# Why Do Accelerated Charges Radiate?

Mentor
I have often wondered why, when you consider the equivalence principle, accelerated charges radiate. Its not something the EM books I have read seem to actually address.

Anyone know the answer or is it tied up with weird stuff like runaway solutions to the Lorentz-Dirac equation that really requires QED.

Thanks
Bill

Staff Emeritus
2021 Award
Radiation involves multipoles, which are extended objects. The equivalence principle is purely local - indeed, it tells us how to define a gravitational field: not by its acceleration, a la Newton, but by its tides.

bhobba
Mentor
Radiation involves multipoles, which are extended objects.

Got it.. If you have say a charge sitting on a table and you go to a freely falling local frame so the charge accelerates upwards the field outside this local frame still resides in a gravitational field. Its not inertial and Maxwell's equations don't strictly apply - you need GR.

Thanks
Bill

Hi,

I am not sure if I got the question and your conclusion right...

If you regard for example a single accelerated particle you can first get to the Larmor formula (non-relativistic). Elementary particles can accellerate hellacious, so you can formulate this in a SRT way. See J.D. Jackson, chapter 14 - which is needed in particle accelerators.

GRT is not needed here in any way. Naturally you can write the Maxwell equations in a GRT way which look the same as the SRT ones if you use the coordinate free language (differential forms). Nevertheless, the standard radiation you observe has nothing to do with this.
The GRT part would be interesting if you watch as a free falling observer a charged particle itself free falling in your reference frame. Is this case you would measure the acceleration relative to your position - which is an higher order effect depending purely from the curvature - which is normally very very small.

Best regards,
Jens

tech99
Gold Member
I have often wondered why, when you consider the equivalence principle, accelerated charges radiate. Its not something the EM books I have read seem to actually address.

Anyone know the answer or is it tied up with weird stuff like runaway solutions to the Lorentz-Dirac equation that really requires QED.

Thanks
Bill
I wonder if the animation at the following URL will be helpful: http://www.tapir.caltech.edu/~teviet/Waves/empulse.html
It is based on the radiation mechanism proposed by J J Thompson.