The main focus of this volume is the question: is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a mathematical model of a real four-dimensional world with time entirely given as the fourth dimension? The book contains fourteen invited papers which either directly address the main question of the nature of spacetime or explore issues related to it.

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Springer : Springer e-books

Kluwer Academic Publishers

Springer London, Limited

Springer Nature

Fundamental theories of physics, v. 153, Dordrecht, the Netherlands, 2007

Fundamental theories of physics, v. 153, Dordrecht, 2008

Springer Nature, Dordrecht, the Netherlands, 2007

United States, United States of America

1 edition, October 8, 2007

1, 20071008

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Title 4
Copyright 5
Preface 6
Contents 10
List of Contributors 16
1. The Meaning of Dimensions 18
1.1 Introduction 18
1.2 Dimensions and Fundamental Constants 19
1.3 Eddington and His Legacy 22
1.4 Campbell and His Theorem 24
1.5 Summary 27
2. Some Remarks on the Space-Time of Newton and Einstein 30
2.1 Introduction 30
2.2 Geometry 31
2.3 Classical Mechanics 33
2.4 Special Relativity 38
2.5 The 4D Formulation of Special Relativity 40
3. The Adventures of Space-Time 48
3.1 Introduction 48
3.2 Mathematical Space-Time 51
3.3 Physical Space-Time 55
3.4 Concluding Remarks 61
4. Physics in the Real Universe: Time and Space-Time 66
4.1 The Block Universe 66
4.2 The Unfolding of Time 68
4.2.1 A Broken Wine Glass, Coarse-graining 70
4.2.2 Friction, Coarse-graining 72
4.2.3 Quantum Uncertainty 74
4.2.4 Space-Time Curvature: Time-dependent Equations of State 75
4.2.5 Emergent Complexity and Human Intentions 77
4.2.6 Overall: A Lack of Predictability in the Real Universe 80
4.3 A Realistic Space-Time Picture 81
4.3.1 The Newtonian Case 82
4.3.2 Special Relativity 83
4.3.3 General Relativity 83
4.4 The Emergence of a Block Universe 87
4.4.1 Classical Cases 87
4.4.2 Quantum Indeterminism 88
4.4.3 Global Issues 89
4.4.4 The Far Future Universe 89
4.4.5 Summary: An Evolving Block Universe 90
4.5 Overall: AMore Realistic View 90
4.5.1 Determinism and Becoming 91
4.5.2 The Block Universe and Free Will 92
4.5.3 The Chronology Protection Conjecture 92
4.5.4 The Arrow of Time 93
4.5.5 Issues of Ontology 93
5. The Real World and Space-Time 98
5.1 Introduction 98
5.2 The Space-Time of Relativistic Physics 100
5.3 The 3D World vs. the 4D World 107
5.4 The Observable World 115
6. Four-dimensional Reality and Determinism; an Answer to Stein 118
6.1 Introduction 118
6.2 Reality of a Mirror Reflecting My Light Signal Now at a Distance 119
6.3 Further Verification of the Above Thought Experiment 121
6.4 As Influences from the Future Sometimes Appear (Retroaction), the Future Itself has to Exist 123
6.5 A Thought Experiment Showing Here and Now that the Future Elsewhere Exists 124
6.6 EPR is Highly Relevant to the Problems of Reality at a Distance and Determinism 126
6.7 The Clock Paradox too Demonstrates that Physical Processes at a Distance Realistically Behave According to "merely metrical" Relativistic Relations 127
6.8 Comments on Ohanian's Criticism 129
7. Relativity, Dimensionality, and Existence 132
7.1 Introduction 132
7.2 Special Relativity is Impossible in a Three-dimensional World 133
7.2.1 Relativity of Simultaneity is Impossible in a Three-dimensional World 134
7.2.2 Conventionality of Simultaneity is Impossible in a Three-dimensional World 140
7.2.3 The Existence of Accelerated Observers in Special Relativity is Impossible in a Three-dimensional World 142
7.3 Physical Objects are Four-dimensional Worldtubes 144
7.3.1 Length Contraction Would be Impossible if the Contracting Meter Stick were a Three-dimensional Object 144
7.3.2 The Twin Paradox Would be Impossible if the Twins Were Three-dimensional Bodies 148
8. Canonical Relativity and the Dimensionality of the World 154
8.1 Introduction 154
8.2 Canonical Relativity 157
8.2.1 ADM Formulation 158
8.2.2 Relational Observables 160
8.2.3 Recovering the Minkowski Background 162
8.3 Challenges and Resolutions 165
8.3.1 Singularities 165
8.3.2 Quantum Aspects 166
8.3.3 Resolutions 166
8.4 Conclusions 167
9. Relativity Theory Does Not Imply that the Future Already Exists: A Counterexample 170
10. Absolute Being versus Relative Becoming 180
10.1 Introduction 180
10.2 The Status of Becoming Within Special Relativity 183
10.3 A Purely Heraclitean Generalization of Relativity 188
10.3.1 Fresh Look at the Proper Duration in Special Relativity 189
10.3.2 Physical Implications of the Generalized Theory of Relativity 196
10.3.3 The Raison D'être of Time: Causal Inevitability of Becoming 200
10.4 Prospects for the Experimental Metaphysics of Time 204
10.4.1 Testing Heraclitean Relativity Using Cosmic Neutrinos 205
10.4.2 Testing Heraclitean Relativity Using γ-ray Binary Pulsars 206
10.5 Concluding Remarks 210
11. An Argument for 4D Block World from a Geometric Interpretation of Nonrelativistic Quantum Mechanics 214
11.1 Introduction 214
11.2 Motivating the Geometric Interpretation: STR versus NRQM on the Dimensionality of the World 215
11.3 The Relativity of Simultaneity and Nonrelativistic Quantum Mechanics 218
11.3.1 NRQM: Space-Time Structure for Commutation Relations 220
11.3.2 Heterodoxy: NRQM Does not Live in Galilean Space-Time 222
11.3.3 Philosophical Significance 223
11.4 Density Matrix via Symmetry Group 224
11.4.1 Formalism 224
11.4.2 Philosophical Significance 226
11.5 Geometric Interpretation of NRQM 227
11.5.1 Interpretive Consequences of Our Geometrical NRQM 229
11.6 Conclusion: NRQM Resides in a 4D Block World 232
12. Space-time: Arena or Reality? 234
12.1 Introduction 234
12.2 Kerr–Newman Solution 235
12.2.1 The Kerr-Newman Metric 235
12.2.2 The Hawking-Ellis Extended Interpretation 236
12.2.3 Causality Versus Singularity 237
12.3 The KN Solution as a Dirac Particle 238
12.3.1 Preliminaries 238
12.3.2 Wave-Particle Duality 240
12.3.3 Topological Structure 240
12.3.4 Existence of Space-time Spinorial Structures 241
12.3.5 Evolution Equation 242
12.4 Concluding Remarks 242
13. Dynamical Emergence of Instantaneous 3-Spaces in a Class of Models of General Relativity 246
13.1 Introduction 246
13.2 Newton's Absolute Distant-Simultaneity 252
13.3 Special Relativity: Conventional Distant Simultaneity 254
13.4 General Relativity: Dynamically Determined Distant Simultaneity 258
13.5 Conclusions 270
14. Lorentzian Space-Times from Parabolic and Elliptic Systems of PDEs 278
14.1 Introduction 278
14.2 Analogue Models of General Relativity 279
14.3 A Simple Parabolic Model 281
14.4 A Simple Elliptic Model 283
14.5 Characteristic Surfaces 284
14.6 Discussion 285
ISBN-13:,9781402063176

"All physicists would agree that one of the most fundamental problems of the 21st century physics is the dimensionality of the world. In the four-dimensional world of Minkowski (or Minkowski spacetime) the most challenging problem is the nature of the temporal dimension. In Minkowski spacetime it is merely one of the four dimensions, which means that it is entirely given like the other three spacial dimensions. If the temporal dimension were not given in its entirely and only one constantly changing moment of it existed, Minkowski spacetime would be reduced to the ordinary three-dimensional space." "But if the physical world, represented by Minkowski spacetime, is indeed four-dimensional with time being the fourth dimension, then such a world is drastically different from its image based on our perceptions. Minkowski four-dimensional world is a block Universe, a frozen world in which nothing happens since all moments of time are given 'at once, ' which means that physical bodies are four-dimensional worldtubes containing the whole histories in time of the three-dimensional bodies of our everyday experience. The implications of a real Minkowski world for physics itself and especially for our world view are enormous." "The main focus of this volume is the question: is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a mathematical model of a real four-dimensional world with time entirely given as the fourth-dimension? It contains fourteen invited papers which either directly address the main question of the nature of spacetime or explore issues related to it."--Jacket

All physicists would agree that one of the most fundamental problems of the 21st century physics is the dimensionality of the world. In the four-dimensional world of Minkowski (or Minkowski spacetime) the most challenging problem is the nature of the temporal dimension. In Minkowski spacetime it is merely one of the four dimensions, which means that it is entirely given like the other three spacial dimensions. If the temporal dimension were not given in its entirety and only one constantly changing moment of it existed, Minkowski spacetime would be reduced to the ordinary three-dimensional space. But if the physical world, represented by Minkowski spacetime, is indeed four-dimensional with time being the fourth dimension, then such a world is drastically different from its image based on our perceptions. Minkowski four-dimensional world is a block Universe, a frozen world in which nothing happens since all moments of time are given ‘at once', which means that physical bodies are four-dimensional worldtubes containing the whole histories in time of the three-dimensional bodies of our everyday experience. The implications of a real Minkowski world for physics itself and especially for our world view are enormous. The main focus of this volume is the question: is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a mathematical model of a real four-dimensional world with time entirely given as the fourth dimension? It contains fourteen invited papers which either directly address the main question of the nature of spacetime or explore issues related to it.

Preface -- The Meaning Of Dimensions / Paul S. Wesson -- Some Remarks On The Space-time Of Newton And Einstein / Graham Hill -- The Adventures Of Space-time / Orfeu Bertolami -- Physics In The Real Universe: Time And Space-time / George F.r. Ellis -- The Real World And Space-time / Hans C. Ohanian -- Four-dimensional Reality And Determinism; An Answer To Stein / Wim Rietdijk -- Relativity, Dimensionality, And Existence / Vesselin Petkov -- Canonical Relativity And The Dimesnsionality Of The World / Martin Bojowald -- Relativity Theory Does Not Imply That The Future Already Exists: A Counterexample / Rafael D. Sorkin -- Absolute Being Versus Relative Becoming / Joy Christian -- An Argument For 4d Block World From A Geometric Interpretation Of Nonrelativistic Quantum Mechanics / Michael Silberstein, W.m. Stuckey, And Michael Cifone -- Space-time: Arena Or Reality? / H.i. Arcos And J.g. Pereira -- Dynamical Emergence Of Instantaneous 3-spaces In A Class Of Models Of General Relativity / Luca Lusanna And Massimo Pauri -- Lorentzian Space-times From Parabolic And Elliptic Systems Of Pdes / Carlos Barceló. Edited By Vesselin Petkov. Includes Bibliographical References.

Content: Preface1. The Meaning of Dimensions
Paul Wesson.2. Some Remarks on the Space-Times of Newton and Einstein
Graham Hall.3. The adventures of Spacetime
Orfeu Bertolami.4. Physics in the Real Universe: Time and Spacetime
George F. R. Ellis.5. The Real World and Spacetime
Hans C. Ohanian.6. Four-dimensional Reality and Determinism: an Answer to Stein
Wim Rietdijk.7. Relativity, Dimensionality, and Existence
Vesselin Petkov.8. Canonical Relativity and the Dimensionality of the World
Martin Bojowald.9. Relativity theory does not imply that the future already exists: a counterexample
Rafael D. Sorkin.10. Absolute Being versus Relative Becoming
Joy Christian. 11. An Argument for 4D Blockworld from a Geometric Interpretation of Non-relativistic Quantum Mechanics
Michael Silberstein, W.M. Stuckey, and Michael Cifone.12. Spacetime: Arena or Reality? H. I. Arcos and J. G. Pereira.13. Dynamical emergence of instantaneous 3-spaces in a class of models of general relativity
Luca Lusanna and Massimo Pauri. 14. Lorentzian spacetimes from Parabolic and Elliptic systems of PDEs
Carlos Barcelo.

2017-10-15