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Perspectives of the Numerical Order of Material Changes in Timeless Approaches in Physics


Wheeler–deWitt equation as well as some relevant current research (Chiou’s timeless path integral approach for relativistic quantum mechanics; Palmer’s view of a fundamental level of physical reality based on an Invariant Set Postulate; Girelli’s, Liberati’s and Sindoni’s toy model of a non-dynamical timeless space as fundamental background of physical events) suggest that at a fundamental level the background space of physics is timeless, that the duration of physical events has not a primary existence. By taking into consideration the two fundamental theories of time represented by the Jacobi-Barbour-Bertotti theory and by Rovelli’s approach, here it is shown that the view of time as emergent quantity measuring the numerical order of material changes (which can above all be derived from some significant current research, such as Elze’s approach of time, Caticha’s approach of entropic time and Prati’s model of physical clock time) introduces a suggestive unifying re-reading.

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  1. 1.

    Mach, E.: Die Mechanik in ihrer Entwicklung historisch-kritsch dargestellt. Barth, Leipzig (1883). In: English Translation: The Science of Mechanics, Open Court, Chicago (1960)

  2. 2.

    Mittelstaedt, P.: Der Zeitbegriff in der Physik. B.I.-Wissenschaftsverlag, Mannheim (1976)

    Google Scholar 

  3. 3.

    Yourgrau, P.: A World without Time: The Forgotten Legacy of Godel and Einstein. Basic Books, New York (2006).

  4. 4.

    Barbour, J.B., Bertotti, B.: Mach’s principle and the structure of dynamical theories. Proc. R. Soc. A 382(1783), 295–306 (1982)

    ADS  Article  MATH  MathSciNet  Google Scholar 

  5. 5.

    Anderson, E., Barbour, J.B., Foster, B.Z., Kelleher, B. Murchadha, N.Ó.: “The physical gravitational degrees of freedom”. Class. Quantum Gravity 22, 1795–1802 (2005). e-print arXiv:gr-qc/0407104

  6. 6.

    Barbour, J.B., Foster, B.Z. Murchadha, N.Ó: “Relativity without relativity”. Class. Quantum Gravity 19, 3217–3248 (2002). e-print arXiv:gr-qc/0012089.

  7. 7.

    Anderson, E., Barbour, J.B., Foster, B., Murchadha, N.Ó.: “Scale-invariant gravity: Geometrodynamics”. Class. Quantum Gravity 20, 1543–1570 (2003). e-print arXiv:gr-qc/0211022

  8. 8.

    Kuchař, K.V.: Time and interpretations of quantum gravity. In: Kunstatter, G., Vincent, D., Williams, J. (eds.) In: Proceedings of the 4th Canadian Conference on General Relativity and Relativistic Astrophysics, pp. 211–314. World Scientific, Singapore, (1992)

  9. 9.

    Anderson, E.: “Problem of time in quantum gravity”. Annalen der Physik 524(12), 757–786 (2012). e-print arXiv:1206.2403v2 [gr-qc] (2012)

  10. 10.

    DeWitt, B.S.: Quantum theory of gravity. 1. The canonical theory. Phys. Rev. 160(5), 1113–1148 (1967)

    ADS  Article  MATH  Google Scholar 

  11. 11.

    Isham, C.J.: “Canonical quantum gravity and the problem of time”. arXiv:gr-qc/9210011v1 (1992)

  12. 12.

    Gambini, R., Pullin, J.: “Relational physics with real rods and clocks and the measurement problem of quantum mechanics”. Found. Phys. 37(7), 1074–1092 (2007). e-print arXiv:quant-ph/0608243

  13. 13.

    Gambini, R., Porto, R.A., Pullin, J.: “Lost of entanglement in quantum mechanics due to the use of realistic measuring rods”. Phys. Lett. A 372(8), 1213–1218 (2008). e-print arXiv:0708.2935 [quant-ph]

  14. 14.

    Gambini, R., Porto, R.A., Pullin, J.: “Fundamental decoherence from quantum gravity: a pedagogical review”. Gener. Relativ. Gravit. 39(8), 1143–1156 (2007). e-print arXiv:gr-qc/0603090

  15. 15.

    Gambini, R., Porto, R.A., Pullin, J.: “Free will, undecidability, and the problem of time in quantum gravity”. (2009) arXiv:0903.1859v1 [quant-ph]

  16. 16.

    Woodward, J.F.: Killing time. Found. Phys. Lett. 9(1), 1–23 (1996)

    Article  MathSciNet  Google Scholar 

  17. 17.

    Barbour, J.B.: “The Nature of Time”. arXiv:0903.3489 (2009)

  18. 18.

    Chiou, D.-W.: “Timeless path integral for relativistic quantum mechanics”. Class. Quantum Gravity 30(12), 125004 (2013). e-print arXiv:1009.5436v3 [gr-qc] (2009)

  19. 19.

    Palmer, T.N.: “The invariant set hypothesis: a new geometric framework for the foundations of quantum theory and the role played by gravity”. arXiv:0812.1148 (2009)

  20. 20.

    Girelli, F., Liberati, S., Sindoni, L.: “Is the notion of time really fundamental?”. arXiv:0903.4876v1 [gr-qc] (2009)

  21. 21.

    Barbour, J.B.: The timelessness of quantum gravity. 1: The evidence from the classical theory. Class. Quantum Gravity 11, 2853–2873 (1994)

    ADS  Article  MathSciNet  Google Scholar 

  22. 22.

    Kiefer, C.: Quantum Gravity. Clarendon, Oxford (2004)

    MATH  Google Scholar 

  23. 23.

    Anderson, E.: “The problem of time and quantum cosmology in the relational particle mechanics arena”. (2011). arXiv:1111.1472

  24. 24.

    Barbour, J.B.: The End of Time: The Next Revolution in Physics. Oxford University Press, Oxford (2000)

    Google Scholar 

  25. 25.

    Clements, G.M.: “Astronomical time”. Rev. Mod. Phys. 29(1), 2–8 (1957)

  26. 26.

    Gryb, S.: “Jacobi’s principle and the disappearance of time”. Phys. Rev. D 81, 044035 (2010). e-print arXiv: 0804.2900v3 [gr-qc]

  27. 27.

    Faddeev, L.D.: Feynman integral for singular Lagrangians. Theor. Math. Phys. 1(1), 1–13 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  28. 28.

    Rovelli, C.: Time in quantum gravity: an hypothesis. Phys. Rev. D 43(2), 442–456 (1991)

    ADS  Article  MathSciNet  Google Scholar 

  29. 29.

    Rovelli, C.: Quantum mechanics without time: a model. Phys. Rev. D 42(8), 2638–2646 (1991)

    ADS  Article  Google Scholar 

  30. 30.

    Rovelli, C.: Quantum evolving constants. Phys. Rev. D 44(4), 1339–1341 (1991)

    ADS  Article  MathSciNet  Google Scholar 

  31. 31.

    Rovelli, C.: What is observable in classical and quantum gravity? Class. Quantum Gravity 8, 297–316 (1991)

    ADS  Article  MathSciNet  Google Scholar 

  32. 32.

    Rovelli, C.: Quantum reference systems. Class. Quantum Gravity 8, 317–331 (1991)

    ADS  Article  MathSciNet  Google Scholar 

  33. 33.

    Rovelli, C.: “Is there incompatibility between the ways time is treated in general relativity and in standard quantum mechanics?”. In: Ashtekar, A., Stachel, J. (eds.) Conceptual Problems of Quantum Gravity. Birkhauser, New York (1991)

    Google Scholar 

  34. 34.

    Rovelli, C.: Analysis of the different meaning of the concept of time in different physical theories. Il Nuovo Cimento B 110(1), 81–93 (1995)

    ADS  Article  MathSciNet  Google Scholar 

  35. 35.

    Rovelli, C.: “Partial observables”. Phys. Rev. D 65, 124013 (2002). e-print arXiv:gr-qc/0110035

  36. 36.

    Rovelli, C.: “A note on the foundation of relativistic mechanics. II: Covariant hamiltonian general relativity”. arXiv:gr-qc/0202079 (2002)

  37. 37.

    Rovelli, C.: Quantum Gravity. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  38. 38.

    Rovelli, C.: Statistical mechanics of gravity and thermodynamical origin of time. Classical and Quantum Gravity 10(8), 1549–1566 (1993)

    ADS  Article  MATH  MathSciNet  Google Scholar 

  39. 39.

    Rovelli, C.: The statistical state of the universe. Class. Quantum Gravity 10(8), 1567–1578 (1993)

    ADS  Article  MATH  MathSciNet  Google Scholar 

  40. 40.

    Rovelli, C.: “Forget time”. arXiv:0903.3832v3 [gr-qc] (2009)

  41. 41.

    Gózdz, A., Stefanska, K.: Projection evolution and delayed choice experiment. J. Phys. 104, 012007 (2008)

    Google Scholar 

  42. 42.

    Sorli, A., Fiscaletti, D., Klinar, D.: Time is a reference system derived from light speed. Phys. Essays 23(2), 330–332 (2010)

    ADS  Article  Google Scholar 

  43. 43.

    Sorli, A., Fiscaletti, D., Klinar, D.: Replacing time with numerical order of material change resolves Zeno problems on motion. Phys. Essays 24(1), 11–15 (2011)

    ADS  Article  Google Scholar 

  44. 44.

    Elze, H.T.: “Quantum mechanics and discrete time from “timeless” classical dynamics”. Lect. Notes Phys. 633, 196 (2003). arXiv:gr-qc/0307014v1

  45. 45.

    Elze, H.T., Schipper, O.: Time without time: a stochastic clock model. Phys. Rev. D 66, 044020 (2002)

    ADS  Article  MathSciNet  Google Scholar 

  46. 46.

    Elze, H.T.: Emergent discrete time and quantization: relativistic particle with extra dimensions. Phys. Lett. A 310(2–3), 110–118 (2003)

    ADS  Article  MATH  MathSciNet  Google Scholar 

  47. 47.

    Caticha, A.: “Entropic dynamics, time and quantum theory”. J. Phys. A 44(22), 225303 (2011). e-print arXiv:1005.2357v3 [quant-ph]

  48. 48.

    Prati, E.: “The nature of time: from a timeless Hamiltonian framework to clock time of metrology”. (2009) arXiv:0907.1707v1 [physics.class-ph]

  49. 49.

    Anderson, E.: “Machian classical and semiclassical emergent time”. (2013) arXiv:1305.4685v2 [gr-qc]

  50. 50.

    Rovelli, C.: “Loop quantum gravity”. Living Rev. Relativ. 1(1), (1998). doi:10.12942/lrr-1998-1

  51. 51.

    Rovelli, C.: “A new look at loop quantum gravity”. Class. Quantum Gravity 28(11), 114005 (2011). e-print arXiv:1004.1780v1 [gr-qc]

  52. 52.

    Licata, I.: Minkowski space-time and dirac vacuum as ultrareferential reference frame. Hadron. J. 14, 3 (1991)

    MathSciNet  Google Scholar 

  53. 53.

    Sorli, A., Klinar, D., Fiscaletti, D.: New insights into the special theory of relativity. Phys. Essays 24, 2 (2011)

    ADS  Google Scholar 

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Correspondence to Davide Fiscaletti.

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Fiscaletti, D., Sorli, A. Perspectives of the Numerical Order of Material Changes in Timeless Approaches in Physics. Found Phys 45, 105–133 (2015).

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  • Space
  • Time
  • Numerical order of material changes
  • General relativity
  • Quantum mechanics
  • Timeless approaches