Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Emergence of Time

  • 91 Accesses


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.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4


  1. 1.

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

  2. 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. 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. 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. 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. 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. 7.

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

  8. 8.

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

  9. 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. 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.


  1. 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)

  2. 2.

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

  3. 3.

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

  4. 4.

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

  5. 5.

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

  6. 6.

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

  7. 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)

  8. 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. 9.

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

  10. 10.

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

  11. 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)

  12. 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)

  13. 13.

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

  14. 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. 15.

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

  16. 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)

  17. 17.

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

  18. 18.

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

  19. 19.

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

  20. 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)

  21. 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

  22. 22.

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

  23. 23.

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

  24. 24.

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

  25. 25.

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

  26. 26.

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

  27. 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)

  28. 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. 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)

  30. 30.

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

  31. 31.

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

  32. 32.

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

  33. 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

  34. 34.

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

  35. 35.

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

  36. 36.

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

  37. 37.

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

  38. 38.

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

  39. 39.

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

  40. 40.

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

  41. 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)

  42. 42.

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

  43. 43.

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

  44. 44.

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

  45. 45.

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

  46. 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. 47.

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

  48. 48.

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

  49. 49.

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

  50. 50.

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

  51. 51.

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

  52. 52.

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

  53. 53.

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

  54. 54.

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

  55. 55.

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

  56. 56.

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

  57. 57.

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

  58. 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)

  59. 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)

  60. 60.

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

  61. 61.

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

  62. 62.

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

  63. 63.

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

  64. 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)

  65. 65.

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

  66. 66.

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

  67. 67.

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

  68. 68.

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

  69. 69.

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

  70. 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)

  71. 71.

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

  72. 72.

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

  73. 73.

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

  74. 74.

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

  75. 75.

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

  76. 76.

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

  77. 77.

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

  78. 78.

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

  79. 79.

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

  80. 80.

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

  81. 81.

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

  82. 82.

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

Download references


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.

Author information

Correspondence to George F. R. Ellis.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation


  • Evolving block universe
  • Arrow of time
  • Direction of time
  • Wave function collapse
  • Quantum gravity