Historical research guide · 0569 · 2019
Stochastic Electrodynamics: The Closest Classical Approximation to Quantum Theory
Timothy H. Boyer
In one minute
Timothy Boyer of City College of New York has spent fifty years asking a simple question: how much of quantum physics is really the ordinary physics of charges and fields, once you stop assuming that empty space is empty? This review is his short answer. Stochastic electrodynamics keeps Maxwell’s equations and Newton’s laws exactly as they are, and changes one thing — the source-free part of the field is not zero but a sea of random classical radiation carrying an energy of one half h-bar omega in every mode. Boyer points out that this is not an assumption but a measurement: the Casimir force between cold plates refuses to vanish at absolute zero, and fitting the data returns exactly that energy. With the sea present, atoms no longer collapse, the blackbody spectrum comes out with Planck’s formula, specific heats fall correctly, and van der Waals forces match quantum theory term for term. His conclusion is careful and bold at once: this is the closest classical theory to quantum mechanics we have.
Connection
Chapter 2 says the vacuum is a real, structured medium; Boyer is the physicist who shows what follows if you take that literally inside ordinary classical physics — atoms held up by the field, and Planck’s constant appearing in a theory with no quanta in it. It is the cleanest published bridge between the zero-point field of chapter 2 and the matter-and-inertia arguments of chapter 3.
From the source
Stochastic electrodynamics is classical electrodynamics with a single change: the source-free solution of Maxwell’s equations is not taken to be zero but random classical radiation with a Lorentz-invariant spectrum carrying an energy of one half h-bar omega per normal mode. Because that scale is set by Planck’s constant, a fully classical theory now contains h-bar.Section 2.1, Theoretical Assumptions
The presence of that random radiation is inferred from measurement rather than assumed. Measured Casimir forces do not vanish as the temperature falls toward absolute zero; they go over to a temperature-independent law falling as the inverse fourth power of the plate separation, and fitting the constant to the data returns exactly one half h-bar per normal mode.Section 2.2, Inference from Measurements on the Casimir Effect
For charged harmonic oscillators the classical and quantum answers agree exactly at equilibrium — the same average energy at every temperature, the same fall-off of specific heats at low temperature, the same van der Waals forces both retarded and unretarded, and the same diamagnetism of molecules.Sections 3.1 and 3.2
The problem of atomic collapse dissolves once zero-point radiation is present: an orbiting electron absorbs energy from the random field while radiating energy away, exactly as a harmonic oscillator does. Cole and Zou’s numerical calculation returned a position distribution close to the quantum ground state; Nieuwenhuizen and Liska’s later calculation found self-ionisation instead. What to watch: a relativistic calculation of the classical hydrogen atom, because the plunging orbits the disagreement turns on are precisely the ones relativity changes most.Sections 3.3 and 3.4
With zero-point radiation included, the classical arguments of the early twentieth century lead directly to Planck’s blackbody spectrum plus a zero-point term, and a relativistic scattering calculation shows that detailed balance holds for the zero-point spectrum — the equilibrium result the non-relativistic calculations could not reach.Section 3.5, Planck Spectrum of Blackbody Radiation
Reanalysing the 1910 Einstein–Hopf model with zero-point radiation included changes the damping at low temperature from a velocity-dependent force to a force that acts only when the particle accelerates at the walls. Boyer reports that the resulting low-temperature behaviour has the frictionless aspects usually associated with superfluidity. What to watch: a full classical calculation of superfluid behaviour from zero-point radiation alone.Section 4.4, Superfluid Behavior
The way in
https://doi.org/10.3390/atoms7010029How to cite it
Timothy H. Boyer (2019) Stochastic Electrodynamics: The Closest Classical Approximation to Quantum Theory doi:10.3390/atoms7010029