"Next to Kirchhoff's theorem of the proportionality of emissive and absorptive power, the so-called displacement law, discovered by and named after W. Wien, which includes as a special case the Stefan-Boltzmann law of dependence of total radiation on temperature, provides the most valuable contribution to the firmly established foundation of the theory of heat radiation." --Max Planck, 1901. (Apparently he was kind of like William Faulkner in his use of commas to extend a sentence almost to its breaking point.)
I haven't discussed Kirchhoff's law until now, because different discussions of it have seemed to be saying different things, and I couldn't get a clear idea of its significance. Now I'm ready to discuss it, starting with quotations from various authors.
From the statement above, copied from Planck's paper
On the Law of Distribution of Energy in the Normal Spectrum
Max
Planck
Annalen der Physik
vol. 4, p. 553,
vol. 4, p. 553,
(Just an aside to be investigated later: an oscillator is also a clock. This is something to consider when thinking about the difference in classical and quantum oscillators.)
The first description below is from Russia, last one is from France, and in between are two from our well-known, oft-quoted writers in Los Alamos and Austin, repsectively.
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Kirchhoff's radiation law says that the ratio of emissive
power ε(λ,T) of bodies to their absorptivity α(λ,T) is
independent of the nature of the radiating body.
This ratio is equal to the
emissive power of the black body ε0(λ,T) (because its
absorptivity is equal to 1) and depends on the radiation wavelength λ and on
the absolute temperature T:
The function ε0(λ,T)
is given by Planck’s radiation formula.
Kirchhoff’s radiation law is one of
the fundamental laws of thermal radiation and does not apply to other types of
radiation. The law was established by G. R. Kirchhoff in 1859 on the basis of the
second law of thermodynamics and was subsequently confirmed experimentally.
According to Kirchhoff’s radiation law a body that, at a given temperature,
exhibits a stronger absorptivity also exhibits a more intensive emission. One example: when a platinum plate partially covered with platinum black is
heated to incandescence, the blackened end will glow much brighter than the
light end.
--from The Great Soviet Encyclopedia, 3rd Edition. S.v. "Kirchhoff's Radiation Law." Retrieved February 18, 2016 from http://encyclopedia2.thefreedictionary.com/Kirchhoff%27s+Radiation+Law
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In 1860 Kirchhoff derived a general relation between
the radiative and absorptive strengths of a body held at a fixed temperature T.
According to Kirchhoff’s law the ratio of the radiative strength to the
absorption coefficient for radiation at wavelength λ is the same for all bodies at temperature T, and defines a
universal function F(λ, T). This led to the abstraction of an ideal
blackbody for which the absorption coefficient is unity at every wavelength,
corresponding to total absorption. Thus F(λ, T) characterizes the radiative
strength at wavelength λ of a
blackbody at temperature T. The problem was to determine the universal
function F(λ, T).
--Peter W. Milonni, The Quantum Vacuum, pages 1 & 2. © 1994 Academic Press Inc.
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Physicists in the last decades of the nineteenth
century were greatly concerned to understand the nature of black-body
radiation—radiation that had come into thermal equilibrium with matter at a
given temperature T. The energy ρ(υ,T)dυ per volume at frequencies between υ and υ+dυ had been
measured, chiefly at the University of Berlin, and it was known on
thermodynamic grounds that ρ(υ,T) is
a universal function of frequency and temperature, but how could one calculate
this function?
--Steven Weinberg, Lectures
on Quantum Mechanics, p. 1., 1st ed., Cambridge University Press, © S. Weinberg 2013.
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The great conceptions of Nature are those which are
free from specifical properties of objects, at the price of an abstract
formulation which offers dreadful problems of interpretation. This is the case
for the fundamental law of dynamics, for the law of gravitation, for the law of
conservation of energy, for the second principle of thermodynamics.
…
The Kirchhoff theorem on the independence of the law
of black-body radiation upon the material nature of the cavity is some kind of
“miracle” which has to be included in every theory, even if some explanation
for it is not given. This is indeed the gateway through which Planck proceeded
when he introduced abstract oscillators whose physical nature was left
undefined.
These oscillators are in some way present in Quantum
Mechanics which appears in many circumstances as a general model of harmonic
oscillator. A striking example being
given by the universality of the response theory of quantum systems: there is a
unique general form for the fluctuation-dissipation theorem. This simplicity of
the quantum case is in sharp contrast to the with the high specificities of the
classical case.
--Simon Diner, from “The wave-particle duality as an
interplay between order and chaos,” a presentation given at a symposium held at
the University of Perugia during April 1982 in honor of the 90th birthday of
Louis de Broglie. The proceedings of the symposium were published as The Wave-Particle Dualism: A Tribute to
Louis de Broglie on his 90th Birthday, © 1984 by D. Reidel Publishing
Company.
Post Script: Kirchhoff is also known for his current and voltage laws, which might better be called rules, used in analyzing electric and electronic circuits: "sum of currents into a junction is zero" (ingoing current equals outgoing current, a consequence of electric charge conservation), and "sum of voltages around a closed loop is zero" (voltage drops around loop must be equal to and opposite in sign from voltage sources such as batteries in the loop; a consequence of energy conservation). I started my physics training in basic electronics, so I learned about and used Kirchhoff's current and voltage rules before I learned about Kirchhoff's radiation law. Planck (top of page) referred to the latter as Kirchhoff's theorem.
