The problem of time : quantum mechanics versus general relativity / Edward Anderson.
Anderson, Edward.
2017
QC178
Available Online

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Title The problem of time : quantum mechanics versus general relativity / Edward Anderson.
Author Anderson, Edward.
ISBN 9783319588483 (electronic book)
3319588486 (electronic book)
9783319588469
331958846X
Publication Details Cham : Springer, 2017.
Language English
Description 1 online resource.
Call Number QC178
Dewey Decimal Classification 530.12
530
Summary This book is a treatise on time and on background independence in physics. It first considers how time is conceived of in each accepted paradigm of physics: Newtonian, special relativity, quantum mechanics (QM) and general relativity (GR). Substantial differences are moreover uncovered between what is meant by time in QM and in GR. These differences jointly source the Problem of Time: Nine interlinked facets which arise upon attempting concurrent treatment of the QM and GR paradigms, as is required in particular for a background independent theory of quantum gravity. A sizeable proportion of current quantum gravity programs - e.g. geometrodynamical and loop quantum gravity approaches to quantum GR, quantum cosmology, supergravity and M-theory - are background independent in this sense. This book's foundational topic is thus furthermore of practical relevance in the ongoing development of quantum gravity programs. This book shows moreover that eight of the nine facets of the Problem of Time already occur upon entertaining background independence in classical (rather than quantum) physics. By this development, and interpreting shape theory as modelling background independence, this book further establishes background independence as a field of study. Background independent mechanics, as well as minisuperspace (spatially homogeneous) models of GR and perturbations thereabout are used to illustrate these points. As hitherto formulated, the different facets of the Problem of Time greatly interfere with each others' attempted resolutions. This book explains how, none the less, a local resolution of the Problem of Time can be arrived at after various reconceptualizations of the facets and reformulations of their mathematical implementation. Self-contained appendices on mathematical methods for basic and foundational quantum gravity are included. Finally, this book outlines how supergravity is refreshingly different from GR as a realization of background independence, and what background independence entails at the topological level and beyond. .
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Series Fundamental theories of physics ; v. 190.
Available in Other Form Print version: 9783319588469
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The Problem of Time; Preface; From the Accepted Paradigms of Physics to Quantum Gravity; Differing Roles of Time and Space Throughout the Paradigms of Physics; Background Independence in Mechanics, GR and Quantum Gravity; The Problem of Time; Concerning This Book's Three Parts, Appendices and Epilogues; Acknowledgements; Contents; Part I: Time in Fundamental Physics; Chapter 1: Introduction: Conceptual Outline of Time; 1.1 Time-Related Notions; 1.2 Space-Related Notions Make for Useful Comparison; 1.3 Physical Limitations on Intuitive Notions of Time and Space; 1.4 Events

1.5 Philosophical Worldviews of Time1.6 Some Properties Attributed to Time; 1.7 Continuum Mathematics Models for Time; 1.8 Some Basic Properties of Timefunctions; 1.9 Non-continuum Modelling of Time; 1.10 Mathematical Modelling of Space; 1.11 Advent of Notions of Spacetime; 1.12 `Measuring Time': Extra Connotations in the Word `Clock'; 1.13 Measuring Length; Chapter 2: Time, Space and Laws in Newtonian Mechanics; 2.1 Newton's Laws of Mechanics; 2.2 Impact of Newtonian Mechanics; 2.3 Newtonian Absolute Space; 2.4 Newtonian Absolute Time

2.5 Aristotelian, Galilean and Newtonian Paradigms Compared2.6 Newton's Bucket; 2.7 Newtonian Gravity; 2.8 Electrostatics; 2.9 Gravitation and Electrostatics Compared; 2.10 Magnetostatics; 2.11 Light Flashes; 2.12 Cartesian and Curvilinear Tensors Within the Newtonian Paradigm; 2.13 Principles of Dynamics (PoD) formulations of Mechanics; Chapter 3: Absolute Versus Relational Motion Debate; 3.1 Two Centuries of Critique of the Newtonian Paradigm; 3.2 Concrete Example of Relational Particle Mechanics (RPM); 3.3 Ephemeris Time as a Realization of Mach's Time Principle

3.4 Universality of Relational Thinking3.5 Electromagnetic Uni cation and the Luminiferous Aether; Chapter 4: Time, Space, Spacetime and Laws in Special Relativity; 4.1 Special Relativity (SR); 4.2 Invariant Interval, Inde nite Metric and Proper Time; 4.3 Minkowski Spacetime's Geometrical Structure and Its Physical Meaning; 4.4 Lorentzian Tensors (Alias 4-Tensors); 4.5 Minkowskian Paradigm of Physics; 4.6 More on Time and Spacetime in the Minkowskian Paradigm; 4.7 More on SR Clocks; 4.8 Length Measurement in SR; 4.9 Einstein's Eventual Opinion on the Theoretical Status of Clocks and Rods

4.10 Exercises I. Time in Mechanics and SRChapter 5: Time and Ordinary Quantum Mechanics (QM); 5.1 A Simple Axiomatization of QM; 5.2 Experimental Support for QM and Examples; 5.3 Time in Nonrelativistic QM; 5.4 Clocks in QM; 5.5 Advent of Atomic Clocks; 5.6 Quantum Inputs to Measuring Lengths and Masses; Chapter 6: Quantum Field Theory (QFT); 6.1 Free Spin-0 Field; 6.2 Free Spin-1/2 Field; 6.3 Free Spin-1 Field: Electromagnetism, and Its Gauge Symmetry; 6.4 Time in Quantum SR; 6.5 Interacting Field Theories, Including Quantum Electrodynamics (QED)

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