Book contents
- Frontmatter
- Contents
- Preface and acknowledgements
- Part I Einstein's revolution
- Part II Philosophical progress
- 8 Who invented space?
- 9 Zeno's paradoxes: is motion impossible?
- 10 Philosophers at war: Newton vs. Leibniz
- 11 The philosophy of left and right
- 12 The unreality of time
- 13 General relativity: is space curved?
- 14 The fall of geometry: is mathematics certain?
- 15 The resurrection of absolutes
- 16 The resilience of space
- Part III Frontiers
- Appendix A Spacetime diagrams
- Appendix B Symmetry and Lorentz's minority interpretation
- Appendix C Simple formulas for special relativity
- Appendix D Websites
- Appendix E Guide to further reading
- Index
13 - General relativity: is space curved?
from Part II - Philosophical progress
- Frontmatter
- Contents
- Preface and acknowledgements
- Part I Einstein's revolution
- Part II Philosophical progress
- 8 Who invented space?
- 9 Zeno's paradoxes: is motion impossible?
- 10 Philosophers at war: Newton vs. Leibniz
- 11 The philosophy of left and right
- 12 The unreality of time
- 13 General relativity: is space curved?
- 14 The fall of geometry: is mathematics certain?
- 15 The resurrection of absolutes
- 16 The resilience of space
- Part III Frontiers
- Appendix A Spacetime diagrams
- Appendix B Symmetry and Lorentz's minority interpretation
- Appendix C Simple formulas for special relativity
- Appendix D Websites
- Appendix E Guide to further reading
- Index
Summary
Errors of thought cost me two years of excessively hard work, until I finally recognised them as such at the end of 1915 and, after having ruefully returned to Riemann's idea of curved space, succeeded in linking the theory with the facts of astronomical experience. Now the happy achievement seems almost a matter of course, and any intelligent student can grasp it without too much trouble. But the years of anxious searching in the dark, with their intense longing, their alterations of confidence and exhaustion and the final emergence into the light – only those who have experienced it can understand that.
(Einstein, 1934)The 1905 special theory of relativity was limited to measurements made by equipment moving without acceleration. The general theory of relativity eliminates this special restriction. To achieve this, however, Einstein had to even more deeply revolutionize our concepts of space and time. Building on the insights of the earlier theory, he now argued that space can be bent by matter.
Thus we have reached a third stage in the philosophy of space and time. The atomists first proclaimed that space or “nothing” existed in order to solve the problem of change. Newton revived this doctrine when, despite the criticisms of Aristotle and Descartes, he needed absolute space for his broader theory. Einstein now completes his revolution with the momentous claim that space changes. That is, space has evolved from a static structure proposed to make sense of motion to a structure that itself changes.
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- Space, Time and EinsteinAn Introduction, pp. 139 - 148Publisher: Acumen PublishingPrint publication year: 2002