A Covariant Approach to Entropic Dynamics

TL;DR

This paper develops a covariant formulation of Entropic Dynamics that incorporates local entropic time, aligning with relativity and ensuring path independence through Poisson bracket constraints.

Contribution

It introduces a covariant approach to Entropic Dynamics using local entropic time and Poisson constraints, enhancing compatibility with relativistic principles.

Findings

Achieves manifest Lorentz symmetry in entropic dynamics

Introduces local entropic time compatible with relativity

Ensures path independence via Poisson bracket constraints

Abstract

Entropic Dynamics (ED) is a framework for constructing dynamical theories of inference using the tools of inductive reasoning. A central feature of the ED framework is the special focus placed on time. In previous work a global entropic time was used to derive a quantum theory of relativistic scalar fields. This theory, however, suffered from a lack of explicit or manifest Lorentz symmetry. In this paper we explore an alternative formulation in which the relativistic aspects of the theory are manifest. The approach we pursue here is inspired by the works of Dirac, Kuchar, and Teitelboim in their development of covariant Hamiltonian methods. The key ingredient here is the adoption of a local notion of time, which we call entropic time. This construction allows the expression of arbitrary notion of simultaneity, in accord with relativity. In order to ensure, however, that this local time dynamics is compatible with the background spacetime we must impose a set of Poisson bracket constraints; these constraints themselves result from requiring the dynamcics to be path independent, in the sense of Teitelboim and Kuchar.