Preludes to dark energy: Zero-point energy and vacuum speculations

What it claims

1. 01Zero-point energy arrived with Planck’s second quantum theory. In the version he presented from 1911, only emission was quantised while absorption stayed classical, and the arithmetic left an oscillator with an average energy of half a quantum at absolute zero — what Planck called a rest energy: the oscillator cannot lose it, because it does not emit until its energy reaches a whole quantum. Planck also saw the difficulty at once. The new expression differs from the old by an additive constant, so it changes neither the spectrum nor the specific heat, and he wrote that a direct experimental test appeared not really possible.Section 2, Planck’s second quantum theory

   Settled physics

2. 02The first person to put that energy into empty space was a chemist. In a communication read to the German Physical Society on 28 January 1916, Walther Nernst proposed that space itself — which he still called the ether — is filled with electromagnetic zero-point radiation whether or not any matter is radiating, and that a vibrating electron continuously exchanges energy with it. He went further than Planck in two ways: his zero-point energy belonged to the radiation as well as to matter, and energy conservation for a single atom held only statistically, because the atom trades energy with the hidden pool in empty space.Section 4, Nernst’s cosmic quantum-ether

   Settled physics

3. 03Nernst calculated how much, and the number was enormous. Taking the classical Rayleigh-Jeans law with the thermal energy replaced by a quantum, the density grows with the cube of the frequency and the integral over all frequencies diverges, so he cut it off at ten to the twentieth hertz — a shortest wavelength of three times ten to the minus ten centimetres — and obtained a lower limit of 1.52 times ten to the twenty-third erg per cubic centimetre, which by mass-energy equivalence is about 150 grams per cubic centimetre. In his own words the amount of zero-point energy in the vacuum is quite enormous, so that extraordinary fluctuations in it would exert great actions. He also showed that compressing such radiation changes neither its energy density nor its spectrum — the invariance that would reappear much later as a property of the false vacuum of inflation and of dark energy.Section 4, Nernst’s energy-density calculation and the invariance result

   Settled physics

4. 04The evidence that made half-quanta respectable came from band spectra. Robert Mulliken’s work on the band spectrum of boron monoxide, announced in 1924 and reported in full in 1925, concluded that the minimum vibrational energy of the molecule is half a quantum, and his paper was widely taken as the final confirmation of half-quanta and, by implication, of a zero-point energy — months before Heisenberg’s new quantum mechanics supplied the theoretical justification.Section 3, Half-quanta and zero-point energy, on Mulliken 1924 and 1925

   Settled physics

5. 05Lemaître said it plainly in 1933, and nobody picked it up. Speaking to the United States National Academy of Sciences on 20 November 1933, Georges Lemaître wrote that everything happens as though the energy in vacuo were different from zero, and that in order that motion relative to the vacuum not be detectable one must associate with that energy density a pressure equal to its negative — which, he said, is essentially the meaning of the cosmical constant. Kragh’s point is that the insight did not depend on the expanding universe, could have been stated years earlier, and when it was stated attracted no interest.Section 6, Steps toward dark energy, on Lemaître’s 1933 address published in 1934

   Settled physics

6. 06The quantum vacuum and the cosmological constant were only joined in the late 1960s, and the join opened the gap. Erast Gliner proposed a vacuum-like state with negative pressure; Yakov Zel’dovich, in papers of 1967 and 1968, wrote that one can speak of an energy density of the vacuum and a pressure of the vacuum, and taking a cut-off at the proton mass got about ten to the seventeenth grams per cubic centimetre, comparing a calculated constant of about ten to the minus tenth per square centimetre with an observational limit below ten to the minus fifty-fourth. That is the birth of the cosmological constant problem, and Kragh notes the discrepancy soon proved much larger than Zel’dovich estimated. The gap is still the open number, and the measurement that moves it is the dark-energy equation of state.Section 6, Steps toward dark energy, on Gliner and Zel’dovich; Section 7, Conclusion

   What to watch

The way in

https://arxiv.org/abs/1111.4623Posted as arXiv:1111.4623, version 1 on 20 November 2011, under the arXiv.org perpetual non-exclusive distribution licence, which grants arXiv distribution rights and nothing further — checked on the arXiv record on 2026-09-08, where no Creative Commons statement appears. The manuscript was submitted to Archive for History of Exact Sciences, where it was published in 2012. So this sheet holds the summary, the claims and the author’s own abstract and sends the reader to the source. The claims are read against the preprint, whose section numbering is used in the locators, and figures are not reproduced. Helge Kragh wrote it at the Centre for Science Studies, Aarhus University.

How to cite it

Helge Kragh (2011) Preludes to dark energy: Zero-point energy and vacuum speculations. arXiv:1111.4623

Where it sits in the curriculum

What the vacuum isThe unified picture