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Emergence of Time

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Abstract

Microphysical laws are time reversible, but macrophysics, chemistry and biology are not. This paper explores how this asymmetry (a classic example of a broken symmetry) arises due to the cosmological context, where a non-local Direction of Time is imposed by the expansion of the universe. This situation is best represented by an Evolving Block Universe, where local arrows of time (thermodynamic, electrodynamic, gravitational, wave, quantum, biological) emerge in concordance with the Direction of Time because a global Past Condition results in the Second Law of Thermodynamics pointing to the future. At the quantum level, the indefinite future changes to the definite past due to quantum wave function collapse events.

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Notes

  1. For a parallel discussion of how this works in quantum theory, see [33].

  2. In cases where there is no initial singularity, a surface of constant density \(\rho\) that corresponds to a bounce if that happens; else in an emergent universe [40, 42], an arbitrarily chosen surface of constant density that occurs way before inflation starts.

  3. It is true that closed buildings or boxes can exclude the CMB; however (a) they cannot occur on an astronomical scale, where in any event many other forms of radiation will generically occur and prevent a vacuum; (b) on a micro scale such a box cannot contain an exact vacuum for technological reasons, and it itself will move on a timelike worldline.

  4. We are ignoring here the arrow of time associated with the Weak Force, which is weakly time asymmetric. This is an important issue to be tackled later. The justification for omitting it is that it does not directly impact the dynamics of every day life, but its role in the early universe (e.g. baryosynthesis) and in astrophysics needs consideration.

  5. Tim Maudlin pointed out to us in a private communication that due to its statistical nature the second law of thermodynamics is not really a law. This touches upon very interesting philosophical questions relating to the nature of physical laws in general and the second law of thermodynamics in particular that we will not pursue here. In fact, there is no general agreement on what precisely the second law of thermodynamics is [79].

  6. In fact, the transformation (17) that is usually viewed as a time reversal transformation can also be interpreted differently: as Tim Maudlin pointed out to us, speaking of an evolution from an initial to a final state always defines a forward time direction, and in this sense time itself is never reversed, but the momenta and ensuing trajectories are.

  7. In the latter case, see [35], pp. 281–282 for details.

  8. The equation for the rate of change of the matter specific entropy is (3.13) in [28].

  9. Various authors suggest to introduce an entropy of the gravitational field in order to follow the way entropy changes during these processes [17, 66]. We will not pursue that issue here.

  10. The authors comment furthermore on higher-order theories that can include both types of propagators and thus both causal directions. In this situation, there is causal uncertainty on short timescales.

References

  1. Adamek, J., Clarkson, C., Coates, L., Durrer, R., Kunz, M.: Bias and scatter in the Hubble diagram from cosmological large-scale structure. Phys. Rev. D 100, 021301 (2019)

    ADS  MathSciNet  Google Scholar 

  2. Ade, P.A., et al.: Planck 2015 results-xiii. Cosmological parameters. Astron. Astrophys. 594, A13 (2016)

    Google Scholar 

  3. Aghanim, N., et al.: “Planck 2018 results. VI. Cosmological parameters.” arXiv preprint arXiv:1807.06209 (2018)

  4. Albert, D.: Time and Chance. Harvard University Press, Cambridge, MA (2000)

    MATH  Google Scholar 

  5. Anderson, P.W.: More is different. Science 177, 393–396 (1972)

    ADS  Google Scholar 

  6. Arnol’d, V.I.: Mathematical Methods of Classical Mechanics. Springer, Berlin (1989)

    MATH  Google Scholar 

  7. Arnold, V.I., Kozlov, V.V., Neishtadt, A.I.: Mathematical Aspects of Classical and Celestial Mechanics, vol. 3. Springer Science and Business Media, Berlin (2007)

    MATH  Google Scholar 

  8. Arnowitt, R., Deser, S., Misner, C.W.: (1962) “The dynamics of general relativity”. In: Louis Witten (Ed.) Gravitation: An Introduction to Current Research. Wiley, Amsterdam, pp. 227–265. Reprinted in Gen. Rel. Grav. 40: 1997 (2008)

  9. Barbour, J.: The End of Time: The Next Revolution in Physics. Oxford University Press, Oxford (2001)

    Google Scholar 

  10. Berridge, Cell Signalling Biology Portland Press (2014). https://doi.org/10.1042/csb0001001 http://www.cellsignallingbiology.co.uk/csb/

    Google Scholar 

  11. Breuer, R.A., Ehlers, J.: Propagation of high-frequency electromagnetic waves through a magnetized plasma in curved space-time. I. Proc. R. Soc. Lond A 370, 389–406 (1980)

    ADS  MathSciNet  Google Scholar 

  12. Breuer, R.A., Ehlers, J.: Propagation of high-frequency electromagnetic waves through a magnetized plasma in curved space-time. II. Application of the asymptotic approximation. Proc. R. Soc. Lond A 374, 65–86 (1981)

    ADS  MathSciNet  Google Scholar 

  13. Buchert, T.: On average properties of inhomogeneous fluids in general relativity: perfect fluid cosmologies. Gen. Relativ. Gravit. 33, 1381–1405 (2001)

    ADS  MathSciNet  MATH  Google Scholar 

  14. Callender, C.: Thermodynamic Asymmetry in Time. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/archives/win2016/entries/time-thermo/ (2016)

  15. Campbell, N.A., Reece, J.B.: Biology. Benjamin Cummings, San Francisco (2005)

    Google Scholar 

  16. Clarkson, C., Ellis, G., Larena, J., Umeh, O.: Does the growth of structure affect our dynamical models of the Universe? The averaging, backreaction, and fitting problems in cosmology. Rep. Prog. Phys. 74, 112901 (2011)

    MathSciNet  Google Scholar 

  17. Clifton, T., Ellis, G.F., Tavakol, R.: A gravitational entropy proposal. Class. Quantum Gravity 30, 125009 (2013)

    ADS  MathSciNet  MATH  Google Scholar 

  18. Dodelson, S.: Modern Cosmology. Academic Press, Cambridge (2003)

    Google Scholar 

  19. Donoghue, J.F., Meneze, G.: Arrow of causality and quantum gravity. Phys. Rev. Lett 123, 171601 (2019)

    ADS  MathSciNet  Google Scholar 

  20. Drossel, B.: On the relation between the second law of thermodynamics and classical and quantum mechanics. In: Falkenburg, B., Morrison, M. (eds.) Why More is Different. Springer Verlag, Heidelberg (2015)

    Google Scholar 

  21. Drossel, B.: Ten reasons why a thermalized system cannot be described by a many-particle wave function. Stud. Hist. Philos. Sci. B 58, 12–21 (2017). arXiv:1509.07275

    MATH  Google Scholar 

  22. Drossel, B., Ellis, G.: Contextual wavefunction collapse: an integrated theory of quantum measurement. N. J. Phys. 20, 113025 (2018)

    Google Scholar 

  23. Dyson, F.J.: Energy in the universe. Sci. Am. 225(3), 50–59 (1971)

    Google Scholar 

  24. Earman, J.: The ‘past hypothesis’: not even false. Stud. Hist. Philos. Sci. B 37, 399–430 (2006)

    MathSciNet  MATH  Google Scholar 

  25. East, W.E., Wojtak, R., Pretorius, F.: Einstein–Vlasov calculations of structure formation. (2019). arXiv:1908.05683

  26. Eddington, A.S.: The nature of the physical world. Macmillan, New York (2019)

    MATH  Google Scholar 

  27. Ehlers, J., Prasanna, A.R.: A WKB formalism for multicomponent fields and its application to gravitational and sound waves in perfect fluids. Class. Quantum Gravity 13, 2231 (1996)

    ADS  MathSciNet  MATH  Google Scholar 

  28. Ellis, G.F.R.: (1971) “General relativity and cosmology”. In General Relativity and Cosmology, Varenna Course No. XLVII, ed R. K. Sachs (Academic, New York). Reprinted as Golden Oldie, General Relativity and Gravitation41, 581–660 (2009)

  29. Ellis, G.F.: Relativistic cosmology: its nature, aims and problems. In: Bertotti, B. (ed.) General Relativity and Gravitation, pp. 215–288. Springer, Dordrecht (1984)

    Google Scholar 

  30. Ellis, G.F.: Cosmology and local physics. N. Astron. Rev. 46, 645–657 (2002)

    ADS  Google Scholar 

  31. Ellis, G.F.: Physics, complexity and causality. Nature 435, 743 (2005)

    ADS  Google Scholar 

  32. Ellis, G.F.R.: Physics in the real universe: time and spacetime. Gen. Relativ. Gravit. 38, 1797–1824 (2006)

    ADS  MathSciNet  MATH  Google Scholar 

  33. Ellis, G.F.R.: On the limits of quantum theory: contextuality and the quantum-classical cut. Ann. Phys. 327, 1890–1932 (2012). arXiv:1108.5261

    ADS  MathSciNet  MATH  Google Scholar 

  34. Ellis, G.F.R.: The evolving block universe and the meshing together of times. Ann. N. Y Acad. Sci. 1326, 26–41 (2014)

    ADS  Google Scholar 

  35. Ellis, G.F.R.: How Can Physics Underlie the Mind? Top-Down Causation in the Human Context. Springer, Heidelberg (2016)

    Google Scholar 

  36. Ellis, G.F.R.: Foundational issues relating spacetime, matter, and quantum mechanics. J. Phys. 1275, 012001 (2019)

    Google Scholar 

  37. Ellis, G.F.R., Drossel, B.: How downwards causation occurs in digital computers. Found. Phys. 49, 1253–1277 (2019)

    ADS  MathSciNet  MATH  Google Scholar 

  38. Ellis, G.F.R., Goswami, R.: Spacetime and the Passage of Time. Springer Handbook of Spacetime, pp. 243–264. Springer, Berlin (2014)

    Google Scholar 

  39. Ellis, G.F.R., Kopel, J.: The dynamical emergence of biology from physics: branching causation via biomolecules. Front. Physiol. 9, 1966 (2018)

    Google Scholar 

  40. Ellis, G.F.R., Maartens, R.: The emergent universe: inflationary cosmology with no singularity. Class. Quantum Gravity 21, 223 (2003)

    ADS  MathSciNet  MATH  Google Scholar 

  41. Ellis, G.F.R., Sciama, D.W.: Global and non-global problems in cosmology. In: Synge, J.L., O’Raifertaigh, L. (eds.) General Relativity, p. 35. Oxford University Press, Oxford (1972)

    Google Scholar 

  42. Ellis, G.F.R., Murugan, J., Tsagas, C.G.: The emergent universe: an explicit construction. Class. Quantum Gravity 21, 233 (2003)

    ADS  MathSciNet  MATH  Google Scholar 

  43. Ellis, G.F., Meissner, K.A., Nicolai, H.: The physics of infinity. Nat. Phys. 14, 770 (2018)

    Google Scholar 

  44. Fanizza, G., Gasperini, M., Marozzi, G., Veneziano, G.: “Generalized covariant prescriptions for averaging cosmological observables”. (2019) arXiv:1911.09469

  45. Ghirardi, G.: Sneaking a Look at God’s Cards: Unraveling the Mysteries of Quantum Mechanics. Princeton University Press, Princeton (2007)

    MATH  Google Scholar 

  46. Gisin, N.: “Indeterminism in physics, classical chaos and bohmian mechanics. are real numbers really real?” arXiv preprint arXiv:1803.06824 and Erkenntnis https://doi.org/10.1007/s10670-019-00165-8 (2018)

  47. Hartwell, L.H., Hopfield, J.J., Leibler, S., Murray, A.W.: From molecular to modular cell biology. Nature 402(Supplement), C47–C52 (1999)

    Google Scholar 

  48. Hawking, S.W.: Perturbations of an expanding universe. Astrophys. J. 145, 544 (1966)

    ADS  Google Scholar 

  49. Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Spacetime. Cambridge Uiversity Press, Cambridge (1973)

    MATH  Google Scholar 

  50. Hirsch, M.W.: Differential Topology. Springer, Berlin, Heidelberg (1976)

    MATH  Google Scholar 

  51. Hossenfelder, S.: Minimal length scale scenarios for quantum gravity. Living Rev. Relativ. 16, 2 (2013)

    ADS  MATH  Google Scholar 

  52. Isham, C.J.: Lectures on quantum theory Mathematical and structural foundations. Allied Publishers, New Delhi (2001)

    Google Scholar 

  53. Karplus, M.: Development of multiscale models for complex chemical systems: from H+ H2 to biomolecules. Angew. Chem. Int. Ed. 53, 9992–10005 (2014)

    Google Scholar 

  54. Lamb, J.S., Roberts, J.A.: Time-reversal symmetry in dynamical systems: a survey. Physica D 112, 1–39 (1998)

    ADS  MathSciNet  MATH  Google Scholar 

  55. Lancaster, T., Blundell, S.J.: Quantum field theory for the gifted amateur. OUP, Oxford (2014)

    MATH  Google Scholar 

  56. Lebowitz, J.L.: Statistical mechanics: a selective review of two central issues. Rev. Mod. Phys. 71, S346–S357 (1999)

    Google Scholar 

  57. Loll, R.: Discrete approaches to quantum gravity in four dimensions. Living Rev. Relativ. (1998) https://link.springer.com/journal/41114

  58. McLenaghan, R.G.: An explicit determination of the empty space-times on which the wave equation satisfies Huygens’ principle. Math. Proc. Camb. Philos. Soc. 65, 139–155 (1969)

    ADS  MathSciNet  MATH  Google Scholar 

  59. McLenaghan, R.G.: On the validity of Huygens’ principle for second order partial differential equations with four independent variables. Part I: Derivation of necessary conditions. Ann. Phys. Théor. 20, 153–188 (1974)

    MATH  Google Scholar 

  60. McLenaghan, R.G.: Huygens’ principle. Ann. Phys. Théor. 37, 211–236 (1982)

    MathSciNet  MATH  Google Scholar 

  61. Murugan, J., Weltmann, A., Ellis, G.F.R. (eds.): Foundations of Space and Time: Reflections on Quantum Gravity. Cambridge University Press, Cambridge (2012)

    MATH  Google Scholar 

  62. Noble, D.: Modeling the heart-from genes to cells to the whole organ. Science 295, 1678–1682 (2002)

    ADS  Google Scholar 

  63. Noble, D.: A theory of biological relativity: no privileged level of causation. Interface Focus 2, 55–64 (2012)

    Google Scholar 

  64. O’Gorman, T.J., et al.: Field testing for cosmic ray soft errors in semiconductor memories. IBM J. Res. Dev. 40, 41–50 (1996)

    Google Scholar 

  65. Penrose, R.: The Road to Reality: A Complete Guide to the Laws of the Universe. Vintage, New York (2006)

    MATH  Google Scholar 

  66. Penrose, R.: Fashion, Faith, and Fantasy in the New Physics of the Universe. Princeton University Press, Princeton (2017)

    MATH  Google Scholar 

  67. Perez, A.: Spin foam models for quantum gravity. Class. Quantum Gravity 20, R43 (2003)

    ADS  MathSciNet  MATH  Google Scholar 

  68. Perez, A.: The spin-foam approach to quantum gravity. Living Rev. Relativ. 16, 3 (2013)

    ADS  MATH  Google Scholar 

  69. Peter, P., Uzan, J.-P.: Primordial Cosmology. Oxford Graduate Texts, Oxford (2013)

    Google Scholar 

  70. Pretor-Pinney, G.: The Wave Watcher’s Companion: Ocean Waves, Stadium Waves, and All the Rest of Life’s Undulations. Penguin, New Jersey (2010)

    Google Scholar 

  71. Rovelli, C.: “Where was past low-entropy?” (2018) arXiv:1812.03578

  72. Rovelli, C.: “Neither Presentism nor Eternalism” (2019) arXiv:1910.02474

  73. Scientific American Special Edition (2012) “A Matter of Time” 21, 8–13

  74. Simon, H.A.: The Sciences of the Artificial. MIT Press, Cambridge (1996)

    Google Scholar 

  75. Sommerfeld, A.: Partial Differential Equations in Physics. Academic pPress, New York (1949)

    MATH  Google Scholar 

  76. Strogatz, S.H.: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. CRC Press, Boca Raton (2018)

    MATH  Google Scholar 

  77. Susskind, L., Friedman, A.: Quantum Mechanics: The Theoretical Minimum. Basic Books, New York (2014)

    MATH  Google Scholar 

  78. Tanenbaum, A.S.: Structured Computer Organisation, 5th edn. Prentice Hall, Englewood Cliffs (2006)

    Google Scholar 

  79. Uffink, J.: Bluff your way in the second law of thermodynamics. Stud. Hist. Philos. Sci. B 32, 305–394 (2001)

    MathSciNet  MATH  Google Scholar 

  80. Weinberg, S.: The Quantum Theory of Fields. Vol. 1 Foundations. Cambridge University Press, Cambridge (1995)

    MATH  Google Scholar 

  81. Weinstein, S.: Electromagnetism and time-asymmetry. Mod. Phys. Lett. A 26, 815–818 (2011)

    ADS  MathSciNet  MATH  Google Scholar 

  82. Wheeler, J.A., Feynman, R.P.: Interaction with the absorber as the mechanism of radiation. Rev. Mod. Phys. 17, 157 (1945)

    ADS  Google Scholar 

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Acknowledgements

We thank Carlo Rovelli, John O’Donoghue, John Miller, and Tim Maudlin for useful comments, and Reinhard Stock for proposals that have substantially improved the text.

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Correspondence to George F. R. Ellis.

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Ellis, G.F.R., Drossel, B. Emergence of Time. Found Phys 50, 161–190 (2020). https://doi.org/10.1007/s10701-020-00331-x

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