Rick's Critique of the Cosmic Coincidences: Appendix G

The Running Couplings

In Appendices C, D, E and F we have defined the coupling constants of the gravitational force, the electromagnetic force, the weak nuclear force and the strong nuclear force respectively. The theories described there, in terms of which the coupling constants were defined, have all been superseded by more modern theories. In the case of electromagnetism and the nuclear forces this results in the coupling constants becoming dependent upon the energy of the interaction in question. The coupling constants as explicit functions of energy are known as "running couplings".

The energy dependence of the couplings results from the renormalisation properties of the gauge theories which are now believed to underpin these interactions. Explicit energy functions are given herein, but not derived. The derivations are challenging and require renormalisation group calculations. The coupling strength of the strong nuclear force reduces at higher energies, whilst that of the electroweak field increases. Physically these behaviours result from anti-shielding and shielding effects respectively. The anti-shielding of the strong force is believed to account for the confinement of quarks and gluons - that is, to explain why quarks and gluons are never found as free particles.

The variation of the couplings is substantial, even at energies which are commonly achieved in the laboratory. Thus, the low energy strong coupling constant, gs, is ~13.5 at nuclear energies (tens of MeV), but only ~3.5 at perhaps 640 MeV, falling to ~1.22 at the mass of the Z boson (91 GeV). The electromagnetic fine structure constant, whose low energy value is 1/alpha = 137.036, becomes 127.918 at the Z boson mass. However, caution is needed because the energy dependence is, to a degree, a matter of convention. These energy dependencies are correct if used together with certain conventions in field theory calculations.

The variation of the coulpings with energy effectively discredits attempts to derive 1/alpha = 137.036 from pure mathematics.

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