Historical research guide · 0640 · 2011
Preludes to dark energy: Zero-point energy and vacuum speculations
Helge Kragh
In one minute
Helge Kragh, a historian of physics at Aarhus, traces where the idea of an energy in empty space came from. It starts with Max Planck, who in 1911 rebuilt his quantum theory so that only emission was quantised and found that an oscillator keeps half a quantum of energy even at absolute zero — a residue he could not see how to measure. Then comes the surprise of the story: in 1916 the chemist Walther Nernst proposed that empty space itself is filled with that radiation, worked out how much, and got an enormous number. Kragh follows the idea through the spectroscopists who confirmed half-quanta, through Georges Lemaître, who in 1933 said plainly that the cosmological constant means the energy in a vacuum is not zero, to Erast Gliner and Yakov Zel’dovich in the late 1960s, who finally connected the quantum vacuum to the constant and in doing so opened the gap between calculation and observation that cosmology still lives with.
Connection
Chapter 2 asks what the vacuum is, and this paper shows that the answer the site works from — space is a medium with an energy density — was proposed in 1916 and calculated, not invented recently. Chapter 13 needs the ledger’s longest-standing entry, and Kragh dates the moment the mismatch between the calculated vacuum energy and the measured one first appeared in print.
From the source
Zero-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
The 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
Nernst 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
The 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
Lemaître 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
The 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
The way in
https://arxiv.org/abs/1111.4623How to cite it
Helge Kragh (2011) Preludes to dark energy: Zero-point energy and vacuum speculations arXiv:1111.4623