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In QM, it is explained that atoms emit light by 'jumping' down orbitals, losing energy, and therefore releasing light of a certain frequency. In Electromagnetism, before QM was invented, how was this emission of light explained? It is true that their explanation broke down for high frequencies, and that this difference in prediction and experiment (Blackbody Radiation/Ultraviolet Catastrophe) led to QM's invention, but this means for lower frequencies their explanation, to some extent worked. What was this explanation, based on continuous, non-quantized, light?

In essence, how is the emission of light from atoms explained in Electromagnetism?

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    $\begingroup$ I’m voting to close this question because it belongs on the history of science and math stackexchange $\endgroup$
    – Dale
    Feb 18, 2023 at 17:37
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    $\begingroup$ @Dale The history of science stack exchange is more about certain conventions, such as conventional current, while my question is about a physics theory that is outdated, and is asking about the physics itself. Electromagnetism is still taught, and my question is about its predictions on the emission of light from atoms. This question belongs in the physics stack exchange, and so could you please revoke your vote? That would be great. Thank you very much. $\endgroup$ Feb 18, 2023 at 17:44
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    $\begingroup$ History of science SE is about exactly these kinds of questions, older theories in historical context, their motivations, etc $\endgroup$ Feb 18, 2023 at 19:50
  • $\begingroup$ @Dale How can you really understand physics without understanding how the phenomena motivated the abstractions? $\endgroup$
    – John Doty
    Feb 19, 2023 at 0:35
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    $\begingroup$ @JohnDoty I didn’t say you could. I just said this question belongs in a different place. It is a good question, but not all good questions belong here. $\endgroup$
    – Dale
    Feb 19, 2023 at 0:59

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The ultraviolet catastrophe was a consequence of statistical mechanics, agnostic as to the radiation mechanism.

Hertz had demonstrated that oscillating electric currents radiate electromagnetic waves. There was abundant evidence (electrochemistry, cathode rays, ...) that there was electricity inside atoms. In Thomson's plum pudding model, oscillations of electrons within the pudding potential could radiate, but they couldn't account for atomic spectra. But Bohr's model captured the spectrum of hydrogen, and quantum mechanics took off.

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Your description of electrons "jumping down orbitals and emitting light" is incomplete. What does it mean to "jump down an orbital"?

In both the classical and quantum cases atoms emit light due to the coupling of the electrons in atoms to the electromagnetic field. In both the classical and quantum cases when a charge is accelerated (like an electron in an atom) the charge loses kinetic energy and the electromagnetic field is excited (i.e. the amplitude of the electromagnetic field increases in the vicinity of the accelerating charge).

The classical description failed largely because it predicted atoms would emit radiation until the electron collides with the nucleus at which time the atom would be essentially inert. This was inconsistent with experiments showing atoms had finite and unchanging spatial extent.

Your description of the ultraviolet catastrophe is a bit unrelated to the failure of classical mechanics to describe radiation of light by atoms. That's a different story as explained in John Doty's answer.

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  • $\begingroup$ The plum pudding model didn't suffer from decay. But, of course, it wan't compatible with the discovery of the nucleus. $\endgroup$
    – John Doty
    Feb 18, 2023 at 19:24
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Emission and absorption of light by atoms can be treated by modelling the atom as an oscillating electric dipole and analysing its interaction with an electromagnetic wave.

The model actually explains reasonably well the radiative lifetimes and absorption cross-sections of many transitions, but has numerous points of failure.

It cannot explain why atoms in the ground state don't just radiate until the electrons spiral into the nucleus. It cannot explain why some transitions are much less likely than others (forbidden transitions) and it cannot explain really explain why spontaneous emission occurs in the absence of a stimulating electromagnetic field.

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  • $\begingroup$ > "it cannot explain really explain why spontaneous emission occurs in the absence of a stimulating electromagnetic field." That's a deficiency of non-relativistic theory, classical or quantum. In relativistic EM theory with retarded fields, oscillating dipole loses energy by emission of radiation even in absence of external field, and its charged constituents experience radiation damping. E.g. the Lorentz-Abraham estimation of damping force is of the correct order of magnitude to explain spontaneous emission times of hydrogen excited states. I think this was first analyzed by J. Larmor. $\endgroup$ Feb 20, 2023 at 3:56

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