Time Regained Volume 1: Symmetry and Evolution in Classical Mechanics

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.

1 - Introduction
2 - On Newton On Time
3 - On Leibniz On Time
4 - On Mach On Time
5 - Structure and Possibility
6 - Conservation and Geometry
7 - Irregular Nomic Structure
8 - Diagnosing Dynamical Redundancy
9 - The New Framework
10 - Spatiotemporal Structure and Theory Rearticulation
11 - Local Temporal Symmetry
12 - Reparametrization Invariant Dynamics
13 - Temporal Structure Regained
14 - Conclusion and Prospectus

Sean Gryb is a theoretical physicist and philosopher working on physical and philosophical aspects of spacetime theory, quantum mechanics and cosmology. Much of his work focuses on two important aspects of quantum gravity: the role of time, as expressed by the 'problem of time', and the role of scale, using a theory called 'shape dynamics'. He is currently a Lecturer at University College Groningen. Sean completed a PhD in Physics from the University of Waterloo. Karim Thébault is a researcher working principally within physics and the philosophy of physics. His main research focus is the 'problem of time' in classical and quantum theories of gravity. Further topics of current interest include dynamical approaches to symmetry, black hole physics, analogue gravity, quantum cosmology, the arrow of time in quantum theory, and the foundations of general relativity. Karim is an Associate Professor in Philosophy of Science at the University of Bristol and gained his PhD in Philosophy at the University of Sydney.