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Time in the Theory of Relativity: Inertial Time, Light Clocks, and Proper Time

  • Mario Bacelar Valente
Article
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Abstract

In a way similar to classical mechanics where we have the concept of inertial time as expressed in the motions of bodies, in the (special) theory of relativity we can regard the inertial time as the only notion of time at play. The inertial time is expressed also in the propagation of light. This gives rise to a notion of clock—the light clock, which we can regard as a notion derived from the inertial time. The light clock can be seen as a solution of the theory, which complies with the requirement that a clock to be so must have a rate that is independent from its past history. Contrary to Einstein’s view, we do not need the concept of “clock” as an independent concept. This implies, in particular, that we do not need to rely on the notions of atomic clock or atomic time in the theory of relativity.

Keywords

Inertial time Proper time Light clock Atomic time Atomic clock Relativity 

Notes

Acknowledgements

The criticism and commentaries of the anonymous reviewers helped in arriving at a much clearer and coherent manuscript. To both, I want to express my gratitude.

References

  1. Anderson, J. L., & Gautreau, R. (1969). Operational formulation of the principle of equivalence. Physical Review, 185(5), 1656–1661.CrossRefGoogle Scholar
  2. Bacelar Valente, M. (2011). The relation between classical and quantum electrodynamics. Theoria. An International Journal for Theory, History and Foundations of Science, 26, 51–68.Google Scholar
  3. Bacelar Valente, M. (2014). Einstein’s physical geometry at play: Inertial motion, the boostability assumption, the Lorentz transformations, and the so-called conventionality of the one-way speed of light. arxiv: https://arxiv.org/abs/1306.1361.
  4. Bacelar Valente, M. (2016). Proper time and the clock hypothesis in the theory of relativity. European Journal for Philosophy of Science, 6, 191–207.CrossRefGoogle Scholar
  5. Bacelar Valente, M. (2017). Einstein’s physical chronogeometry. Manuscrito. Revista Internacional de Filosofia, 40, 241–278.Google Scholar
  6. Barbour, J. (1989). The discovery of dynamics. Cambridge: Cambridge University Press.Google Scholar
  7. Barbour, J. (2007). Einstein and Mach’s principle. In J. Renn (Ed.), The genesis of general relativity (Vol. 3, pp. 569–604). Berlin: Springer.Google Scholar
  8. Barbour, J. (2009). The nature of time. arxiv: https://arxiv.org/abs/0903.3489.
  9. Brown, H. (2005). Physical relativity: Spacetime structure from a dynamical perspective. Oxford: Oxford University Press.CrossRefGoogle Scholar
  10. Dickson, M. (2004). A view from nowhere: Quantum references frames, and uncertainty. Studies in History and Philosophy of Modern Physics, 35, 195–220.CrossRefGoogle Scholar
  11. DiSalle, R. (2009). Space and time: Inertial frames. In Zalda, E. (Ed.), Stanford encyclopedia of philosophy (Winter 2016 Edition). https://plato.stanford.edu/archives/win2016/entries/spacetime-iframes/.
  12. Ehlers, J., Pirani, F., & Shild, A. (1972). The geometry of free fall and light propagation. In L. O’Raifeartaigh (Ed.), General relativity: Papers in honor of J. L. Synge (pp. 63–84). Oxford: Clarendon.Google Scholar
  13. Einstein, A. (1905). On the electrodynamics of moving bodies. In The collected papers of Albert Einstein (English translation) (Vol. 2, pp. 140–171). Princeton: Princeton University Press.Google Scholar
  14. Einstein, A. (1907a). On the possibility of a new test of the relativity principle. In The collected papers of Albert Einstein (English translation) (Vol. 2, pp. 232–234). Princeton: Princeton University Press.Google Scholar
  15. Einstein, A. (1907b). On the relativity principle and the conclusions drawn from it. In The collected papers of Albert Einstein (English translation) (Vol. 2, pp. 252–311). Princeton: Princeton University Press.Google Scholar
  16. Einstein, A. (1910). The principle of relativity and its consequences in modern physics. In The collected papers of Albert Einstein (English translation) (Vol. 3, pp. 117–142). Princeton: Princeton University Press.Google Scholar
  17. Einstein, A. (1911). The theory of relativity. In The collected papers of Albert Einstein (English translation) (Vol. 3, pp. 340–350). Princeton: Princeton University Press.Google Scholar
  18. Einstein, A. (1912–1914). Manuscript on the special theory of relativity. In The collected papers of Albert Einstein (English translation) (Vol. 4, pp. 3–88). Princeton: Princeton University Press.Google Scholar
  19. Einstein, A. (1913). On the present state of the problem of gravitation. In The collected papers of Albert Einstein (English translation) (Vol. 4, pp. 198–222). Princeton: Princeton University Press.Google Scholar
  20. Einstein, A. (1914–1918). The Berlin years: Correspondence, 1914–1918. In The collected papers of Albert Einstein (English translation) (Vol. 8). Princeton: Princeton University Press.Google Scholar
  21. Einstein, A. (1915). Theory of relativity. In The collected papers of Albert Einstein (English translation) (Vol. 4, pp. 246–263). Princeton: Princeton University Press.Google Scholar
  22. Einstein, A. (1921a). Geometry and experience. In The collected papers of Albert Einstein (English translation) (Vol. 7, pp. 208–222). Princeton: Princeton University Press.Google Scholar
  23. Einstein, A. (1921b). On a natural addition to the foundation of the general theory of relativity. In The collected papers of Albert Einstein (English translation) (Vol. 7, pp. 224–228). Princeton: Princeton University Press.Google Scholar
  24. Einstein, A. (1922). Four lectures on the theory of relativity, held at Princeton University on May 1921. In The collected papers of Albert Einstein (English translation) (Vol. 7, pp. 261–368). Princeton: Princeton University Press.Google Scholar
  25. Einstein, A. (1923). Fundamental ideas and problems of the theory of relativity. In The collected papers of Albert Einstein (English translation) (Vol. 14, pp. 74–81). Princeton: Princeton University Press.Google Scholar
  26. Einstein, A. (1949). Autobiographical notes. In P. A. Schilpp (Ed.), Albert Einstein: Philosopher-Scientist (pp. 1–94). New York: MJF Books.Google Scholar
  27. Fletcher, S. C. (2013). Light clocks and the clock hypothesis. Foundations of Physics, 43, 1369–1383.CrossRefGoogle Scholar
  28. Friedman, M. (1983). Foundations of space-time theories: Relativistic physics and philosophy of science. Princeton: Princeton University Press.Google Scholar
  29. Frisch, M. (2011). Principle or constructive relativity. Studies in History and Philosophy of Modern Physics, 42, 176–183.CrossRefGoogle Scholar
  30. Geroch, R. (2013 [1972]). General relativity: 1972 lecture notes. Montreal: Minkowski Institute Press.Google Scholar
  31. Giovanelli, M. (2014). “But one must not legalize the mentioned sin”: Phenomenological vs. dynamical treatments of rods and clocks in Einstein’s thought. Studies in History and Philosophy of Modern Physics, 48, 20–44.CrossRefGoogle Scholar
  32. Goenner, H. F. M. (2004). On the history of unified field theories. Living Reviews in Relativity, 7, 2.CrossRefGoogle Scholar
  33. Jammer, M. (1993). Concepts of space. New York: Dover Publications.Google Scholar
  34. Jammer, M. (2006). Concepts of simultaneity: From antiquity to Einstein and beyond. Baltimore: The Johns Hopkins University Press.Google Scholar
  35. Lange, L. (2014 [1885]). On the law of inertia. The European Physical Journal H 39, 251–262.Google Scholar
  36. Marzke, R. F., & Wheeler, J. A. (1964). Gravitation as geometry I: The geometry of space-time and the geometrodynamical standard meter. In H.-Y. Chiu & W. F. Hoffmann (Eds.), Gravitation and relativity (pp. 40–64). New York: W. A. Benjamin, Inc.Google Scholar
  37. Maudlin, T. (2012). Philosophy of physics: Space and time. Princeton: Princeton University Press.Google Scholar
  38. Neumann, C. (1870). Ueber die Prinzipien der Galilei-Newtonschen Theorie. Leipzig: Teubner.Google Scholar
  39. Ohanian, H. C. (1976). Gravitation and spacetime. New York: W. W. Norton & Company.Google Scholar
  40. Pfister, H., & King, M. (2015). Inertia and gravitation: The fundamental nature and structure of space-time. Berlin: Springer.CrossRefGoogle Scholar
  41. Schutz, J. W. (1973). Foundations of special relativity: Kinematic axioms for Minkowski space-time. Berlin: Springer.CrossRefGoogle Scholar
  42. Stachel, J. (1983). Special relativity from measuring rods. In R. S. Cohen & L. Landau (Eds.), Physics, philosophy and psychoanalysis: Essays in honor of Adolf Grünbaum (pp. 255–272). Dordrecht: D. Reidel.CrossRefGoogle Scholar
  43. Synge, J. L. (1960). Relativity: The general theory. Amsterdam: North-Holland.Google Scholar
  44. Torretti, R. (1983). Relativity and geometry. Oxford: Pergamon Press.Google Scholar
  45. Wald, R. M. (1984). General relativity. Chicago: The University of Chicago Press.CrossRefGoogle Scholar

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Universidad Pablo de OlavideSevilleSpain

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