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Since my initial study in QM I have found a lot of quotations about the constant of value "1/137", the fine structure constant. Generally the author gives an introduction about it and says the curiosity that physicists have in knowing "why this value".

Now, there is others dimensionless constants, like the ratio of proton/electron rest mass, but i didn't see an general interesting in this dimensionless constant as there is with respect to the fine structure.

Is there a reason to special to focus on the fine structure constant?

Maybe because Feynman and Fermi were excited specifically about the structure constant, the physics after them was too? Maybe actually there is equal searching for answers for any other dimensionless constant, but that i don't know. Please let me know.

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    $\begingroup$ In reality $\alpha$ is not even a constant, it's value depends on an energy scale. The famous $1/137$ is the value of $\alpha$ at the electron mass. $\endgroup$
    – Davide Morgante
    Commented Feb 6, 2021 at 20:36
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    $\begingroup$ Physicists would like to understand all dimensionless constants. $\endgroup$
    – G. Smith
    Commented Feb 6, 2021 at 22:26

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There are many dimensionless constants used in modelling fluid flow and heat transfer- the Mach number, the Reynolds number, Froude number, Nusselt number, etc. These are used for example when building a scale model of an airplane for testing in a wind tunnel; in this case the Reynolds number tells you how to scale the airflow speed in such a manner as to match the scale factor of the model airplane's size, so the test results from the model can be scaled correctly to predict the real-life behavior of the full-size plane.

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  • $\begingroup$ But is it fruitful to try to derive a deeper "meaning" from the value of these in the same way physicists try to drive a "meaning" in the fine structure constant? (I'm personally not trying to search for meaning; but, similar to the question OP, I am curious to try to understand the mindset of those who do.) $\endgroup$
    – prolyx
    Commented Feb 7, 2021 at 3:34
  • $\begingroup$ @JonathanJeffrey, exactly what you desire has indeed been done for every one of these nondimensional groups. They represent (for example) the relative strengths of viscosity and inertia, of gravity and surface tension, and so on. Look this up on wiki, lots has been written about it. $\endgroup$
    – niels nielsen
    Commented Feb 7, 2021 at 3:48
  • $\begingroup$ Thanks! I asked the question because I was just curious to hear your quick thoughts. When you use the word "groups," do you mean it in the math sense or no? $\endgroup$
    – prolyx
    Commented Feb 7, 2021 at 4:04
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    $\begingroup$ no, not in the group-theory math sense, just in the "grouping of variables" sense. $\endgroup$
    – niels nielsen
    Commented Feb 7, 2021 at 6:49

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