Scaling Mount Planck III: Is That All There Is?

Let’s quickly recollect the main points of the two earlier columns in this series. Gravity appears extravagantly feeble on atomic and laboratory scales, ultimately because the proton’s mass m _p is much smaller than the Planck mass $M Planck = ( ℏ c / G N ) 1 / 2$ ⁠, where ℏ is Planck’s quantum of action, c is the speed of light, and G _N is Newton’s gravitational constant. Numerically, m _p/M _planck ≈ 10⁻¹⁸. If we aspire, in line with Planck’s original vision and with modern ambitions for the unification of physics, to use the natural (Planck) system of units constructed from c, ℏ, and G _N (see “Scaling Mount Planck I: A View from the Bottom,” Physics Today, Physics Today 0031-9228 54 6 2001 12  https://doi.org/10.1063/1.1387576 June 2001, page 12 ), and if we agree that the proton is...