Ultraviolet catastrophe

The ultraviolet catastrophe is the paradoxical prediction of classical statistical mechanics that a perfectly absorbing body — a blackbody — should emit infinite energy at short wavelengths. The Rayleigh-Jeans formula, derived from the classical equipartition theorem, assigns equal energy to each electromagnetic mode in a cavity, and since the number of modes grows without bound as wavelength decreases, the total radiated energy diverges to infinity. This prediction is not merely wrong; it is catastrophically wrong, contradicting both observation and the thermodynamic requirement that a finite-temperature body cannot emit infinite power.

The catastrophe was not a minor anomaly. It was a structural failure of classical physics at the intersection of thermodynamics and electromagnetism, and its resolution required the abandonment of a foundational assumption: the continuity of energy exchange. Max Planck's 1900 introduction of energy quantization — the hypothesis that oscillators exchange energy only in discrete multiples of hν — was explicitly designed to suppress the high-frequency modes that caused the divergence. The ultraviolet catastrophe was thus the forcing function for the quantum revolution, demonstrating that a local failure in one domain (thermal radiation) can destabilize the global architecture of an entire physical theory.