Max PlanckHe Quantized the Vibe

The sticker says He Quantized the Vibe. He did, and for years hoped he had not.

By 1900 the light glowing out of a hot cavity had been measured carefully in Berlin, and nobody could explain the shape of its spectrum. That October Max Planck found a formula that fitted the data at every wavelength, the second one on this page. By his own account it was a guess, a lucky intuition. A fit is not a theory, so he set out to derive it.

He succeeded by 14 December 1900, and paid twice. First, he had to adopt Ludwig Boltzmann's statistical view of entropy, which meant giving up his own conviction that the second law of thermodynamics was absolute rather than overwhelmingly probable. Second, to count the ways energy could be shared among the oscillators in the cavity walls, he had to treat energy as coming in pieces of size hν, frequency times a new constant. He seems to have regarded the pieces as a counting device rather than a fact about nature. It was Einstein, in 1905, who took them literally as particles of light.

The formula carries its own proof that the pieces matter. When hν is small compared with the thermal energy kT, the exponential can be expanded and the classical result comes back. When hν is large, the exponential wins and the radiation is cut off. Without that cut-off, classical physics predicted unlimited energy at short wavelengths, a failure Paul Ehrenfest later named the ultraviolet catastrophe.

Planck received the 1918 Nobel Prize for the discovery of energy quanta. In 2019 his constant took on a new job: h is now fixed at exactly 6.626 070 15 × 10⁻³⁴ joule-seconds, and that number defines the kilogram.

Planck quantized the vibe. The vibe now weighs things.