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What are the intrinsic properties of the two phenomena that makes them part of the same lets say "universe"?

I'm just a graduate mathematician trying to gain physical intuition behind Quantum Mechanics, and, while historical remarks say that Planck solving the ultraviolet catastrophe by the letting energy be not freely available as a continuum and on the other side the existence of the double slit experiment from which were deduced a couple of interesting properties about what we can expect to happen at the atomic scale were the precursors of how QM born as a theory I'm still having troubles to relate them as "different instances of the same set of effects governed by this set of laws" if that makes sense. In other words, how does phenomena appearing on the double slit experiment could somehow appear on the resolution of the ultraviolet catastrophe or vice versa in order to say "this two things are related"? (if that makes my question more understandable).

Maybe I'm just lost at all and I'm not seeing it (?), I'm reading classical books on QM by the way,

  • Cohen-Tannoudji, Claude; Diu, Bernard; Laloë, Franck (1977). Quantum Mechanics. Wiley. ISBN 978-0471164333. Three volumes.

  • Galindo. Quantum mechanics. Springer

and a very math related book which I found to be very pleasant for a mathematician

  • Landsman. Foundations of Quantum Theory. From Classical concepts to Operator Algebras. Springer

Although I found the last one is the most pleasant for me, as mentioned before I want to gain physical intuition initially rather than jumping to C*-algebras right of the bat, if someone can help will be very appreciated.

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The 2 phenomena have nothing to do with each other in terms of their development. Blackbody radiation and the ultraviolet catastrophe was resolved by Planck by hypothesizing that energy is only exchanged as discrete units, quanta.

The development of quantum mechanics proceeded from this hypothesis first by Einstein who explained the photoelectric effect with this, then he explained the specific of heat of solids at cold temperatures amongst other things. Bohr then quantized the orbit of the electron in hydrogen to some success. But after this the Bohr theory broke down relative to experiments in spectroscopy. It wasn't until Heisenberg and Schrödinger took a different approach to explain the spectra. The double-slit experiment wasn't a useful experiment in this development. However, it now serves as a great pedagogic tool to explain the oddness of quantum mechanics when a single particle is used.

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  • $\begingroup$ Maybe I'm gonna encounter this somewhere in the future while reading, but, the classical notion of quanta as conceived by Planck and/or Einstein is still present on Heisenberg/Schrödinger evolution of their theories? $\endgroup$
    – ca-hercor
    Commented Sep 5, 2023 at 20:22
  • $\begingroup$ There is no classical notion of quanta. Moreover, the framework that Planck and Einstein used prior to 1925 wasn't adequate in a large number of ways. So, the "notion" of quanta had to change. The is most evident with matter waves. $\endgroup$
    – JQK
    Commented Sep 5, 2023 at 20:26
  • $\begingroup$ speaking of matter waves, how could you forget de Broglie? $\endgroup$
    – hyportnex
    Commented Sep 5, 2023 at 20:35
  • $\begingroup$ I didn't forget him, just didn't expressly state his name. Many names were left out. $\endgroup$
    – JQK
    Commented Sep 5, 2023 at 20:37
  • $\begingroup$ Thanks for the answer. And for future readers of my own question, I found another gem at my college library just a sec ago, Masayuki Nagasaki - Formation and Logic of Quantum Mechanics which seems to tackle the deductions of the core ideas. $\endgroup$
    – ca-hercor
    Commented Sep 5, 2023 at 21:03

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