Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
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How the Geometries of Newton's Flat and Einstein's Curved Space-Time Explain the Laws of Motion

  • Received : 2018.10.15
  • Accepted : 2019.02.25
  • Published : 2019.02.28
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Abstract

This essay elucidates the way the geometries of space-time theories explain material bodies' motions. A conventional attempt to interpret the way that space-time geometry explains is to consider the geometrical structure of space-time as involving a causally efficient entity that directs material bodies to follow their trajectories corresponding to the laws of motion. Newtonian substantival space is interpreted as an entity that acts but is not acted on by the motions of material bodies. And Einstein's curved space-time is interpreted as an entity that causes the motions of bodies. This essay argues against this line of thought and provides an alternative understanding of the way space-time geometry explain the laws of motion. The workings of the way that Newton's flat and Einstein's curved space-time explains the law of motion is such that space-time geometry encodes the principle of inertia which specifies straight lines of moving bodies.

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References

  1. H. G. ALEXANDER, The Leibniz-Clark Correspondence, Barnes and Noble, New York, 1956.
  2. H. R. BROWN, Physical Relativity: Space-Time Structure from a Dynamical Perspective, Oxford University Press, Oxford, 2005.
  3. H. R. BROWN, O. POOLEY, Minkowski Space-time: A Glorious Non-entity, in D. DIEKS (ed.), Ontology of Spacetime, Elsevier Science, Amsterdam, 2006, 67-92.
  4. R. DISALLE, Understanding Spacetime: The Philosophical Development of Physics from Newton to Einstein, Cambridge University Press, Cambridge, 2006.
  5. J. EARMAN, World Enough and Spacetime: Absolute and Relational Theories of Motion, M. I. T. Press, Boston, 1989.
  6. G. F. R. ELLIS, R. M. WILLIAMS, Flat and Curved Space-times, 2nd edition, Oxford University Press, Oxford, 2000.
  7. M. FRIEDMAN, Foundations of Space-Time Theories: Relativistic Physics and Philosophy of Science, (Princeton University Press, Princeton, 1983.
  8. R. GEROCH, Relativity from A to B, University of Chicago Press, Chicago, 1978.
  9. C. HOEFER, Energy Conservation in GTR, Studies in History and Philosophy of Modern Physics 31 (2000), 187-99. https://doi.org/10.1016/S1355-2198(00)00004-6
  10. C. MISNER, K. THORNE, J. A. WHEELER, Gravitation, Freeman, San Francisco, 1973.
  11. G. NEWTON, The Shape of Space, Cambridge University Press, Cambridge, 1976.
  12. I. NEWTON, The Principia: Mathematical Principles of Natural Philosophy, I. B. COHEN and A. M. WHITMAN (trans.), University of California Press, Berkeley, 1726.
  13. I. NEWTON, De Gravitatione in A. R. HALL, and M. B. HALL, Unpublished Scientific Papers of Isaac Newton, Cambridge University Press, Cambridge, 1962.
  14. J. NORTON, What Can We Learn about the Ontology of Space and Time from the Theory of Relativity? in L. Sklar (ed.), Physical Theory: Method and Interpretation, Oxford University Press, Oxford, 2015, 185-228.
  15. O. POOLEY, The Reality of Spacetime, Unpublished Ph. D thesis, Department of Philosophy, Oxford University, 2002.
  16. C. ROVELLI, Quantum Spacetime, What Do We Know, in C. Callender and N. Huggett (ed.), Physics Meets Philosophy at the Planck Length, Cambridge University Press, Cambridge, 2001.
  17. W. SALMON, Scientific Explanation and the Causal Structure of the World, Princeton University Press, Princeton, 1984.