The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity

Abstract

Entropic dynamics (ED) are a general framework for constructing indeterministic dynamical models based on entropic methods. ED have been used to derive or reconstruct both non-relativistic quantum mechanics and quantum field theory in curved space-time. Here we propose a model for a quantum scalar field propagating in dynamical space-time. The approach rests on a few key ingredients: (1) Rather than modelling the dynamics of the fields, ED models the dynamics of their probabilities. (2) In accordance with the standard entropic methods of inference, the dynamics are dictated by information encoded in constraints. (3) The choice of the physically relevant constraints is dictated by principles of symmetry and invariance. The first of such principle imposes the preservation of a symplectic structure which leads to a Hamiltonian formalism with its attendant Poisson brackets and action principle. The second symmetry principle is foliation invariance, which, following earlier work by Hojman, Kuchař, and Teitelboim, is implemented as a requirement of path independence. The result is a hybrid ED model that approaches quantum field theory in one limit and classical general relativity in another, but is not fully described by either. A particularly significant prediction of this ED model is that the coupling of quantum fields to gravity implies violations of the quantum superposition principle.

Information theory: A foundation for complexity science

“…The first example, Jaynes’s ( 2 ) derivation of statistical mechanics, opened the floodgates to many recent applications shown in the figure. Because theory construction is more ambitious yet less familiar to many, we discuss this in more detail below ( 2 , 15 – 18 , 24 – 66 ).…”

Major Role of Multiscale Entropy Evolution in Complex Systems and Data Science

“…This formulation of Heisenberg's principle describes the statistical nature of these self-adjoint operators q and p in the Hilbert space. The ED formulation of quantum mechanics was introduced in 2009 and has been applied to fields such as quantum measurement problems [5,6], uncertainty relations [7], curved space-time [8], scalar fields [9][10][11], and finance [12]. The ED approach is an alternative formulation of QM, in which the dynamics of a probability distribution are derived from the entropy [13,14].…”

Quantum Mechanics as Hamilton–Killing Flows on a Statistical Manifold

“…This paper focuses on deriving the mathematical formalism of quantum mechanics, but the ED approach has been applied to a variety of other topics in quantum theory. These include the quantum measurement problem [31,32]; momentum and uncertainty relations [33,34]; the Bohmian limit [34,35] and the classical limit [36]; extensions to curved spaces [37]; to relativistic fields [38][39][40]; and the ED of spin [41].…”