Recent evidence suggests a possible increase with time of the fine structure constant over cosmological time scales. This raises the question of which fundamental quantities are truly constant and which might be time-dependent. Several candidate theories exist in which either the electric charge, e, or the speed of light, c, may vary. In a paper in the August 2002 edition of Nature, we point out that black hole thermodynamics may provide a means to potentially discriminate between alternative theories because changes in e and/or c affect the area of a charged black hole. Since the event horizon area is widely accepted as a measure of the entropy of the black hole some variations in the fundamental ‘constants’ could lead to a violation of the generalized second law of thermodynamics.

The utility of the idea lies in distinguishing between varying constant theories, not between varying constants alone, particularly when we are referring to constants with dimensions such as e and c. Without a background theory, in which the ‘constants’ that vary are well defined, a change in a dimensional constant is always degenerate with a change in the measuring apparatus (a change in the units you use to measure). Without a background theory, you need to make some arbitrary assumptions about what should not change. In the example in our paper we assume that the mass of the black hole remains constant during the cosmological variation. Arguments from quantum black holes suggest that it is more likely that mass changes while entropy remains constant.The full implementation of this idea therefore awaits the further development of black hole solutions in varying constant theories. At the moment we are limited to using the general relativistic formula for black hole horizon entropy. Since general relativity is a theory in which no variation of constants occurs we cannot necessarily expect that it would be valid even in the limit of slow variations. This idea therefore provides a strong incentive for developing the varying constant theories to include black hole and entropy solutions.