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Several different cosmologies have been proposed in which the strength of the gravitational interaction is variable. Also, it has been suggested that the gravitational interaction may play a significant role in determining the structure of elementary particles, and in particular that the value of the fine structure constant may depend on the strength of the gravitational interaction. It is shown that these two effects taken together would lead to observable discrepancies in the ages of terrestrial rocks and meterorites as determined by different radioactive decay schemes. Analysis of the geophysical data leads to an upper limit of about 3 parts in 10^13 per year on the rate of change of the fine structure constant. If the assumed relation between gravitation and particle structure were valid, this would correspond to a limit on variations in the strength of the gravitational interaction of 2 parts in 10^11 per year. This upper limit is one-fifth of the size of the variations expected according to Dirac's cosmology, and roughly as big as the variation to be expected according to the Brans-Dicke cosmology. It is concluded that either the assumed connection between gravitation and elementary particles does not exist, or, if the connection does exist, that the geophysical data provide a significant limit on possible variations in the strength of the gravitational interaction.
Peebles et al. (Sat,) studied this question.
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