Nature 292, 436 - 437 (30 July 1981); doi:10.1038/292436a0

A refined estimate of the fine structure constant

John Ellis & D. V. Nanopoulos

CERN, CH 1211 Geneva 23, Switzerland

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 , 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 interactions^4,5. 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 quantization^4,5. Stability of baryons in GUTs requires the grand unification energy scale m _x to be 10¹⁴ GeV. Couplings in renormalizable field theories such as QED evolve logarithmically with energy, and for the effective 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 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 , and we find it hard to believe that the experimental value of = 1/137 is a coincidence.

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