zlacker

This is definitely related, though not the whole story. Quantization did get rid of some infinities, but as GP kind of states, it also introduced others. My comment focuses on what we do for those.

>>knzhou+(OP)
> In the limit of d -> 0, the energy released -> infinity.

I believe the poster's general premise to be false. While renormalization may be useful in resolving infinities in general, I don't think it's necessary for this one.

You can't commute the dp*dx of a Hamiltonian to be zero in a quantized world, so if gravity has quantum properties, you don't need to worry about what happens when d -> 0. There is no "0" distance.

>>aberna+X
I guess, but it depends on how one parses the poster's setup. You're correct that for particles interacting under a 1/r^2 force, the energy turns out finite in quantum mechanics. My comment was referring to the fact that once you quantize the field that gives rise to that force, the infinities return, but for a different reason.