Gravitational Constant: Limits on Variations

Newton's gravitational constant G has been measured in the laboratory with reasonable accuracy only for a limited range of distances. A priori there is no guarantee that G has the same numerical value at much larger distances, and neither is it clear that its value has always been the same in the past. As long as we have no consistent quantum theory of gravity, it is hard to find any theoretical argument pro or con such variations. This makes it all the more important to see to what extent observations can put limits on possible variations of G in space and time.

Around 1980, the uncertainty in the comparison between the value of G at laboratory scales and at astrophysical distances was estimated to be roughly 40%. At that time, I realized that I could use white dwarfs in order to further tighten this value. Even though neutron stars have a much stronger gravitational field, there are far greater uncertainties in the equation of state of a neutron star than in that of a white dwarf. In the paper:

• A Constraint on the Distance Dependence of the Gravitational Constant, by Hut, P., 1981, Phys. Lett. 99B, 174-178.

I concluded that the two values of G were the same within 10%.

A few years later, these limits were further tightened at larger scales through improved geophysical measurements in mine shafts, and many years later at shorter scales through a set of ingenious experiments in Seattle at the University of Washington to distances of less than 1 mm, and subsequently in Boulder, Colorado at even smaller distances around 0.1 mm; cf. J.C. Long et al., 2003, Nature 421, 922.

If the gravitational constant would be subject to variations in time, as Dirac once speculated, any two bodies revolving around each other in a gravitationally bound orbit would slowly change their orbital parameters. We improved upon previous derivations of these changes, generalizing those more limiting cases, in the paper:

• The Two-Body problem with a Decreasing Gravitational Constant, by Hut, P. & Verhulst, F., 1976, Mon. Not. R. astr. Soc. 177, 545-549.

For a much more recent paper on this topic, see A new white dwarf constraint on the rate of change of the gravitational constant, by Marek Biesiada and Beata Malec.