When r=0 in Coulomb's law; electron self-repulsion

[nomadreid]

Given that
(a) the electrostatic force is inversely proportional to r²
(b) that the electron is (when it is determined) a point
(c) that the repulsion for an electron to itself is therefore r=0
(d) that r=0 would naively end up with infinite force
What is the way out of this problem?
Thanks

 

[Dale]

The electron must not be a classical point particle.

 

[nomadreid]

The electron must not be a classical point particle.

OK, that "classical" in the answer is perhaps the key. But it is, according to Fermilab, http://www.fnal.gov/pub/today/archive/archive_2013/today13-02-15_NutshellReadMore.html, a point particle, even if not classical. That site hints that the solution lies in the quantum foam, but it isn't very explicit in its explanation.

 

[Orodruin]

Even when viewing the electron as a classical point particle, there is no force acting on it from its own potential. The total potential energy (although technically infinite) does not depend on where the electron is located and the force is given by how the total potential depends on the position.

 

[nomadreid]

Orodruin: Ah, looking at it from the point of view of potential energy... that makes sense, thanks.