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Spacetime as Described by EFT

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Effective Spacetime

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Abstract

This chapter examines the idea of treating GR as an EFT, and, drawing from the ideas presented in the previous chapters (Chaps. 2–4), explores what we might learn of emergent spacetime through the framework of EFT. Examples of both top–down and bottom–up EFT are considered; the former case is represented by analogue models of (and for) gravity, which describe spacetime (an effective curved geometry, to be more precise) as emergent from a condensed-matter system at high-energy.

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Notes

  1. 1.

    See Bain (2008, 2013); Crowther (2013); Dardashti et al. (Forthcoming).

  2. 2.

    See Barceló et al. (2011) for a review. The earliest instance the authors identify is Gordon’s 1923 use of an effective gravitational metric field to mimic a dielectric medium. A later example is Unruh’s “Experimental black hole radiation” (1981), which used an analogue model based on fluid flow to explore Hawking radiation from actual GR black holes. Barceló et al. (2011), p. 42 present this example as being the start of what they call the “modern era” of analogue models.

  3. 3.

    See Footnote 2.

  4. 4.

    Since here I am concerned with emergent spacetime, I will not Volovik’s model’s replication of the standard model in any detail.

  5. 5.

    In particular, the A-phase of \(^{3}{\mathrm {He}}{}\) is characterised by pairs of \(^{3}{\mathrm {He}}{}\) atoms spinning about anti-parallel axes that are perpendicular to the plane of their orbit. See Volovik (2003) or the short review in Bain (2008).

  6. 6.

    For details see Volovik (2003, pp. 82, 96). This summary follows Bain (2008, pp. 309–311).

  7. 7.

    Barceló et al. (2001), Hu (2009), Visser (2008), Volovik (2003).

  8. 8.

    The idea of background independence is discussed further in the next chapter (Sect. 6.4).

  9. 9.

    These include considering the Planck temperature (1032 K) as “low temperature”, given that BECs only exist at very low temperatures and spacetime is supposed to exist at this temperature in the early universe, for example.

  10. 10.

    The gravitational coupling constant (Newton’s constant), G, has mass dimension \(-2\) in units where \(\hbar =c=1\), recalling from footnote (10) this means that we expect conventional perturbative QFT to be applicable only for energies \(E^2\ll 1/G\).

  11. 11.

    Burgess (2004); Donoghue (1994, 1997).

  12. 12.

    Following Weinberg (2009).

  13. 13.

    This sentiment is also expressed by many proponents of so-called “discrete” approaches to quantum gravity, as discussed in the next chapter.

  14. 14.

    This is similar to QCD, except that QCD is also asymptotically free, having a fixed point of zero; usually, in asymptotic safety, the fixed point is finite, but not zero.

  15. 15.

    And so accords with the philosophy of “effective EFT”.

  16. 16.

    This explanation is based on Niedermaier and Reuter (2006), Percacci (2009).

  17. 17.

    For a brief overview, see Percacci (2009).

  18. 18.

    Weinberg (1979), Kawai et al. (1993), Kawai et al. (1996), Niedermaier (2003), Niedermaier (2010).

  19. 19.

    Smolin (1982), Percacci and Perini (2003), Percacci (2006).

  20. 20.

    Ambjørn et al. (2004, 2005).

  21. 21.

    Reuter and Saueressig (2002); Reuter and Weyer (2009); Lauscher and Reuter (2002); Codello and Percacci (2006). For an extended list of references see Weinberg (2009).

  22. 22.

    However, recall from discussion in Chap. 1 that there is more to recovering GR than simply an emergent metric and an effective dynamics for spacetime, and it is not clear that these models are capable of representing these extra features, see Carlip (2014).

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  1. Department of Philosophy, University of Pittsburgh, Pittsburgh, PA, USA

    Karen Crowther

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Crowther, K. (2016). Spacetime as Described by EFT. In: Effective Spacetime. Springer, Cham. https://doi.org/10.1007/978-3-319-39508-1_5

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