system
Given the following post, respond as if you're commenting on Reddit:
human
If particles are point-like, how are they not gravitational singularities?

I understand gravitational singularities are not a matter of mass, but density. I also understand that particle colliders have established an upper-limit to the volume of an electron. If the fundamental particles are truly point-like, then whatever their mass, they would necessarily form gravitational singularities. Would the event horizons of these particles themselves be extremely small? They would still undergo hawking radiation I presume, which would mean that they would evaporate rapidly..?


I thought maybe the answer depends on quantum mechanics, that the wave-function means that though the particle is point-like its possible positions are distributed through space? But flipping the question around, what is the quantum state of a black hole? Does it too have a wave function, and is that wave function entirely contained within the event horizon? (apart from hawking radiation)

Is this just the great unsolved problem in physics of reconciling gravity and quantum mechanics, the micro and the macro?
gpt
Indeed, the true answer to this question must rely on a complete theory of quantum gravity which we don't have. But it's common to make a hand-waving argument based on quantum mechanics and general relativity separately.

Very simply, a particle of mass m has an associated quantum-mechanical length scale (Compton wavelength) equal to hbar/mc which is (in a vague sense) a measure of the quantum fuzziness of its position. A black hole of mass m has a radius of ~Gm/c^(2). Combining these you find that a particle's Compton wavelength is smaller than its Schwarzschild radius (required for it to be a black hole) only if m is greater than the Planck mass, about 10^-5 grams. Since all the known particles are much lighter than that, we *expect* (although we do not *know* for sure) that fundamental particles are not black holes.

There are other reasons to suspect otherwise, such as the expectation that black holes violate certain conservation laws like baryon number which are obeyed by particle decays. But these are also not known for sure, just expected based on what we know about non-quantum gravity.