An Etymological Dictionary of Astronomy and Astrophysics
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A → dimensionless number representing the ratio of various → physical constants. For example:
1) The ratio of the → Coulomb force to the → gravitational force for a proton-electron pair (e²/Gm_pm_e), which is of the order of 10⁴⁰.
2) The age of Universe (T = 10-20 x 10⁹ years) in units of the → elementary time: T/t_e≅ 10⁴⁰.
3) The square root of the total number of particles in the Universe ≅ 10⁴⁰.

→ large; → number.

The idea whereby the coincidence of various → large numbers would bear a profound sense as to the nature of physical laws and the Universe. Dirac suggested that the coincidence seen among various large numbers of different nature is not accidental but must point to a hitherto unknown theory linking the quantum mechanical origin of the Universe to the various cosmological parameters. As a consequence, some of the → fundamental constants cannot remain unchanged for ever. According to Dirac's hypothesis, atomic parameters cannot change with time and hence the → gravitational constant should vary inversely with time (G∝ 1/t). Dirac, P. A. M., 1937, Nature 139, 323; 1938, Proc. R. Soc. A165, 199.

→ large; → number; → hypothesis.