Minkowski Spacetime: A Hundred Years Later (Fundamental Theories of Physics, 165)

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. Minkowski Spacetime: A Hundred Years Later Preface References Contributors Raum und Zeit/Space and Time Part I The Impact of Minkowski Spacetime on the Twentieth Century Physics from a Historical Perspective 1 Hermann Minkowski, Relativity and the Axiomatic Approach to Physics 1.1 Introduction 1.2 The Principle of Relativity 1.3 The Basic Equations of Electromagnetic Processes in Moving Bodies 1.3.1 Three Meanings of ``Relativity'' 1.3.2 Axioms of Electrodynamics 1.3.3 Relativity and Mechanics 1.3.4 Relativity and Gravitation 1.4 Space and Time 1.4.1 Groups of Transformations 1.4.2 Empirical Considerations 1.4.3 Relativity and Existing Physical Theories 1.5 Max Born, Relativity, and the Theories of the Electron 1.6 Summary and Concluding Remarks References 2 Minkowski's Modern World 2.1 The Geometry of Physical Space Circa 1907 2.2 World-Geometry (1907--1908) 2.3 The Reception of ``Raum und Zeit'' 2.4 Minkowski's Modern World References Part II Implications of Minkowski Spacetime for Theoretical Physics 3 Hermann Minkowski and Special Relativity 3.1 Introduction 3.2 Newtonian Mechanics 3.3 Special Relativity 3.4 Minkowski and Special Relativity; Geometry and Kinematics 3.5 Minkowski and Special Relativity; Electromagnetic Theory 1 3.6 Minkowski and Special Relativity; Electromagnetic Theory 2 3.7 Conclusions References 4 The Rich Structure of Minkowski Space 4.1 General Introduction 4.2 Minkowski Space and Its Partial Automorphisms 4.2.1 Outline of General Strategy 4.2.2 Definition of Minkowski Space and Poincaré Group 4.2.3 From Metric to Affine Structures 4.2.4 From Causal to Affine Structures 4.2.5 The Impact of The Law of Inertia 4.2.6 The Impact of Relativity 4.2.7 Local Versions 4.3 Selected Structures in Minkowski Space 4.3.1 Simultaneity 4.3.2 The Lattices of Causally and Chronologically Complete Sets 4.3.3 Rigid Motion Appendix 1: Sets and Group Actions Appendix 2: Affine Spaces Appendix 3: Affine Maps Appendix 4: Affine Frames, Active and Passive Transformations References 5 Minkowski Space-Time and Quantum Mechanics 5.1 Time, Space, and Quantum Mechanics 5.2 Heisenberg Representation 5.3 Relation Between Quantum Field Theories and Quantum Mechanics 5.3.1 Particles 5.4 Locality 5.4.1 Leggett's Extention of Bell's Theorem for Non-Linear Classical System 5.5 Conclusion References 6 Modern Space-Time and Undecidability 6.1 Introduction 6.2 Quantum Mechanics with Real Clocks 6.3 Fundamental Limits to Realistic Clocks 6.4 Possible Experimental Implications 6.5 Conceptual Implications 6.6 Undecidability and the Laws of Physics 6.7 Discussion References 7 Quantum Space-Times 7.1 Introduction 7.2 Quantum Nature of the Big Bang 7.2.1 Issue of the Beginning and the End 7.2.2 Some Key Questions 7.2.3 FRW Models and The WDW Theory 7.2.4 Loop Quantum Cosmology: New Quantum Mechanics 7.2.5 LQC: Dynamics 7.3 Black Holes 7.3.1 Horizons 7.3.2 Hawking Radiation and Information Loss 7.3.3 CGHS Black Holes 7.3.4 Quantum Geometry 7.4 Discussion References 8 Space-Time Extensions in Quantum Gravity 8.1 Introduction 8.2 Space-Time in Classical Cosmology 8.3 Atomic Quantum Space-Time 8.3.1 Loop Quantum Cosmology 8.3.2 Harmonic Cosmology 8.3.2.1 Effective Friedmann Equation 8.3.2.2 Cosmic Forgetfulness 8.3.3 Interactions: How Quantum Is The Bounce? 8.3.4 Black Holes 8.4 Effective Equations and Lorentz Invariance 8.5 Conclusions References Part III Conceptual and Philosophical Issues of Minkowski Spacetime 9 The Adolescence of Relativity: Einstein, Minkowski, and the Philosophy of Space and Time 9.1 Introduction 9.2 Einstein and the Definition of Space and Time 9.3 Minkowski's Analysis of Space and Time 9.4 Intermezzo: Space-Time Coordinates as Physical Properties 9.5 Simultaneity, Symmetries and Conventionality References 10 Hermann Minkowski: From Geometry of Numbers to Physical Geometry 10.1 Introduction 10.2 Geometry of Numbers 10.3 Spacetime Diagrams 10.4 Physical Axiomatics 10.5 Conclusion References 11 The Mystical Formula and The Mystery of Khronos 11.1 The Mystical Formula 11.2 The Mystery of Kronos 11.3 Arrows of Time 11.4 Open Questions 11.4.1 Are The Arrows of Time Correlated ? 11.4.2 Time in Quantum Gravity 11.4.3 Closed Time-Like Curves and Time Travel 11.4.4 A Cyclic Time ? 11.5 Conclusions and Outlook References 12 Physical Laws and Worldlines in Minkowski Spacetime 12.1 Introduction 12.2 Minkowski Spacetime and Reality 12.3 Newton's Three Laws and Worldlines 12.4 Spacetime and Gravity 12.5 Spacetime and Quantum Physics 12.6 Conclusions References 13 Time as an Illusion 13.1 Introduction 13.2 Physics and the Flow of Time 13.3 Time as a Subjective Ordering Device 13.4 Mathematics and Reality 13.5 Conclusion References 14 Consequences of Minkowski's Unification of Space and Time for a Philosophy of Nature 14.1 Philosophy of Nature 14.2 What Is Space? 14.3 Atom, Monad and Aporon 14.4 The Velocity of Communication 14.5 Space-Time Instead of Space and Time This volume is dedicated to the one hundredth anniversary of the publication of Hermann Minkowski's paper "Space and Time" in 1909. His work on the spacetime representation of special relativity had a huge impact on the twentieth century physics to the extent that modern physics would be impossible without the notion of spacetime. While there is consensus on the mathematical significance of spacetime in theoretical physics, for a hundred years there has been no consensus on the nature of spacetime itself. We owe Minkowski a clear answer to the question of the nature of spacetime -- whether it is only a mathematical space or represents a real four-dimensional world. A century after its publication the original Minkowski paper still represents an enrichment to the physicists, especially the relativists, who read it with the intent to fully investigate the depth of Minkowski's ideas on space and time and the physical meaning of special relativity. The volume begins with an excellent retranslation of Minkowski's paper by Dennis Lehmkuhl, accompanied by the original German version of the article. The fourteen contributions are divided into three parts entitled "The Impact of Minkowski Spacetime on the Twentieth Century Physics from a Historical Perspective", "Implications of Minkowski Spacetime for Theoretical Physics", and "Conceptual and Philosophical Issues of Minkowski Spacetime."