Wilczek replies: It is true and significant that the Planck length arises naturally when one considers the ultimate limits to measurement. Crudely, it happens because refined length measurement requires large momentum, according to Heisenberg’s uncertainty principle, but when the momentum becomes too large, its gravitational effect becomes strong, curving spacetime and distorting the interval one seeks to measure. Thus a fundamental difficulty arises in resolving lengths below the Planck scale. This point has been “rediscovered” many times, but C. Alden Mead’s discussion is the earliest I’m aware of. It nicely supplements the article, in which the Planck length was introduced in a somewhat different way.

One can understand the source of the bias Mead encountered, and in the process highlight an important principle: What quantities one chooses to regard as fundamental can depend on what domain one seeks to describe. A good approximate description of much of chemistry and molecular biology can be obtained by taking only the electron mass and charge as inputs, using Planck’s constant ħ as the unit of action, and regarding atomic nuclei as infinitely massive point-particles. In this system, the Bohr radius ħ2/e2m appears as the fundamental unit of length; indeed this sets the scale for atomic and molecular sizes. A good approximate description of strong-interaction physics can be obtained by taking only the quantum chromodynamics mass scale Λ as input, using Planck’s constant and the speed of light c as units of action and velocity. In this system the fundamental unit of length is Λ/ħc; and indeed this sets the scale for proton and nuclear sizes. In the 1960s and early 1970s, strong-interaction physics was the primary focus of fundamental physics, and this system (implicitly) seemed most natural.