I have been playing a bit with the units of coupling constants. Instead of setting c=1, h=1 (natural units) it is interesting to set c=1 but still to keep h explicit in the formulae.(adsbygoogle = window.adsbygoogle || []).push({});

You may know that in natural units there is a basic difference between electromagnetism and gravity, namely that gravity is a dimensional constant with dimensions of area, while electromagnetism is not.

But if we do not put h=1, then other difference appears. In one of them, h is in the numerator, in the other h is in the denominator.

So I wonder, can we use this to generate four kinds of coupling constant? The two new ones should be

a) As the gravity, but without the area term: we get a constant force, depending on masses but not in distance.

b) As the electromagnetism, but with the area term: we get a weaker force, decreasing as the fourth power of distance.

(a) is not exactly the strong force, because there is not a show of asymtotical freedom, and (b) is not exactly the Fermi weak force. But it is an interesting rule. On the other hand, it should imply that gravity unifies with SU(3)... I have never heard such a thing.

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# Force constants and semi-natural units

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