Random electrodynamics
T. W. Marshall
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In one page
This is the paper that started stochastic electrodynamics. T. W. Marshall asks what a purely classical world would have to look like for its harmonic oscillators to sit still in the same statistical shape as a quantum oscillator in its ground state. He builds an ensemble of ordinary classical oscillators whose position and momentum distributions match the quantum ground state exactly, and then notices that if the oscillating particle carries charge, the arrangement cannot stay put on its own. A particular random electromagnetic field has to be present to hold it there. Marshall calculates the intensity distribution of that required field and finds it identical to the photon vacuum of quantum electrodynamics — the sea that quantum field theory writes down as a formal device. His suggestion is that it might be there in the ordinary classical sense. Warm the system up and the field’s spectrum is simply the Planck distribution added to that zero-temperature sea.
Why it matters hereChapter 2 rests on the vacuum being a real, structured medium rather than an accounting convention, and Marshall is the first person to derive its spectrum from a classical requirement instead of postulating it. Chapter 3 inherits his central move directly: a particle holds its ground state because it is in balance with the field, which is the argument Puthoff later carried into the hydrogen atom, inertia and gravity.
What it claims
01Take a statistical ensemble of classical harmonic oscillators that is stationary in time and whose position and momentum distribution functions are those of the corresponding quantum-mechanical oscillator in its ground state. Such an ensemble can be written down within ordinary classical mechanics.Abstract, Proceedings of the Royal Society A 276, pages 475 to 491
Published and peer-reviewed02If the oscillating particle is charged, that distribution cannot remain stationary by itself: a certain random electromagnetic field must be present to maintain it. The field is a requirement of the classical problem, not an assumption added to it.Abstract, Proceedings of the Royal Society A 276, pages 475 to 491
Published and peer-reviewed03The intensity distribution of that required radiation field, calculated, is identical with the photon vacuum of quantum electrodynamics — so Marshall suggests this field, which quantum field theory treats entirely formally, might exist in the classical sense.Abstract, Proceedings of the Royal Society A 276, pages 475 to 491
Published and peer-reviewed04Extended to the excited states, the corresponding classical ensembles have probability distributions that may go negative. When attention shifts to the quantum-mechanical mixture rather than the pure state, that is no longer the case.Abstract, Proceedings of the Royal Society A 276, pages 475 to 491
Published and peer-reviewed05At temperature T the intensity distribution of the radiation field is simply the sum of the Planck distribution and the zero-temperature field obtained earlier — the thermal spectrum sits on top of the zero-point sea rather than replacing it.Abstract, Proceedings of the Royal Society A 276, pages 475 to 491
Published and peer-reviewed06The treatment is non-relativistic throughout, yet radiative corrections of the type that give rise to the Lamb shift are an integral part of the theory. How far the classical field reproduces those shifts, and how the programme fares once it is made relativistic, is where the theory has to be tested.Abstract, closing sentence, Proceedings of the Royal Society A 276, pages 475 to 491
What to watch
The way in
https://doi.org/10.1098/rspa.1963.0220LICENCE. Published as Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, volume 276, pages 475 to 491, 1963. Licence checked directly on 2026-09-08: Crossref lists only the Royal Society’s data-sharing and mining policy, and Crossref, Unpaywall and OpenAlex all return closed with a null licence; there is no Creative Commons statement. SOURCE. The publisher answers automated requests with a bot-challenge page rather than the article, and no repository or preprint copy of a 1963 paper exists, so the full text could not be read for this sheet. The summary and the claims below are written from the author’s own published abstract as carried in the Crossref record for this digital object identifier, together with the bibliographic record; the locators cite the abstract and the article’s page range rather than interior sections, and the complete paper is at the source. The author’s affiliation is not asserted here because the article itself could not be read. REGISTRY NOTE. This work reached the library’s dispatch list described as a 1975 paper by Timothy Boyer; the digital object identifier resolves to T. W. Marshall’s 1963 paper of the same title, which is the earlier work, and this sheet is written for Marshall. Boyer’s own statements of the programme are on this site at /library/stm-2d2d42369d, /library/stm-5909a0938f and /library/stm-1011f1af4f.
How to cite it
T. W. Marshall (1963) Random electrodynamics. doi:10.1098/rspa.1963.0220
Where it sits in the curriculum