Ultraviolet catastrophe
In physics, the ultraviolet catastrophe, also called the Rayleigh-Jeans catastrophe, is the classical prediction 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.The ultraviolet catastrophe results from the fact that in classical statistical mechanics, all modes (degrees of freedom) of a system at equilibrium have equal energy kT, and the the number of electromagnetic modes in three dimensions, 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, an impossibility. (This was called the "ultraviolet" catastrophe because the ultraviolet frequencies lie at the high end of the spectrum.)
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). These packets later came to be called photons, and played a key role in the quantum description of electromagnetism. The average number of photons is determined by the Maxwell-Boltzmann distribution, which makes the existence of photons with energy (frequency) much larger than kT unlikely—thus, the radiated power goes to zero at high frequencies, and the total predicted power is finite.
In particular, the expected number of photons was shown to follow what were later called Bose-Einstein statistics (simply the consequence of the Maxwell-Boltzmann distribution for the discrete-packet energy description), since photons are bosons. The formula for the radiated power for an idealized system (blackbody) came to be called Planck's law of black body radiation, and was confirmed in numerous experiments.
The term ultraviolet catastrophe has also been applied to similar situations in quantum electrodynamics in which summing across all energies results in an infinite value because the higher energy terms do not decrease quickly enough to create finite values.