In analogy to the fine structure constant, the dimensionless coupling constant of gravity is defined as some reference mass divided by the Planck mass, squared.(adsbygoogle = window.adsbygoogle || []).push({});

But what is the reference mass?? I have read thread https://www.physicsforums.com/threa...-fine-structure-constant.428622/#post-2878965 and other stuff, and conclude that currently the most popular suggestions are: The electron mass, the molecular mass of some gas a star is made from, the QCD scale. None of them appears as fundamental.

I can see the following three fundamental possibilities:

- the smallest mass in the universe (whose deBroglie wavelength is as large as the entire universe); in this case the coupling constant would in fact be tiny

- the Planck mass; the coupling constant is unity identically

- the entire mass-equivalent of the universe; in this case the coupling constant would be huge.

I tend towards the point of view that the coupling constant is unity identically. Has anyone a view on that? Furthermore, Wilczek argues that the coupling constant (for the electron mass inserted?) is tiny at our energy scales but runs towards unity at higher scales. I know the story about running coupling constants, but do not think that this is any answer to the question about their values (which are those at low energies like 1/137).

Thank you in advance for any comment.

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# I Dimensionless coupling constant of gravity

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