A covariant approach to entropic dynamics

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 [4][5] 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, Kuchař, 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 Kuchař.

Entropic Dynamics: Quantum Mechanics from Entropy and Information Geometry

“…In a relativistic theory there is a greater freedom in the choice of instants and this translates into a greater flexibility with the notion of simultaneity. Conversely, as we have shown elsewhere, the requirement that these different notions of simultaneity be consistent with each other places strict constraints on the allowed forms of relativistic ED …”

“…This paper focuses on the derivation of the Schrödinger equation but the ED approach has been applied to a variety of other topics including the quantum measurement problem; momentum and uncertainty relations; the Bohmian limit and the classical limit; extensions to curved spaces and to relativistic fields are also available.…”

The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity

“…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.…”

“…Building on these developments are the previous efforts by Ipek, Abedi, and Caticha (IAC) [28,29] to model the ED of quantum scalar fields on a fixed curved background. Of particular interest to us are the manifestly covariant methods developed by IAC, which introduced several novel features to ED.…”

“…In previous work, in the context of a flat space-time [26,27], it was appropriate to introduce a global notion of time, in which all spatial points were updated uniformly. As discussed in [28,29], however, this assumption must be relaxed in a curved space-time in favor of a local notion of entropic time. This raises an important challenge, namely, the construction of an updating scheme that is local in nature.…”