Why gravity has no choice: bulk spacetime dynamics is dictated by information entanglement across horizons

Abstract

The principle of equivalence implies that gravity affects the light cone (causal) structure of the space-time. It follows that there will exist observers (in any space-time) who do not have access to regions of space-time bounded by horizons. Since physical theories in a given coordinate system must be formulated entirely in terms of variables which an observer using that coordinate system can access, gravitational action functional must contain a foliation dependent surface term which encodes the information inaccessible to the particular observer. I show that: (i) It is possible to determine the nature of this surface term from general symmetry considerations and prove that the entropy of any horizon is proportional to its area. (ii) The gravitational action can be determined using a differential geometric identity related to this surface term. The dynamics of spacetime is dictated by the nature of quantum entanglements across the horizons and the flow of information, making gravity inherently quantum mechanical at all scales. (iii) In static space-times, the action for gravity can be given a purely thermodynamic interpretation and the Einstein equations have a formal similarity to laws of thermodynamics. (iv) The horizon area must be quantized with A horizon = (8 Għ/c³)m with m = 1, 2, in the semi-classical limit.