Information and gravitation

Abstract

An information-theoretic approach is shown to derive both the classical weak-field equations and the quantum phenomenon of metric fluctuation within the Planck length. A key result is that the weak-field metric$\bar h_{\mu \nu }$ is proportional to a probability amplitude φ_uv, on quantum fluctuations in four-position. Also derived is the correct form for the Planck quantum length, and the prediction that the cosmological constant is zero. The overall approach utilizes the concept of the Fisher information I acquired in a measurement of the weak-field metric. An associated physical information K is defined as K=I−J, where J is the information that is intrinsic to the physics (stress-energy tensor T_μv) of the measurement scenario. A posited conservation of information change δI=ΔJ implies a variational principle δK=0. The solution is the weak-field equations in the metric$\bar h_{\mu \nu }$ and associated equations in the probability amplitudes φ_uv. The gauge condition φ ^uv_v =0 (Lorentz condition) and conservation of energy and momentum T_v ^μv=0 are used. A well-known “bootstrapping” argument allows the weak-field assumption to be lifted, resulting in the usual Einstein field equations. A special solution of these is well known to be the geodesic equations of motion of a particle. Thus, the information approach derives the classical field equations and equations of motion, as well as the quantum nature of the probability amplitudes φ_uv.