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Defining a crisis: the roles of principles in the search for a theory of quantum gravity

  • S.I.: First Principles in Science
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Abstract

In times of crisis, when current theories are revealed as inadequate to task, and new physics is thought to be required—physics turns to re-evaluate its principles, and to seek new ones. This paper explores the various types, and roles of principles that feature in the problem of quantum gravity as a current crisis in physics. I illustrate the diversity of the principles being appealed to, and show that principles serve in a variety of roles in all stages of the crisis, including in motivating the need for a new theory, and defining what this theory should be like. In particular, I consider: the generalised correspondence principle, UV-completion, background independence, and the holographic principle. I also explore how the current crisis fits with Friedman’s view on the roles of principles in revolutionary theory-change, finding that while many key aspects of this view are not represented in quantum gravity (at the current stage), the view could potentially offer a useful diagnostic, and prescriptive strategy. This paper is intended to be relatively non-technical, and to bring some of the philosophical issues from the search for quantum gravity to a more general philosophical audience interested in the roles of principles in scientific theory-change.

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Notes

  1. Almost as soon as GR was completed, Einstein was aware of the need for a quantum theory of gravity; Einstein (1916, p. 202) writes of a possible conflict between GR and the principles of quantum theory. See also the papers in Blum and Rickles (Forthcoming).

  2. Note that, although each of these approaches is incomplete, and faces its own set of problems in addition to these general difficulties, it is still possible—and indeed, worthwhile—to engage with the philosophy of QG, as well as to consider what QG might tell us about other philosophical questions (See, e.g., Butterfield and Isham 2001; Callender and Huggett 2001; Rickles 2008a).

  3. See also, Crowther and Rickles (2014), Crowther and Linnemann (2017), Smolin (2017).

  4. When I refer to “current principles”, I mean those that feature within, or led to the development of, existing theories (typically the current best theories of physics). This is in contrast with new principles that are being appealed to (e.g., the holographic principle), which have not yet led to, or featured within, any successful, accepted scientific theories.

  5. As I discuss, the generalised correspondence principle does feature as a sort of meta-principle in what Friedman (2001) calls “communicative rationality”.

  6. An effective theory in physics is one that is valid only at a given range of energy (length) scales, and is thus not considered fundamental.

  7. Although UV-completion (the idea that a theory be formally predictive up to all possible high energy scales) is often presented as part of the definition of QG, Crowther and Linnemann (2017) argue against taking it as a criterion of acceptance in QG. Nevertheless, it plays a role in motivating the search for QG, and may usefully act as a guiding principle.

  8. Note, too, that Dawid (2013) presents the UEA in conjunction with two other arguments, in order to establish limits on the underdetermination of the new theory, and together paint a picture that is much more nuanced than what I present here.

  9. But see Footnote 8.

  10. Dawid (2013), and string theorists, of course, would challenge this statement, asserting string theory’s success in doing exactly this. However, string theory is currently not at a stage where such assertions represent compelling arguments.

  11. English translation, Poincaré (1905a); also appears as Chapters VII–IX of Poincaré (1907).

  12. See, e.g., Poincaré (1905b), Ch. VI, Poincaré (1907), Ch. X. 4.

  13. Including Brownian motion, radioactivity, the Michelson-Morley experiment, and experiments involving electrons accelerated to very high velocities.

  14. Cf. Samaroo (2015).

  15. An idea attributed to Reichenbach and Schlick, see Friedman (2001, pp. 76–79).

  16. See, e.g., Crowther (2016, §1); Rickles (2008a, §3).

  17. Although, as Crowther and Linnemann (2017) point out, QG need not be a fundamental theory, it would represent progress in this direction.

  18. For more detail see, Butterfield and Isham (1999, 2001), Rickles (2008a).

  19. See, e.g., Anderson (2012), Huggett et al. (2013), Rickles (2006a).

  20. See, e.g., Pitts (2014, 2017), Pons et al. (2010), Thbault (2012).

  21. I take some of these examples from (Rickles 2008a, §3.6.1), see also, Butterfield and Isham (2001).

  22. See Mathur (2009) for a technical review; and Belot et al. (1999), Wallace (2018) for introductions more accessible to philosophers.

  23. Almheiri et al. (2013).

  24. Thanks to a referee for pointing this out.

  25. However, physically relevant QFTs also contain non-observable fields, some of which are non-local.

  26. Highlighting the problems are, e.g., Belot and Earman (2001), Earman (2006), Pooley (2015) and Rickles (2006b, 2008b, 2012). Arguments for local observables are in, e.g., Bergmann and Komar (1960), Pitts (2014, 2017), Pons et al. (2010), Pons (2005) and Rovelli (1991, 2002).

  27. See, e.g., Huggett and Callender (2001), Mattingly (2005, 2006, 2009) and Wüthrich (2005).

  28. GR treated in the framework of QFT is apparently perturbatively non-renormalisable, breaking down at energies approaching the Planck scale, and so cannot represent a theory of QG, if QG is required to describe physics at this scale. The idea of asymptotic safety is that this apparent problem with GR treated as a QFT may be an artifact of the misapplication of perturbation theory, and that the theory is in fact non-perturbatively renormalisable. Reviews: Niedermaier and Reuter (2006), Percacci (2009).

  29. Actually, string theory is usually considered to possess an additional symmetry, conformal symmetry, making it a 2-dimensional conformal field theory.

  30. Friedman (e.g., 2001, Lecture II, and Chapter 4).

  31. Examples include the “prediction” of a minimal length in LQG (Rovelli 2004), and dimensional reduction in causal dynamical triangulations and HořavaLifshitz gravity, see Carlip (2017), ’t Hooft (1993).

  32. E.g., Rovelli (2004).

  33. For general reviews outlining the main approaches to QG, see Carlip (2001), Kiefer (2006), Rickles (2008a). It is also worthwhile to consult Butterfield and Isham (2001).

  34. The idea is essentially what Nickles (1973) calls “reduction2”.

  35. See, e.g., Hartmann (2002), Radder (1991), Post (1971).

  36. See, Bokulich (2014).

  37. See, Butterfield and Isham (1999, 2001), Wüthrich (2017).

  38. Causal set theory sees the desideratum of “being quantum” in the same way that string theory views the principle of “being background indpendent”, i.e., an ultimate aspiration, but one that need not be implemented at the initial stages.

  39. Perturbative renormalisability is insufficient to establish UV-completion, since a theory may be perturbatively renormalisable may still face a Landau Pole, as is the case in quantum electrodynamics.

  40. Butterfield and Bouatta (2015), Crowther and Linnemann (2017), Dvali et al. (2011), Zee (2010).

  41. Cf. Cao and Schweber (1993), Shankar (1999), Weinberg (1979, 1999).

  42. Cf. Crowther and Linnemann (2017).

  43. For Brans-Dicke gravity, see, Haba (2002) contra Deser and Nieuwenhuizen (1974) and ’t Hooft and Veltman (1974); for Hořava-Lifshitz gravity, see Orlando and Reffert (2009).

  44. For details on (i–iii) see Pooley (2017), and for (iv), see Belot (2011).

  45. Further details: Giulini (2007); Pitts (2006); Pooley (2017); Read (2016).

  46. Cf. Norton (2003), also Brown (2005, §5.3.1).

  47. See references in Fn. 45.

  48. However, given the above discussion, one might wonder whether the principle should be viewed as being so significant—a thought that gains further weight with the recognition that particle physicists in the 1930s–70s managed to derive Einstein’s equations of GR from entirely unrelated principles, including universal coupling and avoidance of ghosts (e.g., Desser 1970; Nieuwenhuizen 1973). (Thanks to a referee for offering this food for thought).

  49. The meaning of this is explored by, e.g., Butterfield (Forthcoming), Dawid (2017), de Haro (2017), Read and Møller-Nielsen (2018), Rickles (2011), Teh (2013).

  50. See, e.g., Polchinski (2017).

  51. Many philosophers have thus recommended caution in interpreting these results as physically meaningful, but cf. Wallace (2017a, b), which take a firmer stance.

  52. Some work has been done in investigating the area scaling law. Oppenheim (2003), for example, uses an analogue model of a black hole with long-range interactions and shows how the entropy goes from scaling with volume to scaling with area as the strength of the interactions increases. Chandran et al. (2016) recounts the applicability of the area law for entanglement entropy, showing under what conditions it scales differently.

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Acknowledgements

Thanks to Niels Linnemann, Ashton Green, Christian Wüthrich, James Read, and three anonymous reviewers for comments and suggestions.

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    Karen Crowther

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Crowther, K. Defining a crisis: the roles of principles in the search for a theory of quantum gravity. Synthese 198 (Suppl 14), 3489–3516 (2021). https://doi.org/10.1007/s11229-018-01970-4

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