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As below, so before: ‘synchronic’ and ‘diachronic’ conceptions of spacetime emergence

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Abstract

Typically, a less fundamental theory, or structure, emerging from a more fundamental one is an example of synchronic emergence. A model (and the physical state it describes) emerging from a prior model (state) upon which it nevertheless depends is an example of diachronic emergence. The case of spacetime emergent from quantum gravity and quantum cosmology challenges these two conceptions of emergence. Here, I propose two more-general conceptions of emergence, analogous to the synchronic and diachronic ones, but which are potentially applicable to the case of emergent spacetime: an inter-level, hierarchical conception, and an intra-level, ‘flat’ conception. I then explore whether, and how, these ideas may be applicable in the case of several putative examples of relativistic spacetime emergent from the non-spatiotemporal structures described by different approaches to quantum gravity, and of spacetime emergent from a non-spatiotemporal ‘big bang’ state according to different examples of quantum cosmology.

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Notes

  1. Ignoring the problem of dark matter, which may indicate a problem with GR at large length scales.

  2. See, e.g., Burgess (2004).

  3. Here, and throughout the paper, I follow Huggett and Wüthrich (2013, 2018) in using “non-spatiotemporal” to refer to any theory or model that describes physics that is “less than fully spatiotemporal in some significant regard”.

  4. This characterisation is supposed to be compatible with the idea of ‘top-down causation’, depending on how the ‘higher level’ and ‘lower level’ labels are applied in the particular proposals (e.g., ‘higher level’ could not refer to a less fundamental theory on this account).

  5. See Crowther (2018).

  6. Here, ‘micro’ is used purely in a figurative sense, as a means of distinguishing the degrees of freedom described by QG from those (‘macro’ degrees of freedom) of current physics. ‘High-energy scales’ and ‘short-length scales’ are used interchangeably, and are also used to signify the domain expected to be described by QG. The scare quotes indicate that this may not literally be true, because QG may describe a regime where the idea of length (and, correspondingly, energy) are not meaningful.

  7. See, e.g. Butterfield and Isham (1999), as well as Oriti (2018a, b), which provide a taxonomy as well as many concrete examples from different approaches to QG.

  8. See, e.g., Batterman (2005, 2011), Crowther (2015), Franklin (2018) and Hartmann (2001).

  9. See, e.g., the discussion in Wüthrich (2017).

  10. Regarding this second possibility, see e.g. Penrose (1999, 2002).

  11. Such a positive conception of emergence is now familiar in the philosophy of physics generally, and in the philosophy of QG in particular, having been employed, e.g., by Butterfield (2011a, b), Crowther (2015, 2016), de Haro (2017), Dieks et al. (2015), Linnemann and Visser (2018), among others.

  12. While I will argue that these examples plausibly can be interpreted as candidates for spacetime emergence, however, there is also scope for arguing that we don’t need to understand them as emergence, and instead adopt a different metaphysical interpretation of the relationship between spacetime and the structures described by QG; cf. Le Bihan (2018). Another option is to utilise the idea of ‘partial functionalism’, rather than metaphysical accounts of emergence, cf. Baron (2019).

  13. See Footnote 6.

  14. For details see, e.g., Barceló et al. (2011) for a review, or Bain (2008, 2013) for a description aimed at philosophers.

  15. See also Franklin (2018), who distinguishes two different senses of autonomy related to EFT and theoretical naturalness.

  16. See, e.g., ’t Hooft (1993), Verlinde (2011), Rickles (2013), Teh (2013), Dieks et al. (2015), de Haro (2017) and Vistarini (2017).

  17. This is a loose characterisation, and one may debate its adequacy in general (particularly regarding the idea of “physical quantities”). Questions regarding the specific nature of dualities are beyond the scope of this paper, but interested readers are encouraged to dig into the philosophical literature, including Butterfield (2018), Dawid (2017), Read and Møller-Nielsen (2018) and the special issue Castellani and Rickles (2017).

  18. Cf. the philosophy references in Footnote 16.

  19. Note that an additional argument for F’s relative fundamentality needs to be provided here.

  20. While the Dependence condition is apparently generally satisfied in the (Approx) schema, via the coarse graining, for example, it is less-obvious that this is the case for approaches that fit (BrokenMap).

  21. Other powerful theorems to this effect are shown by Hawking et al. (1976) and Levichev (1987).

  22. For more on causal set theory accessible for philosophers, see Dowker (2005), Henson (2009), Sorkin (2005) and Wüthrich (2012); for a review, see Surya (2019).

  23. Thanks to a referee for emphasising this point.

  24. For more on LQG, see Rovelli (2004), Rovelli and Vidotto (2014). Note that this latter reference is much more up-to-date than the brief sketch of the kinematic aspect of the theory that I present here; in particular, it has much more detail on the dynamics of the theory, using the covariant approach to LQG.

  25. Although these notions may have non-spatiotemporal analogues, e.g., causation without time (Baron and Miller 2014, 2015; Tallant 2019).

  26. Shech (2019) also suggests weakening the novelty condition along these lines.

  27. In fact, causal set cosmology suggests that the universe underwent many cycles of expansion, stasis, and contraction before our ‘big bang’ event. This is used to explain particular aspects of our current universe that are otherwise striking to cosmologists. See, Sorkin (2000).

  28. We could have an even stronger basis for Novelty if we take the big bang state to be emergent compared to the state that penultimately precedes it, i.e., the causet at Stage \(N - 1\), rather than the causet at Stage N. In this case, the contrast would be between a state that has ontological indeterminism, versus one that has no ontological indeterminism.

  29. Recall that in our positive conception of emergence, novelty is symmetric and relative: a measure of how the emergent and basis states differ from one another. Thus, Novelty does not require that the novel power be possessed by the emergent state.

  30. For details on QCH, see, Markopoulou (2009), for quantum graphity, see: Konopka et al. (2008).

  31. Geometrogenesis is also described in group field theory, which is an active research program that utilises, and is useful for, various other approaches to QG, including LQG and causal set theory (Freidel 2005; Oriti 2009, 2014).

  32. See Crowther (2015) and Morrison (2012) for more on the relationship between symmetry-breaking and emergence.

  33. See Bojowald (2011) for a technical introduction, and Huggett and Wüthrich (2018) for one aimed at philosophers.

  34. As suggested by Huggett and Wüthrich in private correspondence.

  35. In other LQC models, however, there may be a notion of continuous evolution with respect to the scalar field as ‘internal time’, and arguably the ‘big bounce’ picture is better-supported.

  36. Cf. Barrau and Grain (2016)

  37. But note that this is not entirely accurate, either, since it implies we can consider the dual of some cellular decomposition (in this case we just have a single cell).

  38. Thank you to a referee for suggesting this point.

  39. Although this may be a misleading representation: the points of the time dimension at other times of course refer to spatial slices in the whole of spacetime, and this one ‘point’ refers just to a space with one more dimension. Thanks to Nick Huggett for this clarification.

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Acknowledgements

Thanks to the participants at the conference on Diachronic Emergence in Cologne, and especially to Olivier Sartenaer and Andreas Hüttemann for organising it. Thanks to Christian Wüthrich, Nick Huggett, Augustin Baas, Sam Baron, as well as audiences in Perth, Turin, Oxford, Lausanne, and Boston. Finally, thanks to the referees for the journal for their helpful feedback. Funding was provided by Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (Grant No. 105212 165702).

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    Karen Crowther

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Crowther, K. As below, so before: ‘synchronic’ and ‘diachronic’ conceptions of spacetime emergence. Synthese 198, 7279–7307 (2021). https://doi.org/10.1007/s11229-019-02521-1

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