Why don't electrons turn into black holes?

[zeromodz]

From my understanding electrons are point particles with zero volume, therefore zero radius.


F = GMm / r^2
F = GMm / (0)^2
F = ∞ N.


Can someone please explain?

 

[diazona]

A point particle doesn't exert a force on itself. That formula only applies to two different particles.

In a broader sense, though, we really don't know why. You're right that treating electrons as point particles causes all sorts of problems. Their true nature is still somewhat mysterious. (This is/was the appeal of string theory, that the fundamental particles could be "strings" or other extended objects rather than points, which helps a lot of problems go away)

 

[giant_bog]

Because its Compton wavelength is bigger than its Schwarzschild radius.