The Philosophy of Space and Time: (Dover Books on Physics)

With unusual depth and clarity, it covers the problem of the foundations of geometry, the theory of time, the theory and consequences of Einstein's relativity including: relations between theory and observations, coordinate definitions, relations between topological and metrical properties of space, the psychological problem of the possibility of a visual intuition of non-Euclidean structures, and many other important topics in modern science and philosophy.While some of the book utilizes mathematics of a somewhat advanced nature, the exposition is so careful and complete that most people familiar with the philosophy of science or some intermediate mathematics will understand the majority of the ideas and problems discussed. Partial CONTENTS: I. The Problem of Physical Geometry. Universal and Differential Forces. Visualization of Geometries. Spaces with non-Euclidean Topological Properties. Geometry as a Theory of Relations. II. The Difference between Space and Time. Simultaneity. Time Order. Unreal Sequences. Ill. The Problem of a Combined Theory of Space and Time. Construction of the Space-Time Metric. Lorentz and Einstein Contractions. Addition Theorem of Velocities. Principle of Equivalence. Einstein's Concept of the Problems of Rotation and Gravitation. Gravitation and Geometry. Riemannian Spaces. The Singular Nature of Time. Spatial Dimensions. Reality of Space and Time.

Table of Contents:
Preface Introduction Chapter I Space 1. The axiom of the parallels and non-Euclidean geometry 2. Riemannian geometry 3. The problem of physical geometry 4. Coordinative definitions 5. Rigid bodies 6. The distinction between universal and differential forces 7. Technical impossibility and logical impossibility 8. The relativity of geometry 9. The visualization of Euclidean geometry 10. The limits of visualization 11. Visualization of non-Euclidean geometry 12. Spaces with non-Euclidean topological properties 13. Pure visualization 14 Geometry as a theory of relations 15. What is graphical representation? Chapter II Time 16. The difference between space and time 17. The uniformity of time 18. Clocks used in practice 19. Simultaneity 20. Attempts to determine absolute simultaneity 21. Time order 22. The comparison of time 23. Unreal sequences Chapter III Space an Time A. The Space-Time Manifold without Gravitational Fields 24. The problem of a combined theory of space and time 25. The dependence of spatial measurement on the definition of simultaneity 26. Consequences for a centro-symmetrical process of propagation 27. The construction of the space-time metric 28. The indefinite space-type 29. The four-dimensional representation of the space-time geometry 30. The retardation of clocks 31. The Lorentz contraction and the Einstein contraction 32. The principle of the constancy of the velocity of light 33. The addition theorem of velocities B. Gravitation Filled Space-Time Manifolds 34. The relativity of motion 35. Motion as a problem of a coordinative definition 36. The principle of equivalence 37. Einstein's concept of gravitation 38. The problem of rotation according to Einstein 39. The analytic treatment of Riemannian spaces 40. Gravitation and geometry 41. Space and time in special gravitational fields 42. Space and time in generall gravitational fields C. The Most General Properties of Space and Time 43. The singular nature of time 44. The number of dimensions of space 45. The reality of space and time Index