Time Regained: Volume 1: Symmetry and Evolution in Classical Mechanics
Time Regained: Volume 1: Symmetry and Evolution in Classical Mechanics
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Abstract
This book is the first volume of a two part project articulating a new approach to the analysis of time in modern physical theory. Our particular concern is with the Problem of Time as it occurs in theories which feature dynamical laws that are invariant under time reparametrization symmetries. The class of such theories includes both simple mechanical theories and the general theory of relativity, and prospective theories of quantum gravity. Our goal is to provide a solution to the problem of time such that determinate time ordering structure can be reconciled with reparametrization symmetry. The present volume is focused on the context of classical mechanical theory within analytical formulations. This restricted context will allow us to develop a new framework for the analysis of symmetry and structure in physical theory and provide a fully general and explicit resolution of the classical mechanical problem of time.
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Front Matter
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1
Introduction
Sean Gryb andKarim P. Y. Thébault
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Part I NATURAL PHILOSOPHY OF TIME
Sean Gryb andKarim P. Y. Thébault -
Part II SYMMETRY AND STRUCTURE
Sean Gryb andKarim P. Y. Thébault-
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Structure and Possibility
Sean Gryb andKarim P. Y. Thébault
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6
Conservation and Geometry
Sean Gryb andKarim P. Y. Thébault
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7
Irregular Nomic Structure
Sean Gryb andKarim P. Y. Thébault
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8
Diagnosing Dynamical Redundancy
Sean Gryb andKarim P. Y. Thébault
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9
The New Framework
Sean Gryb andKarim P. Y. Thébault
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5
Structure and Possibility
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Part III THE PROBLEM OF TIME IN CLASSICAL MECHANICS
Sean Gryb andKarim P. Y. Thébault-
10
Spatiotemporal Structure and Theory Re-Articulation
Sean Gryb andKarim P. Y. Thébault
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11
Local Temporal Symmetry
Sean Gryb andKarim P. Y. Thébault
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12
Reparameterization Invariant Dynamics
Sean Gryb andKarim P. Y. Thébault
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13
Temporal Structure Regained
Sean Gryb andKarim P. Y. Thébault
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14
Conclusion and Prospectus
Sean Gryb andKarim P. Y. Thébault
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10
Spatiotemporal Structure and Theory Re-Articulation
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End Matter
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