Lecture 1: The UV catastrophe

In this lecture, we explore the historical development of blackbody radiation theories and the pivotal concept of the ultraviolet catastrophe, which ultimately led to the birth of quantum theory.

Towards the end of the 19th century, physicists sought to understand how hot objects emit light. Classical physics, using Maxwell's equations and thermodynamics, attempted to explain this phenomenon but encountered a significant problem: the prediction that all objects should emit infinite energy at short wavelengths, known as the ultraviolet catastrophe. This prediction was clearly unphysical and indicated a fundamental flaw in classical physics.

A blackbody is an idealized object that absorbs all incident radiation and re-emits it perfectly. Experiments with cavity radiators, which approximate blackbody behavior, provided valuable data on the spectral distribution of emitted radiation. The Stefan-Boltzmann Law and Wien's Displacement Law were empirical results that described the total radiated output and the peak wavelength of blackbody radiation, respectively, but a comprehensive theoretical explanation was lacking.

Rayleigh and Jeans attempted to derive the spectral energy density of blackbody radiation using classical theories. They modeled the radiation inside a cavity as standing waves and applied the equipartition theorem from thermodynamics, which assumes that energy is equally distributed among all possible wave modes. Their approach led to the Rayleigh-Jeans Law, which accurately described the spectral energy density at long wavelengths but failed catastrophically at short wavelengths, predicting infinite energy.

This failure highlighted the limitations of classical physics and set the stage for Max Planck's revolutionary idea of energy quantization. Planck proposed that energy is exchanged in discrete amounts, or quanta, rather than continuously. This concept successfully resolved the ultraviolet catastrophe and marked the beginning of quantum theory, fundamentally changing our understanding of physics.

The lecture underscores the importance of the ultraviolet catastrophe in the development of modern physics and provides a foundation for understanding the quantization of energy and the subsequent advancements in quantum mechanics.