keeping the (resultant) force constant? If the particle emits a photon then it will recoil, and the resultant force will change over a very short period, giving a non-zero jerk. The Abraham-Lorentz force is a result of the emission, not the cause of it.

 

[Ozgen Eren]

I didn't mean Abraham Lorentz force causes emission, I know its a result of our action upon the charge. I try to think of it as an "emission friction" if that's the right way to put it.

the resultant force will change over a very short period, giving a non-zero jerk

So you suggest that instead of creating an opposite force to balance emission energy, it creates a non-zero jerk which corresponds to a derivative of force on F=ma. That actually makes sense but still the original formula don't seem like supporting it.

If we just apply a constant force to a charge, the derivative of acceleration will be zero as long as F=ma is valid. So no Abraham-Lorentz force, but emission. Thats what I am trying to understand.

 

[Ehsan Farooq]

If you are moving the charge with uniform acceleration ( though inverse square fields produce non uniform acceleration), you are doing some work as dictated by work energy theorm, that is appearing as radiation energy.. I see no paradox

 

[Vagn]

I didn't mean Abraham Lorentz force causes emission, I know its a result of our action upon the charge. I try to think of it as an "emission friction" if that's the right way to put it.
So you suggest that instead of creating an opposite force to balance emission energy, it creates a non-zero jerk which corresponds to a derivative of force on F=ma. That actually makes sense but still the original formula don't seem like supporting it.

If we just apply a constant acceleration to a charge, the derivative of acceleration will be zero as long as F=ma is valid. So no Abraham-Lorentz force, but emission. Thats what I am trying to understand.

The paper below discusses how to resolve the problem.
http://dx.doi.org/10.1016/0003-4916(60)90105-6

 

[Ozgen Eren]

If you are moving the charge with uniform acceleration ( though inverse square fields produce non uniform acceleration), you are doing some work as dictated by work energy theorm, that is appearing as radiation energy.. I see no paradox

No the work is done upon the kinetic energy, not upon the radiation. So what you applied = 1/2*m*V*V, what seems to exist : 1/2*m*V*V + Eradiation.

Fulton, T., & Rohrlich, F. (1960). Classical radiation from a uniformly accelerated charge. Annals of Physics, 9(4), 499-517

I will take a look on that one, thanks.

 

[Ozgen Eren]

The paper below discusses how to resolve the problem.
http://dx.doi.org/10.1016/0003-4916(60)90105-6

Well I didn't buy the original article but found a free one which refers to it and restates the explanation. Here is the link:

http://users.jyu.fi/~ilsamaki/radiation.pdf

saying the following in summary:

"so it would seem the energy needed for the radiation is somehow supplied from the near part of the fields surrounding the particle."
​

Do you really think that is possible? It seemed too vague to me. There is no actual proof that it comes from its own field, its just a claim which would violate Newtons third law in the first place.

Plus electromagnetic waves travel with the speed of light. So even if it were to be effected by its own field, it could never have catched its own field after the instant the field is created. And we cannot suggest it is influenced by its own field at the very instant the field is created, because then it should have been influenced by its own fields in all directions, which would again result in zero net force.

Does someone knows a solid explanation for the energy conservation? I just want to know if there is a plain contradiction or a complete explanation.