Ultraviolet catastrophe

The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, was the prediction of late 19th century and early 20th century classical physics that an ideal black body at thermal equilibrium would emit an unbounded quantity of energy as wavelength decreased into the ultraviolet range.

[1]: 6–7  The term "ultraviolet catastrophe" was first used in 1911 by Paul Ehrenfest,[2] but the concept originated with the 1900 statistical derivation of the Rayleigh–Jeans law.

The phrase refers to the fact that the empirically derived Rayleigh–Jeans law, which accurately predicted experimental results at large wavelengths, failed to do so for short wavelengths.

As the theory diverged from empirical observations when these frequencies reached the ultraviolet region of the electromagnetic spectrum, there was a problem.

Since the first use of this term, it has also been used for other predictions of a similar nature, as in quantum electrodynamics and such cases as ultraviolet divergence.

The Rayleigh-Jeans law is an approximation to the spectral radiance of electromagnetic radiation as a function of wavelength from a black body at a given temperature through classical arguments.

, the expression is instead This formula is obtained from the equipartition theorem of classical statistical mechanics which states that all harmonic oscillator modes (degrees of freedom) of a system at equilibrium have an average energy of

The "ultraviolet catastrophe" is the expression of the fact that the formula misbehaves at higher frequencies; it predicts infinite energy emission because

An example, from Mason's A History of the Sciences,[4] illustrates multi-mode vibration via a piece of string.

In classical physics, a radiator of energy will act as a natural vibrator.

Thus, both the power at a given frequency and the total radiated power is unlimited as higher and higher frequencies are considered: this is unphysical, as the total radiated power of a cavity is not observed to be infinite, a point that was made independently by Einstein, Lord Rayleigh, and Sir James Jeans in 1905.

In 1900, Max Planck derived the correct form for the intensity spectral distribution function by making some assumptions that were strange for the time.

In particular, Planck assumed that electromagnetic radiation can be emitted or absorbed only in discrete packets, called quanta, of energy:

They modified statistical mechanics in the style of Boltzmann to an ensemble of photons.

Einstein's photon had an energy proportional to its frequency and also explained an unpublished law of Stokes and the photoelectric effect.

The ultraviolet catastrophe is the error at short wavelengths in the Rayleigh–Jeans law (depicted as "classical theory" in the graph) for the energy emitted by an ideal black body . The error, much more pronounced for short wavelengths, is the difference between the black curve (as classically predicted by the Rayleigh–Jeans law ) and the blue curve (the measured curve, predicted by Planck's law ).