I suspect I'm missing something obvious, but I'm coming up blank. I've gotten pretty comfortable with so-called natural units over the years: in doing quantum mechanics/QFT, it's common to set $c = ...
Say we want to make an educated guess for critical values of time, distance and mass, where quantum gravity effects are supposed to be non-negligible. These values are given the prefix "Planck-". Now, ...
What is the connection between Planck's constant and gravity? Why is the Planck scale the natural scale for quantum gravity? I would have though the scale would be related to G, not h.