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Incubating a future metaphysics: quantum gravity

Abstract

In this paper, I will argue that metaphysicians ought to utilize quantum theories of gravity (QG) as incubators for a future metaphysics. I will argue why this ought to be done and will present cases studies from the history of science where physical theories have challenged both the dogmatic and speculative metaphysician. I provide two theories of QG and demonstrate the challenge they pose to certain aspects of our current metaphysics; in particular, how they challenge our understanding of the abstract–concrete distinction. I demonstrate how five different accounts of the distinction each fail to hold under the received interpretations of loop quantum gravity and string theory. The central goal of this paper is to encourage metaphysicians to look to physical theories, especially those involving cosmology such as string theory and loop quantum gravity, when doing metaphysics.

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Notes

  1. For ‘empirical adequacy’ see van Fraassen (1980). Alternative concepts might do equally well.

  2. One could always append to any theory a structure which happens to be empirically relevant only in regimes or energy scales beyond that which we can currently engage. This, of course, is nothing more than the infamous problem of underdetermination of theory by data.

  3. This concern applies to physical theories as well. Examples of this can be found in the more excited pronouncements from the string theory community. For why I say ‘essential’ see the following footnote.

  4. Any doctrine meeting the demands of (A) is not merely metaphysical but necessarily so. If \(\mathcal {D}\) is a pure metaphysical doctrine in the actual world, then its truth value is unaffected by which physical laws (\(\mathcal {L}\)) are true of the actual world. In other words, \(\mathcal {D}\) is consistent with any \(\mathcal {L}\). If this is so, then for all \(\mathcal {L}\) there exists some possible world (\(\mathcal {P}_{\mathcal {L}}\)) accessible to the actual world in which both \(\mathcal {L}\) and \(\mathcal {D}\) are true. I will prove that \(\mathcal {D}\) is necessarily metaphysical—in the sense of (A)—by showing that in each \(\mathcal {P}_{\mathcal {L}}\), \(\mathcal {D}\) is consistent with each \(\mathcal {L}^{*}\). If this were not so, then there is some \(\mathcal {L}^{*}\) such that \(\mathcal {P}_{\mathcal {L}^{*}}\) is inaccessible from \(\mathcal {P}_{\mathcal {L}}\). However, if the accessibility relations between possible worlds is both reflexive and transitive (i.e Euclidean), then this is false. In conclusion, if the modal access relations between possible worlds is at least symmetric and transitive, then were \(\mathcal {D}\) an item of pure metaphysics, \(\mathcal {D}\) would be so necessarily.

  5. Where, presumably, the sentence under consideration is not one of mathematics or otherwise known a priori; cf. the previous quote which comes later in his text.

  6. For instance, neither Aristotle nor Kant fall naturally into any of these categories.

  7. I have placed ‘true’ in scare quotes to signal that in the context of conceptual-webs, the proponent, presumably, endorses a deflated notion true: truth-qua-coherence.

  8. Aristotle’s cosmology was formed sometime in the third century BC but got its most developed early treatment in Ptolemy’s Algamest (100–170 AD). Ptolemy was not a strict Aristotelian and deviated from Aristotle’s crystalline-shell structure significantly.

  9. There are some outliers in this regard: Leucippus and Democritus fifth century B.C., Pythagoras and Herclides fourth, and notably, Aristarchus who, in the third century B.C., had a heliocentric model similar to Copernicus’ (Kuhn 1957/2003).

  10. This claim involves only the general dynamics of heavenly bodies such as the shape of the planetary orbits and does not include some particular features of these orbits such as their respective tilt or their orbital speeds. These latter features are physical hypothesis according to Aristotle to be discovered empirically.

  11. Muller and Saunders (2008), Huggett and Norton (2013), and Norton (2015b).

  12. Quantum mechanics threatens not merely the PII, but what we take to be the logical structure of reality. Given most standard interpretations of QM, i.e. not including hidden variable interpretations, not all statements of the form \(P\vee \lnot P\) are true. For instance, when a particle is in an eigen-state of momentum, the particle is described as somehow being located everywhere and yet nowhere. For such a particle, it is neither true of the particle that it is ‘here’ nor is it not true that it is ‘not here’. See Birkhoff and von Neumann (1936).

  13. Noting that non-Euclidean geometry was still to be discovered.

  14. Like most aspects of Kant scholarship what Kant means by the above statements is debated (Smith 2003, p. 117).

  15. To be clear, this example is intended only as an analogy. Taken literally it is not true that GR describes longitudinal lines as being straight. The example is meant to provide a picture for how more than one straight line can intersect the same pair of distinct points.

  16. Not to be confused with the presentist who holds additional commitments such as the passage of time.

  17. Or, in the case that the future is open, those which possibly belong to the future.

  18. In order for this to work, \(\alpha \) has to lie outside our past light cone. Such an event is in our past though, admittedly, not in our causal past.

  19. For a general account of the theory see Rovelli (2004).

  20. Presumably, in the new theory, we will have to update what we take momenta, force, and energy to be. Some of our old concepts will likely be revised and carried over, while other concepts might be abandoned altogether. It is also likely that novel physical concepts will play a role in the new theory which we did not need in the old.

  21. Huggett and Wüthrich (2013), Huggett (2015), Matsubara (2013), Rickles (2011), and Dawid (2007).

  22. Huggett and Wüthrich (2013) and Oriti (2014).

  23. Others have also discussed the relation between abstract and concrete objects and LQG (Lam and Esfeld 2013; Lam 2016; Norton 2015a).

  24. By ‘received’ I do not mean to suggest that the entire community explicitly endorses these interpretations. But rather, that the general thrust or spirit of the interpretations which are endorsed in the literature is in agreement with the interpretations presented as ‘received’.

  25. In fact, the actual world may contain such individuals. Those who suffer from synesthesia, arguably, sense mathematical objects. Interestingly, recent research has shown that the color sensation is not necessarily tied to concrete symbols (Gertner et al. 2013).

  26. There are uncountably many states of LQG and only countably many of these are weave-states.

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Acknowledgements

I would like to thank Max Kistler and Melissa Norton for their comments on earlier drafts of this paper as well as Courtney Fugate for his helpful guidance. I would also like to thank the participants of the New Trends in the Metaphysics of Science (2015) conference for their comments and conversation which inspired the form of this paper. Lastly, I would like to thank the anonymous referees (one tireless referee in particular) for providing very useful and thorough comments.

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Norton, J. Incubating a future metaphysics: quantum gravity. Synthese 197, 1961–1982 (2020). https://doi.org/10.1007/s11229-017-1473-1

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Keywords

  • Metaphysics
  • Philosophy of physics
  • String theory
  • Philosophy of science
  • Loop quantum gravity