Historical research guide · 0416 · 1980

A Brief Survey of Stochastic Electrodynamics

Timothy H. Boyer

In one minute

Timothy Boyer of City College of New York wrote this short survey for A. O. Barut’s 1980 volume on the foundations of radiation theory, and it is his compact statement of a programme he had been building since the late 1960s. Stochastic electrodynamics changes exactly one thing in ordinary classical physics: the source-free solution of Maxwell’s equations is not set to zero, but filled with random classical radiation carrying an energy of one half h-bar omega in every mode. Requiring that sea to look the same to every observer moving at constant speed fixes its spectrum uniquely, and fixes Planck’s constant as its scale — so a theory with no quanta in it nonetheless contains h-bar. Boyer surveys what follows. Casimir and van der Waals forces come out without any quantisation. The Planck blackbody spectrum and the low-temperature fall of specific heats follow from classical statistics once the sea is included. And an orbiting electron no longer spirals in, because it absorbs as much as it radiates.

Connection

Chapter 2 says the vacuum is a real, structured medium with a definite energy density, and this survey is the shortest statement of what that costs and what it buys: keep classical physics, add the field, and quantum results start appearing. Chapter 3 needs exactly that bridge, because a hydrogen atom held in balance against the zero-point field is the same argument Puthoff later carried into inertia and gravity.

From the source

Stochastic electrodynamics is ordinary classical electrodynamics of point charges with one change: the homogeneous, source-free solution of Maxwell’s equations is taken to be random classical radiation rather than zero, carrying an average energy of one half h-bar omega in every normal mode.The survey, pages 49 to 63; the theory is set out in Boyer, Physical Review D 11, 790, 1975
Requiring the random radiation spectrum to be the same for all inertial observers fixes its form uniquely as proportional to the cube of the frequency, and leaves exactly one free constant, which measurement identifies with Planck’s constant — so a fully classical theory acquires h-bar without any quantisation.The survey, pages 49 to 63; derived in Boyer, Physical Review D 11, 790, 1975
The Casimir force between conducting plates and the retarded and unretarded van der Waals forces between molecules follow from classical zero-point radiation alone, in agreement with the quantum-electrodynamic results.The survey, pages 49 to 63; computed in Boyer, Physical Review 174, 1764, 1968 and Physical Review A 11, 1650, 1975
With zero-point radiation included, classical statistical mechanics of a charged harmonic oscillator returns the Planck blackbody spectrum plus a zero-point term, and reproduces the fall of specific heats at low temperature that classical physics without the field cannot explain.The survey, pages 49 to 63; derived in Boyer, Physical Review 182, 1374, 1969
The stability of the atom follows from a balance rather than a postulate: an orbiting electron radiates energy away and absorbs it back from the random field, and the ground-state orbit is where the two rates match. Boyer’s estimate for hydrogen returns the Bohr radius.The survey, pages 49 to 63; the hydrogen estimate is in Boyer, Physical Review D 11, 790, 1975
The agreement with quantum theory is exact for linear systems, above all the harmonic oscillator, while nonlinear systems such as the full hydrogen atom remain the open problem of the programme — which is where Boyer says the theory must be tested.The survey, pages 49 to 63; restated in Boyer’s 2019 review, Atoms 7, 29, sections 3.3 and 3.4

The way in

https://doi.org/10.1007/978-1-4757-0671-0_5

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

LICENCE. Chapter 5 of Foundations of Radiation Theory and Quantum Electrodynamics, edited by A. O. Barut, Plenum Press, New York, 1980, pages 49 to 63; the volume carries the publisher’s standard copyright and no Creative Commons statement, and Crossref, Unpaywall and OpenAlex all mark the chapter closed. SOURCE NOT REACHED. Springer’s chapter page requires a login, no preprint or repository copy of the chapter exists, and the Internet Archive’s scan of the volume is lending-restricted, so the text could not be read for this sheet. The summary and the claims below are therefore written from the bibliographic record together with Boyer’s own published statements of the same programme, which this survey summarises — principally Physical Review D 11, 790 and 809, 1975, and his later review at /library/stm-1011f1af4f — and the locators cite the chapter’s page range and, where a result is derived, the companion paper rather than section numbers this library could not verify. The complete chapter is at the source. Boyer wrote from the Department of Physics, City College of the City University of New York.

How to cite it

Timothy H. Boyer (1980) A Brief Survey of Stochastic Electrodynamics doi:10.1007/978-1-4757-0671-0_5

Where it sits in the curriculum

What the vacuum is