> So if gravity is quantized, that means space-time is also quantized. But that doesn’t work, But... How could space-time not be quantized? That would imply the existence of infinities in the structure of the universe. It is like the ultraviolet catastrophe but in space-time.
But space is quantised, that's what Planck's Constant is. The oddity we see with things at relativistic energies is simply because - as with all discretised representations of continuous-time systems - things get a bit fucky close to Nyquist, and the maths breaks down.
You're thinking of the Planck Length, which is the result of combining the Planck Constant with the speed of light. It also happens to be the wavelength of a photon so short that its energy makes it a black hole, connecting it to gravity.
It's often presented as if it were the fundamental unit of length, but that's a guess at best. There's no specific reason to believe it, other than the fact that it happens to be a way to connect length, charge, and gravity. That's evocative, but hardly proof. There's neither evidence for it nor a well-supported theory behind it.