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In physics, the ultraviolet catastrophe, also called the
Rayleigh-Jeans catastrophe, is the classical
prediction, first made in the late 19th century, that an ideal black body at
thermal equilibrium will emit radiation with infinite power. As this is clearly shown by observation to be false, it was one of
the first clear indications of problems with classical physics. Max Planck's
attempt at solving this problem led to one of the early portions of quantum mechanics.
It was called the "ultraviolet" catastrophe because ultraviolet radiation had the highest frequencies of any radiation known
at the time (X-rays and gamma rays had
not been discovered yet). It was also sometimes called the "violet catastrophe" for short. Since the first appearance of the
term, it has also been used for other predictions of a similar nature, e.g. in quantum electrodynamics (also used in those cases: ultraviolet divergence).
The ultraviolet catastrophe results from the equipartition
theorem of classical statistical mechanics which
states that all modes (degrees of freedom) of a system at equilibrium have an average energy of kT. According to
classical electromagnetism, the number of
electromagnetic modes in a 3-dimensional cavity, per unit frequency, is
proportional to the square of the frequency. This therefore implies that the radiated power per unit frequency should follow the
Rayleigh-Jeans law, and be proportional to frequency squared. Thus, both the power at a given frequency and the total radiated power
go to infinity as higher and higher frequencies are considered: this is clearly an impossibility.
Max Planck resolved this issue by postulating that electromagnetic energy
did not follow the classical description, but could only oscillate or be emitted in discrete packets of energy proportional to
the frequency (as given by Planck's law). This has the effect of reducing
the number of possible modes with a given energy at high frequencies in the cavity described above, and thus the average energy
at those frequencies by application of the equipartition theorem. The radiated power eventually goes to zero at infinite
frequencies, and the total predicted power is finite.
The formula for the radiated power for the idealized system (black body) was
in line with known experiments, and came to be called Planck's law of black body radiation. Based on past experiments, Planck was also able
to determine the value of its parameter, now called Planck's
constant. The packets of energy later came to be called photons, and played a key
role in the quantum description of electromagnetism.
References
- Charles Kittel and Herbert Kroemer, Thermal Physics, 2nd ed. (W. H. Freeman and Company: New York, 1980), chapter
4.
- Claude Cohen-Tannoudji, Bernard Diu, and Franck Laloë, Quantum Mechanics: Volume One (Hermann: Paris, 1977), p.
624–626.
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