Why spontaneous emission?
P. W. Milonni
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In one page
Why does an excited atom eventually give up its light, when nothing is disturbing it? Peter Milonni’s answer, written for physics teachers, is that two things are disturbing it — and they turn out to be one thing counted twice. The first is radiation reaction: a charge that radiates pushes back on itself. The second is the vacuum’s zero-point field, the residual jitter of the electromagnetic field that survives even at absolute zero. Milonni works out each contribution separately and gets exactly half the measured emission rate from each. Add them and Einstein’s A coefficient comes back exactly. For an atom already in its lowest state the two halves cancel instead, which is why a ground-state atom does not soak up energy from the vacuum and fall further. What ties the two together is the fluctuation-dissipation theorem — the same relation that links electrical noise in a resistor to its resistance. And the vacuum’s spectrum is not adjustable: only a spectrum rising as the cube of frequency keeps quantum mechanics consistent.
Why it matters hereChapter 2 argues that the vacuum is a real, structured medium rather than an absence, and this is the paper that makes the case from the most ordinary phenomenon there is — an atom emitting light. Milonni also states, in the same breath, that the Casimir and van der Waals forces belong to exactly the same accounting, which is the bridge chapter 6 is built on.
What it claims
01Spontaneous emission has two equally valid physical descriptions, and each one on its own accounts for exactly half of the measured rate. Treating the atom as a classical dipole driven by its own radiation reaction field gives a decay rate of two times the squared transition dipole moment times the cube of the transition frequency, divided by three times the reduced Planck constant times the cube of the speed of light. Treating it instead as an atom stimulated by the zero-point field gives the identical expression. Each is half the Einstein A coefficient.Sections IV and V, Equations 4.5 and 5.3
Settled physics02The two halves add for an excited atom and cancel for a ground-state one. For an atom in an excited state the radiation-reaction rate plus the zero-point-field rate equals the Einstein A coefficient. In the ground state the same two contributions enter with opposite sign and give zero — which is Milonni’s answer, at least quantum mechanically, to why there is no spontaneous absorption from the zero-point field even though the field is unquestionably present.Section VI, Equation 6.6 and the paragraph following it
Settled physics03The link between the two pictures is the fluctuation-dissipation theorem. Milonni states it directly: just as Johnson-Nyquist voltage fluctuations in an electrical circuit are related to the resistance, so the fluctuations of the zero-point field are related to the radiative resistance, which is radiation reaction. In both cases there is an explicit relation between the dissipative force and the frequency spectrum of the fluctuation that comes with it.Section VI, the paragraph beginning ‘The key to this interplay’
Settled physics04The vacuum spectrum cannot be anything other than what it is. Milonni shows that the zero-point energy spectrum going as the cube of the frequency is exactly what is needed to preserve the position-momentum commutation relation for an electron moving in the vacuum field, because the radiation reaction field goes as the third derivative of position; the two powers of frequency cancel and leave a finite integral. If the spectrum were proportional to any other power of frequency, the commutator would not be preserved.Section VI, Equations 6.4 and 6.5
Settled physics05Which of the two pictures you get is a choice of operator ordering, not a matter of fact. Symmetric ordering of the atom and field operators gives the emission rate as radiation reaction plus zero-point field; normal ordering gives twice the radiation reaction term; a different ordering gives twice the zero-point term minus the radiation reaction term. All three give the same Einstein A coefficient. The number is fixed; only the interpretation of where it comes from moves.Section VII, first two paragraphs
Settled physics06What to watch: Milonni closes by putting the van der Waals and Casimir forces in exactly the same position as spontaneous emission — they too have been attributed to radiation reaction, and, in his words, the theory is essentially no different from that for spontaneous emission. The open question he leaves is therefore an experimental one: whether the vacuum-fluctuation and source-radiation contributions can be separated in the laboratory rather than only summed, which is precisely what modern separation experiments set out to do.Section VII, the paragraph beginning ‘There are many physical effects attributable to the zero-point electromagnetic field’
What to watch
The way in
https://doi.org/10.1119/1.13886WHAT THIS PAGE IS WRITTEN FROM. Published as American Journal of Physics volume 52, number 4, pages 340 to 343, April 1984, received 3 March 1983 and accepted 24 June 1983; the author’s affiliation on the paper is the Department of Physics, University of Arkansas, Fayetteville. Copyright 1984 American Association of Physics Teachers; the record is closed access, Unpaywall and OpenAlex report no open copy, and the article carries no Creative Commons statement. A scanned copy is hosted for teaching by the Facultad de Matemática, Astronomía, Física y Computación of the Universidad Nacional de Córdoba, and the four pages were read there in full on 2026-09-08, which is why the locators below cite the paper’s own section and equation numbers. No text of the paper is reproduced here — everything on this page is the site’s own summary, written from the source. The paper is a pedagogical article: seven short sections, an epigraph from Shelley’s Adonais, and a Feynman anecdote that opens it.
How to cite it
P. W. Milonni (1984) Why spontaneous emission?. doi:10.1119/1.13886
Where it sits in the curriculum