Relativity without Spacetime

Introduction Chapter One: A Critique of Minkowski SpacetimePart I: The Concept of Minkowski Spacetime Chapter Two Minkowski's "Space and Time" 2.1 Minkowski and Gottingen Science 2.2 "Space and Time," Sections I and II 2.3 "Space and Time," Section III 2.4 "Space and Time," Section IV Chapter Three Special Relativity and Spacetime 3.1 The Concept of a Continuum 3.2 The "Geometry of Spacetime": Graphs and Images 3.3 The Role of Invariance in Special Relativity 3.3.1 Invariance and Frame-Independence 3.3.2 Invariance and the Clock Paradox 3.4 Transition to Part II: Conceptual Difficulties of Minkowski Spacetime and the Need for a Historical ApproachPart II: The Symbolic-Algebraic Constitution of the Concept of Spacetime Introduction to Part II The Concept of a Sense-History Chapter Four The Historical Sense-Structure of Symbolic Algebra 4.1 The Concept of Number in Greek Mathematics 4.1.1 Arithmetical Operations in Euclid 4.1.2 The Concept of Ratio in Euclid 4.1.3 Arithmetic and Geometry in Euclid 4.2 Algebraic Equations in Greek Mathematics: Diophantus of Alexandria 4.2.1 The Concept of Number in Diophantus 4.2.2 Algebraic Calculations with "Species" 3.3 Modern Symbolic Algebra 4.3.1 Vieta's Reinterpretation of Diophantine Species 4.3.2 Vieta's Law of Homogeneity and the Symbolic Concept of Number 4.3.3 Vieta's Algebra as Mathesis Universalis 4.4 Descartes and Symbolic Space 4.4.1 Geometrical Representation of Numerical Operations 4.4.2 Symbolic Interpretation of Geometrical Magnitude 4.4.3 Symbolic Space Chapter Five The Historical Sense-Structure of Modern Algebraic Physics 5.1 Pre-Algebraic Physics in Galileo 5.2 The Assimilation of Algebra into Physics 5.3 Case Study: Newton and Quantity of Motion Chapter Six Desedimentation of Minkowski SpacetimePart III General Relativity without Spacetime Chapter Seven The Irrelevance of Minkowski Spacetime in General Relativity 7.1 Tensor Calculus and "Geometrical Objects" 7.1.1 Tensors as Ratio-Compounding Machines 7.1.2 Tensors and Invariance 7.2 Against the Longclothes: Minkowski Spacetime in Einstein's 1916 Review Article 7.2.1 Einstein 1916, Part A: "Fundamental Considerations on the Postulate of Relativity" 7.2.1.1 Part A, 2: The Principle of Equivalence 7.2.1.2 Part A, 3: General Covariance 7.2.1.3 Part A, 4: The "Linear Element" 7.2.2 Einstein 1916, Part B: "Mathematical Aids to the Formulation of Generally Covariant Equations" 7.2.2.1 Part B, 8: Fundamental Tensor 7.2.2.2 Part B, 9: Mathematical Derivation of Geodesic Line 7.2.2.3 Part B, 12: Riemann Tensor 7.2.3 Einstein 1916, Part C: "Theory of the Gravitational Field" 7.2.3.1 Part C, 13: Law of Motion 7.2.3.2 Part C, 14: Vacuum Field Law 7.2.3.3 Part C, 16: General Field Equation and Stress-Energy Tensor 7.3. Geodesic Law by Other MeansConclusion Chapter Eight The Theory of Relativity in Philosophical Perspective 8.1 Relativity and Time 8.1.1 Simultaneity in Special Relativity 8.1.2 Simultaneity in General Relativity 8.1.3 Time and Becoming 8.2 The Dynamical Approach to Relativity 8.2.1 Brown on Bell's "Lorentzian Pedagogy": Single-Frame Lorentz Covariance 8.2.2 Single-Frame Contraction, Acceleration, and Force 8.2.3 Kinematics versus Dynamics 8.2.4 Metrical Dynamics of Lorentz Contraction