Planck’s units—10−6 g, 10−33 cm, 10−44 s—are derived from fundamental parameters that appear in the most basic theories of physics. They are constructed from suitable combinations of the speed of light c, the quantum of action h, and the Newtonian gravitational constant G. These quantities are the avatars of Lorentz symmetry, wave—particle duality, and bending of space—time by matter, respectively.
The mismatch between Planck’s units and the practical units of mass, length, and time—to wit, 1 g, 1 cm, 1 s—is so enormous as to be grotesque. (Our discussion will be smoother using these, rather than the “standard” SI units.) Quantitative disparities of this order pose qualitative challenges for our understanding of the world. Why do we find it helpful to use units that are so far removed from the fundamentals?
The central mission of my recent trilogy of Reference Frame columns, “Scaling Mount Planck,” was...
