Fields running out of energy

1. Jul 10, 2007

urnchurl

When finding the amount of energy stored in the electric field of a point particle, one finds that it is infinite (due to the r = 0 limit in the integral of the energy density). Does this mean then that the field will never "run out" of energy?

How can the electric field of a point charge, or the gravitational field of a point mass contain an infinite amount of energy without resulting in a space-time singularity (if one considers a finite volume containing the point mass or charge)?

Thanks.

2. Jul 10, 2007

belliott4488

It would mean that the field contained an infinite amount of energy. This was a recognized problem in classical E&M and was not really solved until Quantum Electrodynamics was completed.

One way to think of the answer is that as the energy density increases for small r, you get more and more virtual e+/e- pairs, and they "shield" the charge at the center. At least, I think the argument goes something like that.

3. Jul 10, 2007

lalbatros

The 1/r potential is valid as long as you are outside the charged body.
It is reasonable to assume that even an electron has a finite size.
Below a certain scale, classical physics is not applicable anyway.

4. Jul 10, 2007

rdx

Doesn't the Standard Model comprehend point particles? That would seem to be particularly misleading.