Ultraviolet catastrophe

The ultraviolet catastrophe is the classical prediction that a blackbody emits unbounded energy at high frequencies. Experiments contradicted it, and Planck’s quantum hypothesis resolved the discrepancy.

Rayleigh–Jeans law: A classical formula for blackbody spectral radiance that agrees with measurements at low frequencies but diverges at high frequencies. Its high-frequency divergence is the catastrophe’s mathematical expression.
Gustav Kirchhoff: A German physicist whose work established the theoretical importance of universal blackbody radiation. His formulation of the blackbody problem set the stage for later spectral laws.
Blackbody: An idealized object that absorbs all incident radiation and emits a spectrum determined solely by its temperature. The catastrophe concerns the predicted emission of this ideal absorber.
Wien approximation: A short-wavelength approximation to blackbody spectral radiance that decays exponentially with frequency. It avoids the ultraviolet divergence but fails to describe the low-frequency spectrum.
Equipartition theorem: A classical statistical mechanics principle assigning equal average energy to each quadratic degree of freedom at thermal equilibrium. Applied to every electromagnetic mode, it supplies the energy that makes the classical prediction diverge.
Josef Stefan: An Austrian physicist who empirically discovered the temperature dependence of total blackbody emission. His radiation law described total emission, a related part of the same thermal-radiation problem.
Spectral radiance: Radiant power emitted or traveling per unit area, solid angle, and frequency or wavelength interval. The classical divergence concerns spectral radiance as frequency increases.
Classical physics: Physical theories that predate quantum mechanics and describe matter and fields without quantized energy levels. The catastrophe exposed a failure of classical reasoning when applied to radiation at high frequencies.
Planck's law: A formula for blackbody spectral radiance that matches observations across frequencies and temperatures. It replaces the divergent classical spectrum with the observed finite distribution.
Ludwig Boltzmann: An Austrian physicist who developed statistical mechanics and derived the Stefan–Boltzmann law theoretically. His statistical methods helped establish the framework Planck later used.

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