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The Wikipedia entry on Physical Constants says:

With the development of quantum chemistry in the 20th century, however, a vast number of previously inexplicable dimensionless physical constants were successfully computed from theory.

Can you give an example of the dimensionless physical constants derived from theory which this excerpt refers to? They don't have to be related to quantum chemistry, any such instance will do.

My motivation for asking this question is that I was reading the Wikipedia entry on the fine structure constant $\alpha$ and how for many physicists it is a secret obsession to derive the value of $\alpha$ from theory. Feynman speculates that this constant could have some relation to transcendental numbers such as $\pi$ or $e$. So I wonder if there are some dimensionless constants derived from theory which have values like that. If so, this might confirm that the universe is truly mathematical in nature, and this would be an incredible discovery in my opinion.

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  • $\begingroup$ Some particular examples related to atomic physics (if not chemistry) might be the values, for various chemical elements, of the Landé g-factor. $\endgroup$
    – user12262
    Commented Feb 22, 2015 at 23:05
  • $\begingroup$ The question (v5) seems like a list question. $\endgroup$
    – Qmechanic ♦
    Commented Feb 23, 2015 at 8:12
  • $\begingroup$ The list is quite limited I believe. $\endgroup$
    – math_lover
    Commented Feb 23, 2015 at 9:01
  • $\begingroup$ It’s probably worth pointing out that while $\alpha$ appears to be constant in time, it’s not independent of the momentum scale at which you probe it. $\endgroup$
    – ragnar
    Commented Apr 30, 2022 at 17:16

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It is interesting that the same year this question was posted I was publishing a monograph (Quanto-Geometry) that undertook the theoretical derivation of a slew of fundamental constants from first principles, including alpha of interest to Joshua Benabou.

Even more interesting that this question remained with no answer here since posted. So I could not help add these lines. The quote from Wikipedia is however inaccurate, since these constants have never been theoretically derived, though attempts never faltered ever since Arthur Eddington. Only one exception of note, the electron gyromagnetic ratio, which QED touts having derived. In my sense in too much of a convoluted or circular fashion.

Joshua says: "So I wonder if there are some dimensionless constants derived from theory which have values like that. If so, this might confirm that the universe is truly mathematical in nature, and this would be an incredible discovery in my opinion."

This paper I published at Cambridge U is no doubt the beginning of a good satisfactory answer to this question, straight theoretical derivation of the vacuum energy density (aka the cosmological constant) as a dimensionless constant. A couple other interesting ones are there too.

https://www.cambridge.org/engage/coe/article-details/6265b71388636c65971e2c05

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