Historical research guide · 0448 · 1965
A classical treatment of blackbody radiation
T. W. Marshall
In one minute
This is one of the founding papers of stochastic electrodynamics, the programme that asks how much of quantum behaviour classical physics can recover if you grant it one thing: that empty space is filled with a real random electromagnetic field. Trevor Marshall had already shown that an ordinary charged spring, shaken by a random field whose energy rises with the cube of frequency, settles into a state with many of the properties of the quantum ground state. Here he extends that to space with objects in it — surfaces where boundary conditions apply. He shows that for the radiation field between two conducting plates the resemblance to quantum electrodynamics survives, and he then uses the result to calculate the attraction between two parallel metal plates entirely classically. That attraction is the Casimir force. Lifshitz and his co-workers had reached similar ground with a hybrid method, quantum inside, macroscopic boundaries outside; Marshall shows the calculation can be made consistently classical throughout.
Connection
Chapter two argues that the vacuum is a real structured medium rather than an accounting device, and this paper is the earliest clean demonstration that the most famous piece of vacuum evidence — the pull between two mirrors — falls out of a classical random field with the right spectrum. That makes it a chapter one paper too: it is a worked example of the same measurement being explained twice, from two directions, which is how confidence in a physical picture is actually built.
From the source
A charged classical harmonic oscillator placed in a random electromagnetic field with energy spectrum four pi h nu cubed over c cubed reproduces many properties of the quantum-mechanical ground state.Summary, first sentence
The work is extended to the case where other material bodies are present — that is, to surfaces on which macroscopic boundary conditions are imposed.Summary, second sentence
In the case of the radiation field between two conducting plates, the resemblance to quantum electrodynamics is maintained.Summary, third sentence
The result is used to carry out an entirely classical calculation of the attraction between two parallel metal plates due to dispersion forces — the Casimir effect.Summary, fourth sentence
Considerable progress on problems of this type had been made by Lifshitz and co-workers by imposing macroscopic boundary conditions inside a quantum-mechanical calculation, but the exact status of such a hybrid approach had never been quite clear; the present calculation shows how the treatment may be made consistently classical.Summary, fifth and sixth sentences
There seems no reason why the method should not be extended to treat, for instance, the attraction between dielectric plates.Summary, closing clause
The way in
https://doi.org/10.1007/BF02750449How to cite it
T. W. Marshall (1965) A classical treatment of blackbody radiation doi:10.1007/BF02750449