Why don't electrons collaspe into black holes?

Question

An electron has a mass of $9.10938291(40) \times 10^{−31} kg$. It also has a volume of $0 m^3$. This would imply it has infinite density. Shouldn't that make it collapse into a black hole? Why doesn't it?

Answer 1

The angular momentum and charge of an electron are both large enough that a black hole would not form. If you believe classical general relativity all the way down to the scale of an electron (and you really shouldn't), then the electron will form a naked singularity.

More exactly, for the case of a spinning body, the horizon is at the zero of

$$r^{2} - 2Mr + a^{2}$$

Where $a$ is the angular momentum divided by the mass (in $G = c = 1$ units), and $M$ is the black hole's mass. If you put in the numbers for the electron, this equation has no real zeroes. Adding charge to the picture will only make the matter worse.

Answer 2

Why don't electrons collapse into black holes?

Because the electron isn't a point-particle. Its field is what it is. It isn't some speck that has a field, it is that field. There's energy in that field, that energy has a mass-equivalence, and it doesn't have a zero volume. Also note that we can diffract electrons. And that the Einstein-de Haas effect demonstrates that "spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". And that in atomic orbitals electrons "exist as standing waves". I could go on. There's ample evidence for the wave nature of matter. There's no evidence for the point-particle nature of matter. Some will dispute this and point to scattering experiments, but there's a wrong inference at work there. It's like hanging out of helicopter probing a whirlpool with a bargepole, then declaring that because you can't feel the billiard ball that's causing this, it must be really really small.

All in all I'm afraid the people who tell you the electron is a point-particle are promoting a myth that was borne from mathematical simplification. It's quantum field theory, not quantum point particle theory. IMHO pictures like this which say the electron is less than 10^-18 m in size are misleading and irresponsible, and shouldn't even be shown to schoolchildren.