Petkov Minkowski Spacetime: A Hundred Years Later

A Hundred Years Later. (Fundamental Theories of Physics, Vol 165)
1. Auflage 2010
ISBN: 978-90-481-3475-5
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 326 Seiten

Celebrating the one hundredth anniversary of the 1909 publication of Minkowski's seminal paper 'Space and Time', this volume includes a fresh translation as well as the original in German, and a number of contributed papers on the still-controversial subject.

Autoren/Hrsg.

Petkov, Vesselin

Inhaltsverzeichnis

1;Preface;6
1.1;References;9
2;Contributors;12
2.1;Raum und Zeit/Space and Time;15
3;Part I The Impact of Minkowski Spacetime on the Twentieth Century Physics from a Historical Perspective;44
3.1;1 Hermann Minkowski, Relativity and the Axiomatic Approach to Physics;45
3.1.1;1.1 Introduction;45
3.1.2;1.2 The Principle of Relativity;49
3.1.3;1.3 The Basic Equations of Electromagnetic Processes in Moving Bodies;52
3.1.3.1;1.3.1 Three Meanings of ``Relativity'';53
3.1.3.2;1.3.2 Axioms of Electrodynamics;55
3.1.3.3;1.3.3 Relativity and Mechanics;57
3.1.3.4;1.3.4 Relativity and Gravitation;59
3.1.4;1.4 Space and Time;64
3.1.4.1;1.4.1 Groups of Transformations;66
3.1.4.2;1.4.2 Empirical Considerations;68
3.1.4.3;1.4.3 Relativity and Existing Physical Theories;70
3.1.5;1.5 Max Born, Relativity, and the Theories of the Electron;72
3.1.6;1.6 Summary and Concluding Remarks;76
3.1.7;References;81
3.2;2 Minkowski's Modern World;84
3.2.1;2.1 The Geometry of Physical Space Circa 1907;85
3.2.2;2.2 World-Geometry (1907--1908);89
3.2.3;2.3 The Reception of ``Raum und Zeit'';97
3.2.4;2.4 Minkowski's Modern World;100
3.2.5;References;101
4;Part II Implications of Minkowski Spacetime for Theoretical Physics;103
4.1;3 Hermann Minkowski and Special Relativity;104
4.1.1;3.1 Introduction;104
4.1.2;3.2 Newtonian Mechanics;105
4.1.3;3.3 Special Relativity;107
4.1.4;3.4 Minkowski and Special Relativity; Geometry and Kinematics;108
4.1.5;3.5 Minkowski and Special Relativity; Electromagnetic Theory 1;112
4.1.6;3.6 Minkowski and Special Relativity; Electromagnetic Theory 2;117
4.1.7;3.7 Conclusions;119
4.1.8;References;121
4.2;4 The Rich Structure of Minkowski Space;122
4.2.1;4.1 General Introduction;122
4.2.2;4.2 Minkowski Space and Its Partial Automorphisms;124
4.2.2.1;4.2.1 Outline of General Strategy;124
4.2.2.2;4.2.2 Definition of Minkowski Space and Poincaré Group;125
4.2.2.3;4.2.3 From Metric to Affine Structures;128
4.2.2.4;4.2.4 From Causal to Affine Structures;130
4.2.2.5;4.2.5 The Impact of The Law of Inertia;132
4.2.2.6;4.2.6 The Impact of Relativity;134
4.2.2.7;4.2.7 Local Versions;140
4.2.3;4.3 Selected Structures in Minkowski Space;143
4.2.3.1;4.3.1 Simultaneity;143
4.2.3.2;4.3.2 The Lattices of Causally and Chronologically Complete Sets;148
4.2.3.3;4.3.3 Rigid Motion;154
4.2.3.4;Appendix 1: Sets and Group Actions;164
4.2.3.5;Appendix 2: Affine Spaces;165
4.2.3.6;Appendix 3: Affine Maps;166
4.2.3.7;Appendix 4: Affine Frames, Active and Passive Transformations;168
4.2.4;References;170
4.3;5 Minkowski Space-Time and Quantum Mechanics;172
4.3.1;5.1 Time, Space, and Quantum Mechanics;172
4.3.2;5.2 Heisenberg Representation;174
4.3.3;5.3 Relation Between Quantum Field Theories and Quantum Mechanics;175
4.3.3.1;5.3.1 Particles;176
4.3.4;5.4 Locality;179
4.3.4.1;5.4.1 Leggett's Extention of Bell's Theorem for Non-Linear Classical System;183
4.3.5;5.5 Conclusion;187
4.3.6;References;187
4.4;6 Modern Space-Time and Undecidability;188
4.4.1;6.1 Introduction;188
4.4.2;6.2 Quantum Mechanics with Real Clocks;190
4.4.3;6.3 Fundamental Limits to Realistic Clocks;192
4.4.4;6.4 Possible Experimental Implications;193
4.4.5;6.5 Conceptual Implications;194
4.4.6;6.6 Undecidability and the Laws of Physics;198
4.4.7;6.7 Discussion;199
4.4.8;References;199
4.5;7 Quantum Space-Times;201
4.5.1;7.1 Introduction;201
4.5.2;7.2 Quantum Nature of the Big Bang;204
4.5.2.1;7.2.1 Issue of the Beginning and the End;204
4.5.2.2;7.2.2 Some Key Questions;205
4.5.2.3;7.2.3 FRW Models and The WDW Theory;207
4.5.2.4;7.2.4 Loop Quantum Cosmology: New Quantum Mechanics;211
4.5.2.5;7.2.5 LQC: Dynamics;213
4.5.3;7.3 Black Holes;217
4.5.3.1;7.3.1 Horizons;218
4.5.3.2;7.3.2 Hawking Radiation and Information Loss;221
4.5.3.3;7.3.3 CGHS Black Holes;223
4.5.3.4;7.3.4 Quantum Geometry;226
4.5.4;7.4 Discussion;229
4.5.5;References;231
4.6;8 Space-Time Extensions in Quantum Gravity;235
4.6.1;8.1 Introduction;235
4.6.2;8.2 Space-Time in Classical Cosmology;237
4.6.3;8.3 Atomic Quantum Space-Time;237
4.6.3.1;8.3.1 Loop Quantum Cosmology;238
4.6.3.2;8.3.2 Harmonic Cosmology;239
4.6.3.2.1;8.3.2.1 Effective Friedmann Equation;243
4.6.3.2.2;8.3.2.2 Cosmic Forgetfulness;244
4.6.3.3;8.3.3 Interactions: How Quantum Is The Bounce?;246
4.6.3.4;8.3.4 Black Holes;249
4.6.4;8.4 Effective Equations and Lorentz Invariance;252
4.6.5;8.5 Conclusions;256
4.6.6;References;257
5;Part III Conceptual and Philosophical Issues of Minkowski Spacetime;261
5.1;9 The Adolescence of Relativity: Einstein, Minkowski, and the Philosophy of Space and Time;262
5.1.1;9.1 Introduction;263
5.1.2;9.2 Einstein and the Definition of Space and Time;265
5.1.3;9.3 Minkowski's Analysis of Space and Time;272
5.1.4;9.4 Intermezzo: Space-Time Coordinates as Physical Properties;275
5.1.5;9.5 Simultaneity, Symmetries and Conventionality;278
5.1.6;References;282
5.2;10 Hermann Minkowski: From Geometry of Numbers to Physical Geometry;283
5.2.1;10.1 Introduction;283
5.2.2;10.2 Geometry of Numbers;285
5.2.3;10.3 Spacetime Diagrams;287
5.2.4;10.4 Physical Axiomatics;289
5.2.5;10.5 Conclusion;291
5.2.6;References;293
5.3;11 The Mystical Formula and The Mystery of Khronos;294
5.3.1;11.1 The Mystical Formula;294
5.3.2;11.2 The Mystery of Kronos;299
5.3.3;11.3 Arrows of Time;306
5.3.4;11.4 Open Questions;309
5.3.4.1;11.4.1 Are The Arrows of Time Correlated ?;309
5.3.4.2;11.4.2 Time in Quantum Gravity;311
5.3.4.3;11.4.3 Closed Time-Like Curves and Time Travel;313
5.3.4.4;11.4.4 A Cyclic Time ?;314
5.3.5;11.5 Conclusions and Outlook;315
5.3.6;References;316
5.4;12 Physical Laws and Worldlines in Minkowski Spacetime;319
5.4.1;12.1 Introduction;319
5.4.2;12.2 Minkowski Spacetime and Reality;321
5.4.3;12.3 Newton's Three Laws and Worldlines;328
5.4.4;12.4 Spacetime and Gravity;331
5.4.5;12.5 Spacetime and Quantum Physics;336
5.4.6;12.6 Conclusions;338
5.4.7;References;339
5.5;13 Time as an Illusion;341
5.5.1;13.1 Introduction;341
5.5.2;13.2 Physics and the Flow of Time;343
5.5.3;13.3 Time as a Subjective Ordering Device;345
5.5.4;13.4 Mathematics and Reality;348
5.5.5;13.5 Conclusion;349
5.5.6;References;351
5.6;14 Consequences of Minkowski's Unification of Space and Time for a Philosophy of Nature;352
5.6.1;14.1 Philosophy of Nature;352
5.6.2;14.2 What Is Space?;354
5.6.3;14.3 Atom, Monad and Aporon;355
5.6.4;14.4 The Velocity of Communication;356
5.6.5;14.5 Space-Time Instead of Space and Time;357