This book focuses on one of the oldest and most fundamental questions in both physics and philosophy: the nature of time. It presents original theoretical physics research on the 'problem of time' in modern physics, in parallel with a new philosophical framework for the analysis of symmetry and evolution in physical theory, as well as new work on the early modern precursors to the problem of time. Contrary to the standard wisdom, this book argues that a substantive notion of time can, and should, be retained within a consistent formalism for modern physical theory. The book marshals an array of philosophical and formal tools to justify this claim and analyses its physical implications.
This book is the first of a two-volume project articulating a new approach to the analysis of time in modern physical theory. The second volume will extend and apply this approach in the context of classical and quantum gravity including quantum cosmological models.
Author(s): Sean Gryb, Karim P. Y. Thébault
Edition: 1
Publisher: Oxford University Press
Year: 2023
Language: English
Commentary: Publisher PDF | Published: 24 November 2023
Pages: 256
City: New York
Tags: Physics; Time; Physical Theory; Quantum Physics; Classical Mechanics; Symmetry; Determinate Temporal Structure; Philosophy of Physics
Cover
Titlepage
Copyright
Preface
Acknowledgements
Contents
1 Introduction
1.1 The Objects of Our Enquiry
1.2 Symmetry and Evolution
1.3 Transforming Structures
1.4 Time Regained
1.5 Directed Time Ordering and Time's Arrow
2 On Newton On Time
2.1 On Newton's Methodology in the Scholium
2.2 The Tripartite Nature of Newtonian Time
2.3 Was Newton a Functionalist About Time?
2.4 Chapter Summary
3 On Leibniz On Time
3.1 Leibniz's Metaphysics of Time
3.2 The Chronordinal Problem
3.3 The Chronometric Problem
3.4 Chapter Summary
4 On Mach On Time
4.1 Mach's Philosophical Outlook
4.2 The Early Machian View of Time
4.3 Inertial Clocks
4.4 Machian Tensions
4.5 Chapter Summary
5 Structure and Possibility
5.1 Constitutive Structure and Kinematical Possibility
5.2 Nomic Structure and Dynamical Equivalence
5.3 Symmetry and Equivalence
5.4 Chapter Summary
6 Conservation and Geometry
6.1 Canonical Mechanics
6.2 Contact Mechanics
6.3 Conserved Charges and Symmetries
6.4 Isolated Substructures and Narrow Symmetries
6.5 Nomic Structure of Newtonian Mechanics
6.6 Chapter Summary
7 Irregular Nomic Structure
7.1 Irregular Lagrangians
7.2 Constrained Hamiltonian Mechanics
7.3 Dirac's Theorem
7.4 Noether's Second Theorem
7.5 Chapter Summary
8 Diagnosing Dynamical Redundancy
8.1 Variational Symmetries of Histories
8.2 Noether's Second Theorem Revised
8.3 Initial Value Constraints
8.4 Dynamical Redundancy
8.5 Nomic Structure of Barbour{Bertotti Theory
8.6 Chapter Summary
9 The New Framework
9.1 The AIR Classi cation
9.2 The Nomic-AIR Analysis
9.3 Global and Local Structures
9.4 Chapter Summary
10 Spatiotemporal Structure and Theory Re-Articulation
10.1 Structures and Heuristics
10.2 Spatiotemporal Structure in Newtonian Mechanics
10.3 Spatiotemporal Structure in Barbour{Bertotti Theory
10.4 Chapter Summary
11 Local Temporal Symmetry
11.1 Time Reparameterization Invariance
11.2 Dynamical Redundancy and Evolution
11.3 Temporal Leibniz Shifts
11.4 Chapter Summary
12 Reparameterization Invariant Dynamics
12.1 Jacobi Actions as Geodesic Principles on Con guration Space
12.2 Total Energy as a Constant of Motion
12.3 Generalized Hamilton{Jacobi Formalism
12.4 Integrals of Motion and Complete Observables
12.5 Chapter Summary
13 Temporal Structure Regained
13.1 Di erentiating Dynamical Redundancy and Evolution
13.2 A Dynamical View of Hamiltonian Constraints
13.3 The Structure of Jacobi Theories
13.4 Chapter Summary
14 Conclusion and Prospectus
14.1 The Problem of Time in Classical Mechanics
14.2 Quantization and Redundancy
14.3 Gravitation and Refoliation
14.4 The Two Faces of Classical Gravity
14.5 Relational Quantization and the New Copernican Principle
14.6 Resolving the Big Bang
References
Index
