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Emergence of Time

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.

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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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Keywords

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