The Meson and Cosmology

Abstract

THE mean life τ₀ (τ₀ ˜ 2·5 × 10^-6 sec.) of a meson at rest gives us a new fundamental constant of the dimension of time which lies intermediate between the ‘atomic constant’ and the ‘cosmological constant’ t₀ (t₀ ˜ 2 × 10² years). R₀ denotes the ‘classical radius’ of the meson, , where the symbols have their usual meaning. We shall take μ = 170 m, where m is the mass of an electron. We can construct from these basic time units (τ_a, τ₀, t₀) three dimensionless ‘large numbers', , and if, following Dirac and others, we make the hypothesis that ‘large numbers’ are interrelated, we have In comparing such large numbers any differences by factors of about 10³ are to be ignored, as these could be easily taken account of by introducing the dimensionless numbers such as the fine-structure constant hc/e², μ/m and H/m, H being the mass of a proton. Further, on this hypothesis we can connect the above large numbers with the (familiar) large number e²Gμ² ˜ 1·4 × 10²⁸ formed from the gravitational constant G and the atomic constants e, μ. We have: Equation (3a) in the form has already been given by Blackett¹.