An Entropic Dynamics Approach to Geometrodynamics

Abstract

In the Entropic Dynamics (ED) framework quantum theory is derived as an application of entropic methods of inference. The physics is introduced through appropriate choices of variables and of constraints that codify the relevant physical information. In previous work, a manifestly covariant ED of quantum scalar fields in a fixed background spacetime was developed. Manifest relativistic covariance was achieved by imposing constraints in the form of Poisson brackets and of intial conditions to be satisfied by a set of local Hamiltonian generators. Our approach succeeded in extending to the quantum domain the classical framework that originated with Dirac and was later developed by Teitelboim and Kuchar. In the present work the ED of quantum fields is extended further by allowing the geometry of spacetime to fully partake in the dynamics. The result is a first-principles ED model that in one limit reproduces quantum mechanics and in another limit reproduces classical general relativity. Our model shares some formal features with the so-called semi-classical approach to gravity.

The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity

“…Although there is a growing body of work on modifications of classical GR as a prelude to its eventual quantization, in this paper we pursue a more modest goal: to explore the consequence of a first principles derivation of quantum field theory (QFT) while maintaining classical gravity unmodified. Thus our current work, which expands on [30], extends the efforts of IAC in one crucial respect by allowing the background geometry itself to become dynamical. Following DHKT, the transition to a dynamical background is not accomplished by altering the conditions of path independence, but rather, it is made by an appropriate choice of variables for describing the evolving geometry.…”

“…We present a short review of the ED of infinitesimal steps in curved space-time, adopting the notations and conventions of [28][29][30]. Here the object of analysis is a single scalar field χ (x) ≡ χ x that populates space and whose values are posited to be definite, but unknown, and thus amenable to being described by probabilities.…”

“…Among the successes of the ED framework are principled derivations of several aspects of the quantum formalism [20][21][22][23][24][25][26][27][28][29][30], which have led to many key insights. Foremost among these is the notion of probability itself.…”

The Entropic Dynamics Approach to Quantum Mechanics

“…Or, in the spirit of an entropic dynamics, shall we search for an appropriately constrained dynamics of probabilities and information geometries? First steps towards formulating a first-principles theory along these lines are given in [ 114 , 115 ].…”

The Information Geometry of Space-Time

“…Recent developments indicate that they might be closer than previously thought -the link is entropy. Indeed, in the entropic dynamics approach [3]- [6] QT is derived as an application of entropic methods of inference [7] with a central role assigned to concepts of information geometry. 2 And, on the GR side, the link between gravity and entropy has been recognized from the early work of Bekenstein and Hawking and further reaffirmed in more recent thermodynamic approaches to GR [16]- [21].…”