INFORMATION AND GRAVITATION

An information-theoretic approach is shown to derive both the classica l weak-field equations and the quantum phenomenon of metric fluctuatio n within the Planck length. A key result is that the weak-field metric (h) over bar(mu nu) is proportional to a probability amplitude phi(mu nu), on quantum fluctuations in four-position. Also derived is the co rrect form for the Planck quantum length, and the prediction that the cosmological constant is zero. The overall approach utilizes the conce pt of the Fisher information I acquired in a measurement of the weak-f ield metric. All associated physical information K is defined as K = I - J, where J is the information that is intrinsic to the physics (str ess-energy tensor T-mu nu) of the measurement scenario. A posited cons ervation of information change delta I = delta J implies a variational principle delta K = 0. The solution is the weak-field equations in th e metric (h) over bar(mu nu) and associated equations in the probabili ty amplitudes phi mu nu. The gauge condition phi(,nu)(mu nu) = 0 (Lore ntz condition) and conservation of energy and momentum T-,nu(mu nu) = 0 ale used. A well-known ''bootstrapping'' argument allows the weak-fi eld assumption to be lifted, resulting in the usual Einstein field equ ations. A special solution of these is well known to be the geodesic e quations of motion of a particle. Thus, the information approach deriv es the classical field equations and equations of motion, as well as t he quantum nature of the probability amplitudes phi(mu nu).