# Ultraviolet catastrophe

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 $kT/2$ . 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, a point that was made independently by Einstein and by Lord Rayleigh and Sir James Jeans in the year 1905. Einstein pointed out that the difficulty could be avoided by making use of a hypothesis put forward five years earlier by Max Planck. Planck had postulated 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.