Bohr's Correspondence principle tells us that in the limit of large quantum numbers, quantum physics will agree with classical physics. For example, the simple Rutherford atom model of hydrogen, where a point charge electron orbits a point charge proton in a classical Keplerian orbit, will increasingly agree with observation, in terms of rate of radiative decay and frequency of transition radiation, as the electron orbital energy and angular momentum is raised. (The study of so-called Rydberg atoms, that is, atoms where the outer electron is excited to a high energy level compared to the rest, confirms this.) The frequency of the electromagnetic radiation becomes in the limit of large quantum number simply the frequency of revolution of the electron in its classical orbit. The rate of energy loss is also calculable from the radiation intensity predicted for an accelerating point charge according to classical electrodynamics.

At lower energy levels, and apart from the issue of quantized energy levels, the classical model of radiative decay of the system of bound point charges deviates significantly from observation. There are at least two obvious differences from what the classical model predicts. The transition time between two defined energy levels is less than the classical model predicts, and the frequency of the radiation is inconsistent with the classical expectation. The classical expectation is that the radiation of decay between two energy levels will start at the orbital frequency of the higher energy level and end at the (higher) orbital frequency of the lower. Observation however shows that transition radiation is essentially monochromatic, with the frequency predictable based on simply the energy difference between the levels. These seemingly inexplicable differences with the expectations of classical physics led to some despair at the time of their discovery. The initial triumph of quantum theory, even the early quantum theory of Bohr and Sommerfeld, and later the modern version developed particularly by Heisenberg, Schroedinger, and Dirac, was its ability to accurately describe atomic spectra including these features.

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