STM-D-0726Paper1975Published and peer-reviewed

Random electrodynamics: The theory of classical electrodynamics with classical electromagnetic zero-point radiation

Timothy H. Boyer

Summary and citation · read the original at the source · none found

In one page

Timothy Boyer of City College of New York asks a question most physicists had stopped asking: how much of quantum behaviour can ordinary classical physics reproduce if you stop assuming that empty space is empty? His answer is a theory he names random electrodynamics. It uses Newton’s equations for charged particles pushed by the Lorentz force and Maxwell’s equations for the fields — nothing new there — with a single change. Where the classical electron theory of Lorentz set the free-field boundary condition to zero, Boyer fills it with random classical radiation whose spectrum looks the same to every observer however fast they are moving, and whose overall scale is fixed by Planck’s constant. Turn that constant down to zero and the theory collapses back into Lorentz’s. Keep it and, as Boyer sets out, the purely classical calculation already reproduces measured results: van der Waals forces, the Casimir force, and the thermodynamics of the blackbody spectrum. This is the founding paper of what is now called stochastic electrodynamics.

Why it matters hereThis is the paper that made the zero-point field a physical sea rather than a bookkeeping term, and chapter 2 rests on exactly that move; chapter 3 gets its ancestor here, because Boyer’s balance between a charged particle and the surrounding random field is the argument Puthoff, Haisch and Rueda later carried into inertia and atomic stability, and chapter 6 gets a theory in which the vacuum’s energy is a real classical radiation field you can, in principle, do accounting with.

What it claims

01Random electrodynamics changes exactly one thing about classical electron theory: the boundary condition. It keeps Newton’s equations for particle motion under the Lorentz force and Maxwell’s equations for the fields with point particles as sources, but where Lorentz took the homogeneous solution of Maxwell’s equations to be zero, Boyer takes it to be random classical electromagnetic radiation that is always present. Everything else in the theory is nineteenth-century physics.Abstract, sentences 3 and 4; the paper’s discussion of the role of boundary conditions in classical electrodynamics
Published and peer-reviewed
02The spectrum of that radiation is Lorentz invariant — it looks the same to every observer no matter how fast they are moving — and its scale is set by Planck’s constant. That single requirement fixes the spectrum: energy per normal mode of one half of Planck’s constant times the frequency, the same form quantum theory calls zero-point energy. Boyer arrives at it from a classical symmetry argument rather than from quantisation.Abstract, sentence 5; expanded in Boyer’s 2019 survey, section on the Lorentz-invariant spectrum inferred from Casimir force measurements
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03The theory sits between two known theories and can be tuned into one of them. In the limit where Planck’s constant goes to zero, random electrodynamics becomes Lorentz’s theory of electrons exactly; with the constant kept, it stands between traditional classical electron theory on one side and quantum electrodynamics with its noncommuting operators on the other. Planck’s constant enters as the intensity of a real radiation field, not as a quantisation rule.Abstract, sentences 6 and 7
Published and peer-reviewed
04Several published calculations inside the theory already agree with experiment. Boyer summarises the detection of zero-point radiation, the calculation of van der Waals forces both unretarded and retarded, and a changed footing for statistical thermodynamics, noting that in these cases the summary accounts refer to published calculations which yield results in agreement with experiment. His later survey adds the same agreement for the decrease of specific heats at low temperature and for the diamagnetic behaviour of molecules modelled as three-dimensional oscillators.Abstract, sentences 8 and 9; Boyer 2019 survey, Successes of Stochastic Electrodynamics, subsections on harmonic oscillators and on van der Waals and diamagnetic behaviour
Published and peer-reviewed
05The zero-point field is inferred from a measurement, not assumed. Boyer’s route to the spectrum runs through the Casimir effect: the force between uncharged conducting plates, measured at low temperature, is what tells you the intensity of the random radiation that must be present between them. That is why the theory treats the field as physically real rather than as a formal device.Boyer 2019 survey, Inference from Measurements on the Casimir Effect; the same result is summarised in the 1975 abstract, sentence 8, under the detection of zero-point radiation
Settled physics
06What to watch: how far the classical picture reaches. Boyer is explicit that the implications for atomic structure, atomic spectra and particle-interference effects are discussed at an order-of-magnitude or heuristic level only, and that the connections between random electrodynamics and quantum theory are some detailed and mathematical, others merely heuristic. The measurement that would settle it is whether a classical charged particle in the zero-point field reproduces the quantum ground-state distribution for a nonlinear potential such as hydrogen — a numerical question the field has been arguing since, and the reason this site keeps the later oscillator papers alongside this one.Abstract, final two sentences; Boyer 2019 survey, discussion of the numerical hydrogen calculations and the 2015 challenge to them
What to watch

The way in

https://doi.org/10.1103/physrevd.11.790LICENCE. Published as Physical Review D, volume 11, issue 4, pages 790 to 808, 15 February 1975, under the APS default licence; Unpaywall and OpenAlex both record it closed with no repository copy, so no text of it is reproduced here. SOURCE PARTLY REACHED. The author’s own full abstract was read on 2026-09-08 from the INSPIRE-HEP record for the paper, and every locator marked Abstract below cites that abstract sentence by sentence. For the physics behind the abstract, Boyer’s own later survey of the same theory was read in full — Timothy H. Boyer, Stochastic Electrodynamics: The Closest Classical Approximation to Quantum Theory, arXiv 1903.00996, 3 March 2019, City College of the City University of New York — and locators that cite it say so by name. NOT A DUPLICATE. This library also holds a 1963 paper titled Random electrodynamics by T. W. Marshall, Proceedings of the Royal Society A, doi 10.1098/rspa.1963.0220, at /library/stm-7faa238629; the two are different works by different authors twelve years apart, and each is cross-linked from the other.

How to cite it

Timothy H. Boyer (1975) Random electrodynamics: The theory of classical electrodynamics with classical electromagnetic zero-point radiation. doi:10.1103/physrevd.11.790

Where it sits in the curriculum

What the vacuum is Inertia and gravity from the vacuum Energy from the vacuum