How Constant are Fundamental Physical Quantities?
Abstract We reinvestigate Dirac's large number hypothesis (LNH) which implies the variation of one or more basic physical constants with time. We show that the ratio of the inertial masses of elementary particles and the fine structure constant a do not vary with time in the LNH.Using geochemical data on the surface temperature of the earth in the precambrian we can rule out Dirac's conjecture that the gravitational constant G is inversely proportional to cosmic epoch with and without matter creation. Our limit on Ġ/G is one of the best available. We can exclude Gamow's proposal to save the LNH by a variation of the elementary charge e. We also put an upper limit on the variation of the mass of elementary particles.With the data available at present, we cannot rule out Dirac's LNH if either the mass of elementary particles or the velocity of light and Planck's constant are time dependent. A few other models of variable physical constants are also discussed and excluded.