A refined estimate of the fine structure constant

Abstract

Quantum electrodynamics (QED) is an immensely powerful theory whose validity extends over distance scales from 10−16 cm to light years. But it is unsatisfactory for many reasons, not least of which is the arbitrariness of the electromagnetic coupling strength, the fine structure constant α, and the incomprehensible commensurability of the electric charges of different particles. When extending QED to distances smaller than 10−16 cm it is common to combine it first with the weak interactions1–3 and subsequently with the strong interactions into a grand unified theory (GUT) of all elementary particle interactions4,5. The incorporation of QED and the other fundamental interactions into a GUT is only possible if these interactions and the particles experiencing them satisfy some non-trivial constraints6. It is well-known that the incorporation of QED into a simple unifying group imposes charge quantization4,5. Stability of baryons in GUTs requires the grand unification energy scale mx to be ≳1014 GeV. Couplings in renormalizable field theories such as QED evolve logarithmically with energy, and for the effective α to be less than unity—necessary if the GUT is to make sense—then >l/25 (ref. 7). We point out here that within the same standard set of grand unifying assumptions used previously, a much more refined estimate of the fine structure constant is possible: 1/120 ≳ α ≳ 1/170. We use only the general observations6 that light fermions can be grouped into ‘families’ or ‘generations’ of 15 helicity states, that the strong interactions become strong of a scale of the order of 1 GeV, and that any grand unification energy scale must lie between 1014 (for baryons to be stable enough) and 1019 GeV (the energy at which gravity becomes of unit strength). We know of no other theoretical framework8 for particle interactions which can provide such convincing and restrictive constraints on α, and we find it hard to believe that the experimental value of α = 1/137 is a coincidence.