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Relativity is derived from Maxwell's equations, which yield a constant speed of light - a counterintuitive conclusion.

Likewise, which equations and their counterintuitive results yield QM?

I am not asking about QM itself but Max Planck's conclusion in the 1890's that light is quantized.

Can ultraviolet catastrophe be derived or just observed?

I'd prefer a theoretical way to get that just like with speed of light constancy from EM.

I feel electromagnetism has played a similar role in QM just like relativity in terms of those unexpected results.

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    $\begingroup$ Quantum mechanics is not "derived" from anything. As @Roger Vadim mentions, some postulates were built so that the results obtained from them match with experiments. You may find many nicely written books about the history of quantum mechanics. $\endgroup$ Jun 24 at 9:35
  • $\begingroup$ Are you asking about historical reasons for the motivation of quantum mechanics? If so, then the question is probably more suitable for History of Science and Mathematics. $\endgroup$
    – Jakob
    Jun 24 at 9:37
  • $\begingroup$ Tell us what principles are your first principles. Without knowing that, it's hard to help. For example, it seems you consider Maxwell's equations first principles. You might be able to do that, but most people wouldn't consider Maxwell's equations to be first principles. $\endgroup$
    – garyp
    Jun 24 at 10:46
  • $\begingroup$ @garyp of course,maxwell's eq are first principles of relativity, similarly what about old QM of 1890s. $\endgroup$
    – Mini kute
    Jun 24 at 14:13
  • $\begingroup$ I'd love to theoretically get ultraviolet catastrophe, just like constancy oflight-speed from maxwell's eq. @garyp $\endgroup$
    – Mini kute
    Jun 24 at 14:22
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Special relativity is derived from the Einstein postulates - while it is motivated and consistent with Maxwell equations, they are not the basis for the derivation.

Similarly, quantim mechanics is derived from a set of postulates.

The rest is just commentary ;)

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  • $\begingroup$ No The constancy of the speed of light was motivated by Maxwell's theory of electromagnetism. Speed of light constancy is derived from maxwell's eq. Likewise how are the postulates of QM got from classical EM. You misunderstand my motivation. @Roger Vadim $\endgroup$
    – Mini kute
    Jun 24 at 9:21
  • $\begingroup$ Speed of light is an experimental fact. Maxwell equations are a generalization of many experimental facts. The fact that they work very well suggested that the speed of light is important beyond electromagnetic phenomena, but this is motivation, not the derivation. $\endgroup$ Jun 24 at 9:24
  • $\begingroup$ I am talking about 1890's QM which has roots in classical EM. Yes i am talking about the core postulates not QM itself, just like with postulates of relativity, not the theory itself, hence i said first principles which comes down to classical EM. $\endgroup$
    – Mini kute
    Jun 24 at 9:25
  • $\begingroup$ To my knowledge QM was formulated in 1920s. Perhaps, you could revise your question, to make it clearer. $\endgroup$ Jun 24 at 9:27
  • $\begingroup$ I am talking about first principles. 1890s light is emitted in packets. $\endgroup$
    – Mini kute
    Jun 24 at 9:33

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