Richard Borcherds wrote a post a little while back in which he remarked that we shouldn’t take the Planck units very seriously, since Newton’s constant doesn’t have quite the same stature as and .
His argument went more or less as follows: The latter two seem to be quite fundamental, but from a modern point of view (actually ) is just one of the coupling constants that appears in the effective Lagrangian for gravitational fields
where the coupling constant is basically the cosmological constant, normalized by .
So, isn’t privileged in any way. It isn’t the coupling constant of the leading order term; a cursory analysis of the scaling dimensions of and would lead us to believe that the cosmological constant term should be dominant. It isn’t even normalized nicely, what with that . And while it seems quite sensible to work in units where and , we should be a little more cautious about about the meaning we assign to units where . What we’re actually doing is identifying the length scale where our non-renormalizable effective field theory description of gravity should break down.
[Updated: The computation that previously appeared here involved one of the classic blunders: not checking your units. ; that’s a +6, not a -6. Thanks to Thomas Larsson for pointing that I’m an idiot.]