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Instants in Physics: Point Mechanics and General Relativity

  • Domenico GiuliniEmail author
Chapter
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Part of the On Thinking book series (ONTHINKING, volume 4)

Abstract

Theories in physics usually do not address “the present” or “the now”. However, they usually have a precise notion of an “instant” (or state). I review how this notion appears in relational point mechanics and how it suffices to determine durations—a fact that is often ignored in modern presentations of analytical dynamics. An analogous discussion is attempted for General Relativity. Finally we critically remark on the difference between relationalism in point mechanics and field theory and the problematic foundational dependencies between fields and spacetime.

Keywords

Mass Point Point Mechanic Inertial System Spatial Rotation Absolute Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I sincerely thank Albrecht von Müller and Thomas Filk for several invitations to workshops of the Parmenides Foundation, during which I was given the opportunity to present and discuss the material contained in this contribution.

References

  1. 1.
    Baierlein RF, Sharp DH, Wheeler JA (1962) Three-dimensional geometry as carrier of information about time. Phys Rev 126(5):1864–1865CrossRefADSzbMATHMathSciNetGoogle Scholar
  2. 2.
    Barbour JB (1994) The timelessness of quantum gravity: I. The evidence from the classical theory. Classical Quantum Gravity 11(12):2853–2873CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    Barbour JB, Bertotti B (1982) Mach’s principle and the structure of dynamical theories. Proc R Soc A 382(1783):295–306CrossRefMathSciNetGoogle Scholar
  4. 4.
    Barbour JB, Pfister H (1995) Mach’s principle: from newton’s bucket to quantum gravity. In: Einstein studies, vol 6. Birkhäuser, BaselGoogle Scholar
  5. 5.
    Cantor G (1895) Beiträge zur Begrü ndung der transfiniten mengenlehre (Erster Artikel). Mathematische Annalen 46:481–512CrossRefzbMATHGoogle Scholar
  6. 6.
    Christodoulou D (1975) The chronos principle. Il Nuovo Cimento 26 B(1):67–93Google Scholar
  7. 7.
    Clemence GM (1948) On the system of astronomical constants. Astron J 53(6):169–179CrossRefADSGoogle Scholar
  8. 8.
    Giulini D (2007) Some remarks on the notions of general covariance and background independence. In: Seiler E, Stamatescu I-O (eds) Approaches to fundamental physics. Lecture notes in physics, vol 721. Springer, Berlin, pp 105–120. Online available at (arxiv.org/pdf/gr-qc/0603087)Google Scholar
  9. 9.
    Lange L (1885) Über das Beharrungsgesetz. Berichte über die Verhandlungen der königlichen sächsischen Gesellschaft der Wissenschaften zu Leipzig; mathematisch-physikalische Classe 37:333–351Google Scholar
  10. 10.
    Markosian N (2014) Time. In: Zalta EN (ed) The stanford encyclopedia of philosophy (Springer 2014 Ed.) http://plato.stanford.edu/archives/spr2014/entries/time/
  11. 11.
    von Meyenn K (ed) (1979–2005) Wolfgang Pauli: scientific correspondence with Bohr, Einstein, Heisenberg, a.O., Vol. I-IV. In: Sources in the history of mathematics and physical sciences, vols 2, 6, 11, 14, 15, 17, 18. Springer, HeidelbergGoogle Scholar
  12. 12.
    Minkowski H (1909) Raum und Zeit. Verlag B.G. Teubner, Leipzig Address delivered on 21st of September 1908 to the 80th assembly of german scientists and physicians at CologneGoogle Scholar
  13. 13.
    Murchadha N, Roszkowski K (2006) Embedding spherical space- like slices in a Schwarzschild solution. Classical Quantum Gravity 23(2):539–547CrossRefADSzbMATHMathSciNetGoogle Scholar
  14. 14.
    Newton I (1988) Über die gravitation. Vittorio Klostermann, Frankfurt a.MzbMATHGoogle Scholar
  15. 15.
    Norton JD (2011) The hole argument. In: Zalta EN (ed) The stanford encyclopedia of philosophy (Springer 2014 ed.) http://plato.stanford.edu/archives/spr2014/entries/spacetime-holearg/
  16. 16.
    Reissner H (1914) über die Relativität der Beschleunigung in der Mechanik. Physikalische Zeitschrift 15:371–375zbMATHGoogle Scholar
  17. 17.
    Schrödinger E (1925) Die Erfüllbarkeit der Relativitätsforderung in der klassischen Mechanik. Annalen der Physik (Leipzig) 77:325–336CrossRefzbMATHGoogle Scholar
  18. 18.
    Tait PG (1883/1884) Note on reference frames. Proc R Soc Edinb XII:743–745Google Scholar
  19. 19.
    Thomson J (1883/1884) On the law of inertia; the principle of chronometry; and the principle of absolute clinural rest, and of absolute rotation. Proc R Soc Edinb XII:568–578Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute for Theoretical PhysicsLeibniz University HannoverHannoverGermany

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