Can Point Particles Have Infinite Energy in Fields?

[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.

 

[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.

 

[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.

 

[rdx]

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.

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