Space, Time, Matter

INTRODUCTION CHAPTER I EUCLIDEAN SPACE. ITS MATHEMATICAL FORM AND ITS ROLE IN PHYSICS. 1. Derivation of the Elementary Conceptions of Space from that of Equality 2. Foundations of Affine Geometry 3. "Conception of n-dimensional Geometry, Linear Algebra, Quadratic Forms" 4. Foundations of Metrical Geometry 5. Tensors 6. Tensor Algebra. Examples 7. Symmetrical Properties of Tensors 8. Tensor Analysis. Stresses 9. The Stationary Electromagnetic Field CHAPTER II THE METRICAL CONTINUUM 10. Note on Non-Euclidean Geometry 11. Riemann's Geometry 12. Riemann's Geometry (continued). Dynamical View of Metrics 13. Tensors and Tensor-densities in an Arbitrary Manifolds 14. Affinely Connected Manifolds 15. Curvature 16. Metrical Space 17. Remarks on the Special Case of Riemann's Space 18. Space Metrics from the Point of View of the Theory of Groups CHAPTER III RELATIVITY OF SPACE AND TIME 19. Galilei's and Newton's Principle of Relativity 20. Electrodynamics of Varying Fields. Lorentz's Theorem of Relativity 21. Einstein's Principle of Relativity 22. "Relativistic Geometry, Kinematics, and Optics" 23. Electrodynamics of Moving Bodies 24. Mechanics of the Principle of Relativity 25. Mass and Energy 26. Mie's Theory Concluding Remarks 27. "Relativity of Motion, Metrical Field, and Gravitation" 28. Einstein's Fundamental Law of Gravitation 29. Stationary Gravitational Field. Relationship with Experience 30. Gravitational Waves 31. Rigorous Solution of the Problem of One Body 32. Further Rigorous Solutions of the Statical Problem of Gravitation 33. Energy of Gravitation. Laws of Conservation 34. Concerning the Inter-connection of the World as a Whole 35. Word Metrics as the Origin of Electromagnetic Phenomena 36. Application of the Simplest Principle of Action Fundamental Equations of Mechanics APPENDIX I APPENDIX II BIBLIOGRAPHICAL REFERENCES INDEX