Deductive Theory of Space and Time (eBook)

Front Cover 1
A Deductive Theory of Space and Time 4
Copyright Page 5
Contents 9
PART ONE: FOUNDATION 14
Chapter I. What is a Deductive Theory? 16
1 Deductive Physical Theory 16
2 Deductive Abstract Theory 17
3 Definitions 19
4 Theorems 21
5 Symbolic Logic and Deductive Theories 22
Chapter II. Objective Universe 23
1 Introduction 23
2 Observers 25
3 Sensations 25
4 Subjective Entities 27
5 Objectivity 32
Chapter III. Particles 37
1 Parts 37
2 Connection and Separation 39
3 Particles 39
Chapter IV. Events 41
1 Introduction 41
2 Appearance and Disappearance Events 41
3 Coincidence of Events 44
4 Time Order 46
Chapter V. Signals 49
1 Change, Coincidence and Dissociation 49
2 World Lines 51
3 Signal Relation 53
4 First Signals 55
PART TWO: SPACE-TIME GEOMETRY 60
Chapter VI. Clocks and Time Intervals 62
1 Introduction 62
2 Clocks 64
3 Relative Instability 65
4 Standard Clocks 70
5 Time Metric 71
6 Comparison of Time Intervals 74
Chapter VII. Length Measurement and Space Geodesics 78
1 Introduction 78
2 Length Measuring Instruments 79
3 Distance 83
4 Rigidity 84
5 Congruence 86
6 Space Geodesics 89
7 Linear Length Measuring Instruments 90
8 Space Metric 91
Chapter VIII. Geodesic Geometry 92
1 Introduction 92
2 Linear Order 92
3 Linear Order and Space Geodesics 94
4 Collinearity 97
5 The Side Relation 98
6 Congruence 99
Chapter IX. Space Geometry 103
1 Non-Collinearity 103
2 Coplanarity 106
3 Perpendicularity 107
4 Parallel Displacement 109
5 Dimensions 114
6 Geodesic Space Coordinates 115
Chapter X . Space-Time Geometry 119
1 Introduction 119
2 The Fundamental Space-Time Relation 120
3 Neighborhood 123
4 First-Signal Speed 127
5 Metric Coefficients 128
6 Equations of a Space Geodesic 132
7 Free Trajectories 134
8 Inertial Systems 137
9 Concluding Remarks 138
APPENDICES / SYMBOLIC LOGIC AND SET THEORY 140
Introduction to Appendix 142
Appendix A. Foundation 144
1 Concepts 144
2 Interpretations 144
3 Punctuation 146
4 Free and Bound Variables 147
5 Definitions 147
6 Axioms 151
7 Postulates of Classification 151
8 Postulates about True Formulas 153
9 Application of Symbolic Logic 155
Appendix B. Logical Theorems 156
1 Rules of Inference 156
2 Propositions 157
3 Quantifiers 158
4 Descriptions 159
5 Identity 159
6 Set or Class Relations 159
7 Relations 160
References 162
Symbols 164
1 Latin 164
2 German 167
3 Greek 167
4 Miscellaneous 168
5 Logical 169
Conventions 170
Abbreviations 172
Index 174