# The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Statistical Model for Short Steps

#### 2.1. On Microstates

#### 2.2. Maximum Entropy

#### 2.2.1. The Prior

#### 2.2.2. The Global Constraint

#### 2.3. The Transition Probability

## 3. Some Notation

## 4. Entropic Time

#### 4.1. An Instant

#### 4.2. Ordered Instants

#### 4.3. Duration

#### 4.4. The Local-Time Diffusion Equations

#### 4.5. The Phase Functional

## 5. The Structure of Surface Deformations

## 6. Entropic Geometrodynamics

#### 6.1. The Canonical Updating Scheme

#### 6.2. The Canonical Variables

## 7. The Canonical Structure of Space-Time

#### Path Independence

## 8. The Canonical Representation

#### 8.1. The Super-Momentum

#### 8.1.1. Gravitational Super-Momentum

#### 8.1.2. The “Matter” Super-Momentum

#### 8.2. The Super-Hamiltonian

#### 8.2.1. Modified Poisson Brackets

#### 8.2.2. The “Matter” Super-Hamiltonian

#### 8.2.3. The Gravitational Super-Hamiltonian

#### Total super-Hamiltonian

## 9. The Dynamical Equations

#### 9.1. Some Formalism

#### 9.2. The Evolution of the “Matter” Sector

#### 9.2.1. Dynamical Equations for the Probability and Phase

#### 9.2.2. The Local Time Hamilton-Jacobi Equations

#### 9.3. The Evolution of the Geometrical Variables

#### 9.3.1. Evolution of Metric

#### 9.3.2. Evolution of Conjugate Momentum

## 10. Quantum Sources of Gravitation

#### 10.1. Quantum Operators in ED

#### 10.2. Geometrodynamics with Quantum Sources

#### 10.3. Quantum Dynamics

#### But is it Quantum?

## 11. Concluding Remarks

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Ipek, S.; Caticha, A.
The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity. *Symmetry* **2020**, *12*, 1324.
https://doi.org/10.3390/sym12081324

**AMA Style**

Ipek S, Caticha A.
The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity. *Symmetry*. 2020; 12(8):1324.
https://doi.org/10.3390/sym12081324

**Chicago/Turabian Style**

Ipek, Selman, and Ariel Caticha.
2020. "The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity" *Symmetry* 12, no. 8: 1324.
https://doi.org/10.3390/sym12081324