1.2 The Strengths of the Coupling Constants




One of the most important conclusions to be drawn from the empirical evidence relates to the relative strength of the coupling constants. Expressed in nondimensional form as g2/hc, the electromagnetic coupling constant is then the fine-structure constant α = e2/ħc = 1/137. It is small, but not by many orders of magnitude compared to one. The same is true for the strong and weak coupling constant. Only the gravitational coupling constant g2/ħc = Gm2I ħ c makes an exception. For an electron, it is about 42 orders of magnitude smaller. If one asks what the mass of an elementary particle would have to be for its gravitational coupling constant to become equal to one, one finds that it would have to be equal the Planck mass mp for which Gmp2 = hc .

There are theoretical reasons which make us believe that the strong, weak, and electromagnetic interactions become equal, and of the order one, at a mass scale about 103 - 104 times smaller than the Planck mass [1]. Because this so-called GUT scale is on a logarithmic scale surprisingly close to the Planck scale, again suggests that gravity may be at the root of all interactions. However, because a typical spinor mass is so much smaller than a Planck mass, this hypothesis requires the existence of a mass-compensating effect. It was shown by Nussinov [2] that to be consistent with a large body of observational evidence, all interactions except gravity must fall into a narrow "universality strip." Since the gravitational interaction of the Planck mass falls into the same "universality strip," this gives additional weight to the hypothesis that all interactions are reduced to gravity as it was conjectured by Einstein.


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