Skip to main content

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

Synthese volume 198, pages 7279–7307 (2021)Cite this article

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.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

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.

References

  • Bain, J. (2008). Condensed matter physics and the nature of spacetime. In D. Dieks (Ed.), The ontology of spacetime II (pp. 301–329). Oxford: Elsevier. (Chapter 16).

    Chapter  Google Scholar 

  • Bain, J. (2013). Effective field theories. In B. Batterman (Ed.), The Oxford handbook of philosophy of physics (pp. 224–254). New York: Oxford University Press.

    Google Scholar 

  • Barceló, C., Liberati, S., & Visser, M. (2011). Analogue gravity. Living Reviews in Relativity. http://www.livingreviews.org/lrr-2011-3.

  • Baron, S. (2019). The curious case of spacetime emergence. Philosophical Studies. https://doi.org/10.1007/s11098-019-01306-z.

  • Baron, S., & Miller, K. (2014). Causation in a timeless world. Synthese, 191(12), 2867–2886.

    Article  Google Scholar 

  • Baron, S., & Miller, K. (2015). Causation sans time. American Philosophical Quarterly, 52, 27–40.

    Google Scholar 

  • Barrau, A., & Grain, J. (2016). Cosmology without time: What to do with a possible signature change from quantum gravitational origin? arXiv:1607.07589v1.

  • Batterman, R. W. (2005). Critical phenomena and breaking drops: Infinite idealizations in physics. Studies in History and Philosophy of Modern Physics, 36(2), 225–244.

    Article  Google Scholar 

  • Batterman, R. W. (2011). Emergence, singularities, and symmetry breaking. Foundations of Physics, 41, 1031–1050.

    Article  Google Scholar 

  • Bojowald, M. (2011). Quantum cosmology: A fundamental description of the universe. New York: Springer.

    Book  Google Scholar 

  • Brahma, S. (2017). Emergence of time in loop quantum gravity. http://philsci-archive.pitt.edu/13158/.

  • Burgess, C. P. (2004). Quantum gravity in everyday life: General relativity as an effective field theory. Living Reviews in Relativity. www.livingreviews.org/lrr-2004-5.

  • Butterfield, J. (2011a). Emergence, reduction and supervenience: A varied landscape. Foundations of Physics, 41(6), 920–959.

    Article  Google Scholar 

  • Butterfield, J. (2011b). Less is different: Emergence and reduction reconciled. Foundations of Physics, 41, 1065–1135.

    Article  Google Scholar 

  • Butterfield, J. (2018). On dualities and equivalences between physical theories. arXiv:1806.01505.

  • Butterfield, J., & Isham, C. (1999). On the emergence of time in quantum gravity. In J. Butterfield (Ed.), The arguments of time (pp. 116–168). Oxford: Oxford University Press.

    Google Scholar 

  • Castellani, E., & Rickles, D. (2017). Introduction to special issue on dualities. Studies in History and Philosophy of Modern Physics, 59, 1–5.

    Article  Google Scholar 

  • Crowther, K. (2015). Decoupling emergence and reduction in physics. European Journal for Philosophy of Science, 5(3), 419–445.

    Article  Google Scholar 

  • Crowther, K. (2016). Effective spacetime: Understanding emergence in effective field theory and quantum gravity. Heidelberg: Springer.

    Book  Google Scholar 

  • Crowther, K. (2018). Inter-theory relations in quantum gravity: Correspondence, reduction, and emergence. Studies in History and Philosophy of Modern Physics, 63, 74–85.

    Article  Google Scholar 

  • Dawid, R. (2017). String dualities and empirical equivalence. Studies in History and Philosophy of Modern Physics, 59, 21–29.

    Article  Google Scholar 

  • de Haro, S. (2017). Dualities and emergent gravity: Gauge/gravity duality. Studies in History and Philosophy of Modern Physics, 59, 109–125.

    Article  Google Scholar 

  • Dieks, D., van Dongen, J., & de Haro, S. (2015). Emergence in holographic scenarios for gravity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 52, 203–216.

    Article  Google Scholar 

  • Dowker, F. (2005). Causal sets and the deep structure of spacetime. In A. Ashtekar (Ed.), 100 years of relativity: Space-time structure (pp. 445–467). Singapore: World Scientific.

    Chapter  Google Scholar 

  • Franklin, A. (2018). Whence the effectiveness of effective field theories? The British Journal for the Philosophy of Science,. https://doi.org/10.1093/bjps/axy050.

    Article  Google Scholar 

  • Freidel, L. (2005). Group field theory: An overview. International Journal of Theoretical Physics, 44(10), 1769–1783.

    Article  Google Scholar 

  • Guay, A., & Sartenaer, O. (2016). A new look at emergence. Or when after is different. European Journal for Philosophy of Science, 6(2), 297–322.

    Article  Google Scholar 

  • Hartmann, S. (2001). Effective field theories, reductionism and scientific explanation. Studies in History and Philosophy of Modern Physics, 32(2), 267–301.

    Article  Google Scholar 

  • Hawking, S., King, A., & McCarthy, P. (1976). A new topology for curved space-time which incorporates the causal, differential, and conformal structures. Journal of Mathematical Physics, 17(2), 174–181.

    Article  Google Scholar 

  • Henson, J. (2009). The causal set approach to quantum gravity. In D. Oriti (Ed.), Approaches to quantum gravity: Toward a new understanding of space, time and matter (pp. 393–413). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Huggett, N., & Wüthrich, C. (2013). Emergent spacetime and empirical (in)coherence. Studies in History and Philosophy of Modern Physics, 44(3), 276–285.

    Article  Google Scholar 

  • Huggett, N., & Wüthrich, C. (2018). The (a)temporal emergence of spacetime. Philosophy of Science, 85(5), 1190–1203.

    Article  Google Scholar 

  • Konopka, T., Markopoulou, F., & Severini, S. (2008). Quantum graphity: A model of emergent locality. Physical Review D, 77(10), 104029.

    Article  Google Scholar 

  • Le Bihan, B. (2018). Space emergence in contemporary physics: Why we do not need fundamentality, layers of reality and emergence. Disputatio, 10(49), 71–95.

    Article  Google Scholar 

  • Levichev, V. (1987). Prescribing the conformal geometry of a Lorentz manifold by means of its causal structure. Soviet Mathematics Doklady, 35, 452–455.

    Google Scholar 

  • Linnemann, N. S., & Visser, M. R. (2018). Hints towards the emergent nature of gravity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 64, 1–13.

    Article  Google Scholar 

  • Malament, D. (1977). The class of continuous timelike curves determines the topology of spacetime. Journal of Mathematical Physics, 18(7), 1399–1404.

    Article  Google Scholar 

  • Markopoulou, F. (2009). New directions in background independent quantum gravity. In D. Oriti (Ed.), Approaches to quantum gravity (pp. 129–149). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Morrison, M. (2012). Emergent physics and micro-ontology. Philosophy of Science, 79(1), 141–166.

    Article  Google Scholar 

  • Oriti, D. (Ed.). (2009). The group field theory approach to quantum gravity. In Approaches to quantum gravity: Toward a new understanding of space time and matter (pp. 310–331). Cambridge: Cambridge University Press.

  • Oriti, D. (2014). Disappearance and emergence of space and time in quantum gravity. Studies in History and Philosophy of Modern Physics, 46, 186–199.

    Article  Google Scholar 

  • Oriti, D. (2018a). The Bronstein hypercube of quantum gravity. arXiv:1803.02577.

  • Oriti, D. (2018b). Levels of spacetime emergence in quantum gravity. arXiv:1807.04875.

  • Penrose, R. (1999). The central programme of twistor theory. Chaos, Solitons and Fractals, 10(2–3), 581–611.

    Article  Google Scholar 

  • Penrose, R. (2002). Gravitational collapse: The role of general relativity. General Relativity and Gravitation, 34(7), 1141–1165.

    Article  Google Scholar 

  • Read, J., & Møller-Nielsen, T. (2018). Motivating dualities. Synthese. https://doi.org/10.1007/s11229-018-1817-5.

  • Rickles, D. (2013). AdS/CFT duality and the emergence of spacetime. Studies in History and Philosophy of Modern Physics, 44(3), 312–320.

    Article  Google Scholar 

  • Rideout, D., & Sorkin, R. (1999). Classical sequential growth model for causal sets. Journal of Physics Conference Series, 174, 024002.

    Google Scholar 

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

    Book  Google Scholar 

  • Rovelli, C., & Vidotto, F. (2014). Covariant loop quantum gravity: An elementary introduction to quantum gravity and spinfoam theory. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Sartenaer, O. (2018). Flat emergence. Pacific Philosophical Quarterly, 99(S1), 225–250.

    Article  Google Scholar 

  • Shech, E. (2019). Philosophical issues concerning phase transitions and anyons: Emergence, reduction, and explanatory fictions. Erkenntnis, 84(3), 585–615.

    Article  Google Scholar 

  • Sorkin, R. (2009). Does locality fail at intermediate length scales? In D. Oriti (Ed.), Approaches to quantum ravity: Toward a new understanding of space, time and matter (pp. 26–43). Cambridge: Cambridge University Press.

  • Sorkin, R. D. (2000). Indications of causal set cosmology. International Journal of Theoretical Physics, 39(7), 1731–1736.

    Article  Google Scholar 

  • Sorkin, R. D. (2005). Causal sets: Discrete gravity (notes for the valdivia summer school). In D. M. A. Gomberoff (Ed.), Lectures on quantum gravity, proceedings of the Valdivia summer school, Valdivia, Chile, January 2002. Plenum. arXiv:gr-qc/0309009.

  • Surya, S. (2019). The causal set approach to quantum gravity. Living Reviews in Relativity. arXiv:1903.11544.

  • ’t Hooft, G. (1993). Dimensional reduction in quantum gravity. arXiv:gr-qc/9310026.

  • Tallant, J. (2019). Causation in a timeless world? Inquiry, 62(3), 300–316.

    Article  Google Scholar 

  • Teh, N. (2013). Holography and emergence. Studies in History and Philosophy of Modern Physics, 44(3), 300–311.

    Article  Google Scholar 

  • Verlinde, E. (2011). On the origin of gravity and the laws of Newton. Journal of High Energy Physics, 1104, 029.

    Article  Google Scholar 

  • Vistarini, T. (2017). Holographic space and time: Emergent in what sense? Studies in History and Philosophy of Modern Physics, 59, 126–135. Dualities in Physics.

    Article  Google Scholar 

  • Wüthrich, C. (2012). The structure of causal sets. Journal for General Philosophy of Science, 43(2), 223–241.

    Article  Google Scholar 

  • Wüthrich, C. (2017). Raiders of the lost spacetime. In D. Lehmkuhl (Ed.), Towards a theory of spacetime theories (pp. 297–335). London: Birkhäuser.

    Chapter  Google Scholar 

  • Wüthrich, C. (2019). The emergence of space and time. In S. Gibb, R. F. Hendry, & T. Lancaster (Eds.), The Routledge Handbook of Emergence (pp. 315–326). London: Routledge.

    Chapter  Google Scholar 

  • Wüthrich, C., & Callender, C. (2017). What becomes of a causal set? The British Journal for the Philosophy of Science, 68(3), 907–925.

    Article  Google Scholar 

Download references

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).

Author information

Authors and Affiliations

  1. Department of Philosophy, Classics, History of Art and Ideas, University of Oslo, Oslo, Norway

    Karen Crowther

Authors
  1. Karen Crowther
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Karen Crowther.

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

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11229-019-02521-1

Keywords

  • Emergence
  • Quantum gravity
  • Cosmology
  • Spacetime
  • Space
  • Time
  • Flat emergence
  • Hierarchical emergence
  • Levels
  • Fundamentality
  • Diachronic emergence
  • Synchronic emergence
  • Holography
  • Duality
  • Geometrogenesis