Zero-point energy in early quantum theory

In modern physics the vacuum is not a tranquil void but a quantum state with fluctuations having observable consequences. The present concept of the vacuum has its roots in the zero‐point energy of harmonic oscillators and the electromagnetic field, and arose before the development of the formalism of quantum mechanics. This article discusses these roots in the blackbody research of Planck and Einstein in 1912–1913, and the relation to Bose–Einstein statistics and the first indication of wave–particle duality uncovered by Einstein's fluctuation formula. Also considered are the Einstein–Stern theory of specific heats, which invoked zero‐point energy in a way which turned out to be incorrect, and the experimental implications of zero‐point energy recognized by Mulliken and Debye in vibrational spectroscopy and x‐ray diffraction.