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 timedependent. 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.
Tamara Davis, Charles Lineweaver
and Paul Davies
