The Failure of Classical Physics
Analyze the UV catastrophe and the photoelectric effect.
Part 1/3 — Advanced Theory & Mechanics
The transition from classical electrodynamics to quantum mechanics was precipitated by the empirical failure of the Rayleigh-Jeans law to account for the spectral radiance of blackbody radiation at high frequencies. In the late 19th century, the prevailing Maxwellian framework predicted that the energy density per unit frequency, denoted as $u(\nu, T)$, would increase proportionally to the square of the frequency ($\nu^2$). This mathematical divergence, colloquially termed the "Ultraviolet Catastrophe" by Paul Ehrenfest, suggested that a cavity in thermal equilibrium would radiate infinite energy in the ultraviolet and X-ray spectrum, violating the First Law of Thermodynamics and the principle of energy conservation. The resolution of this anomaly required Max Planck’s 1900 introduction of the energy element $\epsilon = h\nu$, a discrete quantization that replaced the continuous energy distribution of the equipartition theorem.