Cover
Background Independence in Classical and Quantum Gravity
Copyright
Contents
Acknowledgments
1. Introduction
2. Models and Gauge
2.1 Three Classes of Model
2.2 Gauge Redundancies
3. Classical Background Independence
3.1 General Covariance
3.2 Diffeomorphism Invariance
3.2.1 Diffeomorphisms
3.2.2 Two Theories
3.2.3 Diffeomorphism Invariance
3.2.4 Diffeomorphism Invariance and Background Independence
3.3 Absolute Objects
3.3.1 Andersonian Absolute Objects
3.3.2 Confined Objects
3.3.3 Background Independence and Absolute Objects
3.4 Fixed and Absolute Fields
3.4.1 Fixed Fields
3.4.2 Absolute Fields
3.5 Variational Principles
3.6 Belotโs Proposal
3.6.1 Geometrical and Physical Degrees of Freedom
3.6.2 Background Independence
3.6.3 Applications
3.6.4 Problems for Belotโs Program
3.7 Non-Trivial Corner Charges
3.8 Functionalism and Structuralism
3.8.1 Structuralism
3.8.2 Spacetime Functionalism
3.9 Close
4. Classical Theories of Spacetime
4.1 Newtonian Gravity and Newton-Cartan Theory
4.1.1 Classical Spacetimes
4.1.2 Newtonian Gravity
4.1.3 Newton-Cartan Theory
4.1.4 Type-II Newton-Cartan Theory
4.1.5 Background Independence
Newtonian Gravitation
Newton-Cartan Theory
Type-II Newton-Cartan Theory
4.2 General Relativity and Teleparallel Gravity
4.2.1 General Relativity
4.2.2 Teleparallel Gravity
Tetrad Fields
Non-Uniqueness of the Tetrad Fields
The Teleparallel Force Law
Field Equations
4.2.3 Background Independence
4.3 Kaluza-Klein Theories
4.3.1 Kaluza-Klein Theory
Transformations
Field Equations
Justifying the Cylinder Condition
Variational Principles
4.3.2 Coordinate-Independent Kaluza-Klein Theory
4.3.3 Background Independence
4.4 Machian Relationism
4.4.1 Newtonian Spacetime Structure
4.4.2 Machian Relationism
Configuration Space
Emergent Temporality
Best Matching
Relativistic Machian Relationism
Machian Relationist Spacetime Settings
4.4.3 Background Independence
Newtonian Machian Theories
Shape Dynamics
4.5 Close
5. Quantum Theories of Spacetime
5.1 Quantum Background Independence
5.1.1 Models, Reprise
5.1.2 Background Independence
5.2 Perturbative String Theory
5.2.1 Background
5.2.2 Fields
Background Fields and Coherent String States
Primitive Worldsheet Ontology
Field Equations
5.2.3 Background Independence
5.2.4 Closing Remarks
5.3 Holography
5.3.1 Holographic Dualities
5.3.2 Bulk Diffeomorphisms
5.3.3 Background Independence
Minimalist Background Independence
Extended Background Independence
5.3.4 Background Independence and Holography
Minimalist Background Independence
Other Approaches
5.3.5 Coda
General Covariance
Inter-Theory Translation and Background Independence
5.4 Loop Quantum Gravity
5.4.1 Background
Spin Networks and Spinfoams
Dynamics
5.4.2 Background Independence
5.4.3 Discussion
6. Conclusions
Bibliography
Index