The Philosophy of Space and Time

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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.

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Product Details

  • ISBN-13: 9780486604435
  • Publisher: Dover Publications
  • Publication date: 6/1/1957
  • Series: Dover Books on Physics Series
  • Pages: 295
  • Sales rank: 621,119
  • Product dimensions: 5.37 (w) x 7.97 (h) x 0.65 (d)

Table of Contents

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
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