Relativity without spacetime

목차 (Table of Contents)

• CONTENTS
• 1 Introduction : A Critique of Minkowski Spacetime = 1
• Part Ⅰ The Concept of Minkowski Spacetime = 9
• 2 Minkowski's "Space and Time" = 11
• 2.1 Minkowski and Gottingen Science = 11
• 2.2 "Space and Time," Sections Ⅰ and Ⅱ = 14
• 2.3 "Space and Time," Section Ⅲ = 20
• 2.4 "Space and Time," Section Ⅳ = 24
• 3 Special Relativity and Spacetime = 35
• 3.1 Spacetime and the Concept of a Continuum = 35
• 3.2 The "Geometry of Spacetime" : Graphs and Images = 39
• 3.3 Invariance and Special Relativity = 48
• 3.3.1 Invariance and Objectivity = 48
• 3.3.2 Invariance and the Clock Paradox = 56
• 3.4 On the Arrow of Explanation = 58
• 3.5 Conceptual Difficulties of Minkowski Spacetime : The Need for a Historical Approach = 60
• Part Ⅱ The Symbolic-Algebraic Constitution of the Concept of Spacetime = 65
• 4 The Historical Sense-Structure of Symbolic Algebra = 69
• 4.1 The Concept Number in Greek Mathematics = 73
• 4.1.1 Arithmetical Operations in Euclid = 73
• 4.1.2 The Concept of Ratio = 74
• 4.1.3 Arithmetic and Geometry in Euclid = 76
• 4.2 Algebraic Equations in Greek Mathematics : Diophantus of Alexandria = 77
• 4.2.1 The Concept of Number in Diophantus = 77
• 4.2.2 Algebraic Calculation with "Species" = 80
• 4.3 Modern Symbolic Algebra = 81
• 4.3.1 Vieta's Reinterpretation of Diophantine Species = 82
• 4.3.2 Vieta's "Law of Homogeneity" and the Symbolic Concept of Number = 83
• 4.3.3 Vietan Algebra as Mathesis Universalis = 87
• 4.4 Descartes and Symbolic Space = 89
• 4.4.1 Geometrical Representation of Arithmetical Operations = 89
• 4.4.2 Descartes' Symbolic Interpretation of Geometrical Magnitude = 91
• 4.4.3 Symbolic Space = 93
• 5 The Historical Sense-Structure of Modern Algebraic Physics = 101
• 5.1 Pre-Algebraic Physics in Galileo = 101
• 5.2 The Assimilation of Algebra into Physics = 104
• 5.3 A Case Study : Newton and "Quantity of Motion" = 108
• 6 Desedimentation of Minkowski Spacetime = 117
• Part Ⅲ General Relativity Without Spacetime = 123
• 7 Minkowski Spacetime and General Relativity = 125
• 7.1 Tensor Calculus and "Geometrical Objects" = 126
• 7.1.1 Tensors as Ratio-Compounding Machines = 126
• 7.1.2 Tensors and Invariance = 128
• 7.2 Against the Long Clothes : Minkowski Spacetime in Einstein's 1916 Review Article = 129
• 7.2.1 Einstein 1916, Part A : "Fundamental Considerations on the Postulate of Relativity" = 130
• 7.2.2 Einstein 1916, Part B : "Mathematical Aids to the Formulation of Generally Covariant Equations" = 141
• 7.2.3 Einstein 1916, Part C : Theory of the Gravitational Field = 146
• 7.3 Geodesic Law by Other Means = 159
• Part Ⅳ Time Without Spacetime = 163
• 8 Relativity and Time = 165
• 8.1 Simultaneity in Special Relativity = 165
• 8.2 Simultaneity in General Relativity = 169
• 8.3 Time and Becoming = 172
• Bibliography = 179
• Index = 187