Thinking About Space and Time: 100 Years of Applying and Interpreting General Relativity: 15 (Einstein Studies)

Einstein Studies Series Preface
Introduction
Contents
List of Contributors
Space and Time 62 Years After the Berne Conference
	1 Historical Context
	2 Classical General Relativity and Beyond
	3 Cosmology
	4 Quantum Theory and Gravity
	5 Summary
	References
Einstein\'s Conflicting Heuristics: The Discovery of General Relativity
	1 Introduction
	2 Einstein\'s Principles
	3 Einstein\'s 1907 Heuristic
	4 Einstein 1907–1912 Theory of Static Gravitational Fields
	5 The Gravitational Field of Uniform Acceleration
	6 Einstein Generalizes Naturally
	7 A Hidden Peril
	8 A Second Hidden Peril Identified
	9 Seeking an Escape
	10 Modifying the Gravitational Field Equation
	11 Conflicting Heuristics
	12 A Method Reused: The Derivation of the “Entwurf” Field Equations
	13 Conflicting Heuristics Again
	14 The Method Lives On
	15 Einstein\'s Two Tier Heuristics
	16 Conclusion
	Appendix 1: Computing Spacetime Curvature in Einstein\'s 1912 Theory
	Appendix 2: Computing the Gravitation Tensor of the Einstein–Grossmann Theory for a Static Gravitational Field
	References
Historical and Philosophical Aspects of the Einstein World
	1 Introduction
	2 Historical Context of the Einstein World
		2.1 Biographical Context
		2.2 Cosmology Before 1917
		2.3 Relativistic Cosmology and the Problem of Boundary Conditions at Infinity
	3 Einstein\'s 1917 Paper
		3.1 On the Basic Assumptions of Einstein\'s Model
		3.2 On Spatial Curvature
		3.3 On the Cosmological Constant
		3.4 On Testing the Model Against Observation
		3.5 On the Stability of the Einstein World
	4 The Einstein–de Sitter Debate
	5 Einstein and the Expanding Universe
	6 Conclusions
	References
Stability in Cosmology, from Einstein to Inflation
	1 Introduction
	2 The Einstein Static Universe
	3 The Flatness Problem
	4 Stability and Fragility
	5 Conclusion
	References
The Einstein–Rosen Bridge and the Einstein–Podolsky–Rosen Argument: Singularities and Separability
	1 Introduction
	2 Weyl, Levi–Civita and Bach: Static Two-Body Problem in General Relativity
	3 Einstein on the Two-Body Problem
		3.1 Einstein and Grommer: The Impossible Is Impossible
		3.2 Silberstein 1933: The Impossible Is Possible
	4 The Einstein–Rosen (ER) Bridge
		4.1 The ER Bridge Paper
		4.2 Two-Body Problem and the ER Bridge
			4.2.1 The Einstein–Silberstein Controversy
			4.2.2 Holes and Bridges
	5 The Einstein–Podolsky–Rosen (EPR) Argument
		5.1 The EPR Paper
		5.2 Two-Body Problem and Contiguity
	6 Concluding Remarks
	References
A Raum with a View: Hermann Weyl and the Problem of Space
	1 Introduction
	2 The Classical Solution
	3 Weyl\'s Problem of Space
	4 Weyl\'s Solution
	5 The Status of the Metric Field
	Appendix 1: The `Postulate of Freedom\'
	Appendix 2: The Nature of the Metric as Background Object
	References
Friedman and Some of His Critics on the Foundations of General Relativity
	1 Introduction
	2 Friedman\'s Approach to the Analysis of Theories
	3 Friedman\'s Analysis of Einsteinian Gravitation
	4 Challenges and Replies
		4.1 Many Ways to Parse a Theory
		4.2 The Equivalence Principle Is Unnecessary for Developing the Field Equations
		4.3 Only Coordinating Principles Are Constitutive
		4.4 The Equivalence Principle and Riemann\'s Theory Are Not Constitutive
	5 Significance
	References
Interpretations of GR as Guidelines for Theory Change
	1 Introduction
	2 Empirical Interpretation(s) of a Physical Theory
		2.1 The Concrete Interpretation in More Detail
			2.1.1 The Dynamical Nature of the Concrete Interpretation
			2.1.2 GR\'s Concrete Interpretation
	3 Guidelines From GR\'s Empirical Interpretation
		3.1 General Approach
		3.2 Specific Approaches
			3.2.1 Chronometric Interpretation
			3.2.2 Thermodynamic Interpretation
	4 Guidelines From GR\'s Conceptual Interpretation
	5 Conclusion
	References
Explanation, Geometry, and Conspiracy in Relativity Theory
	1 Introduction
	2 Background
		2.1 Spacetime Theories
		2.2 Symmetries
		2.3 Special and General Relativity
			2.3.1 Special Relativity
			2.3.2 General Relativity
	3 The Dynamical/Geometrical Debate
		3.1 Special Relativity
			3.1.1 The Geometrical Approach
			3.1.2 The Dynamical Approach
		3.2 General Relativity
			3.2.1 The Geometrical Approach
			3.2.2 The Dynamical Approach
	4 Qualified and Unqualified Explanations
	5 The Geometrical Approach
		5.1 Two Geometrical Approaches
			5.1.1 Special Relativity
			5.1.2 General Relativity
		5.2 The Qualified Geometrical Approach
			5.2.1 Univocal Explanation
			5.2.2 Partial Explanation
			5.2.3 Confident and Cautious Qualified Approaches
		5.3 Two Miracles, Reprise
	6 The Geodesic Principle
	7 Conclusions
	References
Geometry and Motion in General Relativity
	1 Introduction
	2 Two Approaches and Their Discontents
		2.1 Distributions
		2.2 Curve-First
	3 The Miracle of Tracking
		3.1 Definition of Tracking
		3.2 Consequences of Tracking
		3.3 Applications of These Results
	4 Dynamics, Inertia, and Spacetime Geometry
	References
The Metaphysics of Machian Frame-Dragging
	1 Introduction
	2 Rotational Frame-Dragging Effects in GR
	3 Structural Equation Model Analysis
	4 Frame-Dragging as a Nonstandard Determination Relation
	5 What Kind of Dependence?
	6 Conclusion
	References
Approximate Local Poincaré Spacetime Symmetryin General Relativity
	1 Introduction: Explanation, Reduction, and Symmetry
		1.1 Explanation and Reduction
		1.2 Spacetime Symmetries
		1.3 Outline of the Remainder
	2 The Strong Equivalence Principle
	3 Poincaré Symmetry
		3.1 Local and Approximate Spacetime Symmetries
			3.1.1 Local Spacetime Symmetries
			3.1.2 Approximate Spacetime Symmetries
		3.2 Poincaré Invariance of Equations and Poincaré Spacetime Symmetry
			3.2.1 Poincaré Spacetime Symmetry Without Poincaré Invariance of Equations
			3.2.2 Poincaré Invariance of Equations Without Poincaré Spacetime Symmetry
	4 Local Approximate Geometry
	5 Conclusions, and Prospects for a Broader Explanation of the Success of SR
	References