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Loop Quantum Gravity: A New Threat to Humeanism? Part I: The Problem of Spacetime

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Abstract

In this paper, I discuss whether the results of loop quantum gravity (LQG) constitute a fatal blow to Humeanism. There is at least a prima facie reason for believing so: while Humeanism regards spatiotemporal relations as fundamental, LQG describes the fundamental layer of our reality in terms of spin networks, which are not in spacetime. However, the question should be tackled more carefully. After explaining the importance of the debate on the tenability of Humeanism in light of LQG, and having presented the Humean doctrine, I review two cases which present serious threats to Humeanism, one concerning the fundamentality of vectorial quantities and the other concerning quantum entanglement. In particular, I recall the strategies that are usually employed in these two cases in order to save Humeanism: in the first case, the strategy consists in amending the characterization of the Humean mosaic; in the second case, it consists in adopting a realist or nomological interpretation of the wave function. These solutions will turn out to be helpful in my discussion of LQG where, after describing LQG, I show that Humeans might save their doctrine either by endorsing a realist interpretation of spin networks, or by giving them a nomological status and, at the same time, by revisiting the characterization of the Humean mosaic. However, I conclude that both solutions are wanting.

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Notes

  1. See [13, 21, 56, 57].

  2. For a discussion on the connection between the two fundamental roles of spatiotemporal relations, in the Humean mosaic and in Lewis’ metaphysics of modality [31] respectively, see [12].

  3. Moving the debate in this direction is, for example, suggested by Shamik Dasgupta in his talk in Chicago. Access online: https://www.youtube.com/watch?v=gwyKWIJ0Y1c.

  4. These points can be either spacetime points or point-like objects related by spatiotemporal relations.

  5. See [6], for the view that ‘local’ properties can or cannot be ‘intrinsic’. For the opposite view, which classifies intrinsic properties as ‘local properties’, see [38].

  6. For a detailed presentation of the Humean account of lawhood see [10, 36].

  7. The official definitions of simplicity and strength are normally kept vague since their more precise characterization is supplied contextually in specific cases. See [60].

  8. For a more complete exposition, see [39].

  9. The configuration space is actually a state-space—the mathematical space where all the possible states of a quantum system exist—and not a metric space, since there is no relation of distance properly defined.

  10. The primitive ontology approach originated in the work of [14] and [23], and was later on developed in [2, 3, 17, 18].

  11. For a distinction between informationally complete representation of the system and ontologically complete representation of the system, see [40].

  12. Ashtekar variables are meant to replace the spacetime metric. For a clear explanation of why they were introduced, see [48].

  13. For a careful explanation of loop quantum gravity, see [11, 22, 48,49,50,51,52].

  14. See [44, 51,52,53] for more details and exhaustive explanation.

  15. I am proposing the same example as in [22].

  16. For a more exhaustive and technical explanation see [51,52,53].

  17. I take this opportunity to address a potential flaw to which I was alerted by Christian Wüthrich and David Wallace, namely that comparing the wave function with a spin network is methodologically misleading, if not wrong. Indeed, whilst in the case of quantum mechanics we are considering the wave function, which is itself the quantum state, in LQG the spin networks constitute a particular basis of the quantum gravity state, as the loop quantum state is the linear superposition of spin networks’ states. However, this concern would be warranted only if I had argued for an analogy between quantum wave function and spin networks, but I have not. By drawing the parallel between debates on the ontological status of the wave function in Bohmian mechanics and the debate on spin networks, it was my intention neither to presuppose any analogy between the two elements, nor to put them on an equal footing. Rather, what I suggest is that, in both cases, Humeanism can be saved by regarding a mathematical element of the theory either as a physical or a nomological entity.

  18. We are still at a kinematical level, which means that dynamics has not yet entered the theory.

  19. Using ‘space’ instead of spacetime should be more correct, since we are still at a kinematical level (the state is described at a frozen time). However, here and later I speak loosely of ‘spacetime’ in agreement with how the realist interpretation is spelled out in [44] under the name of ‘naïve interpretation’ (see below). It is just assumed that there will be a way of describing the dynamics of the system in terms of spin networks.

  20. An important point to remember is that since we are still at the kinematical level of the theory, and not at the dynamical one, these laws do not describe the temporal evolution of the system, rather they describe the physical state of the system at a frozen time.

  21. The s-knots are objective in so far as they describe reality in the best and most objective way; indeed they are diffeomorphism invariant.

  22. I owe this paragraph to an anonymous referee, whom I would like to thank not only for raising this issue but also for helpful suggestions.

  23. For an outline of the primitive approach, refer to the previous discussion on the Bohmian wave-function (Sect. 3.2.2.).

  24. See this quotation: “Finally, a warning: the quanta of space of loop quantum gravity should not be taken too naively as actual entities […]. Trying to think too literarily in terms of concrete “chunks” […] can be misleading” [53, p. 141].

  25. I also owe this paragraph to an anonymous referee of this journal.

  26. More precisely, spacetime is derived from a series of configurations of atoms of spaces and two laws, namely the Wheeler-De Witt equation and a Bohmian LQG guiding equation. For details of this proposal, refer to [55].

  27. The same strategy is applied to general relativity. Refer to [56] for details.

  28. The supervenience relation is not on any given configuration of atoms of space but on the entire history of the primitive ontology. LQG being an incomplete theory, it is unclear how to account for the dynamics of the primitive ontology.

  29. For a proposal on how Bohmian LQG specified these relations—which in this theory are called ‘contiguity’ or ‘companionship’ relations—refer to [55].

  30. Recall the ‘points’ here mean either spacetime points or point-like objects.

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Acknowledgements

I am grateful to audiences at the Geneva Centre for Philosophy of Science and the UK-European Foundations of Physics Conference in Utrecht for their insightful questions and helpful feedback on the topic of this paper. I also would like to thank an anonymous referee, Joan Bertran-San Millán, Ladislav Kvasz, Aldo Filomeno, Elías Fuentes Guillén and Niels Linnemann for reading and commenting on earlier drafts of this paper, as well as another anonymous referee and Casey McCoy for their useful suggestions in the revision process. Finally, I acknowledge that this paper has greatly benefited from a research stay at the Geneva Centre for Philosophy of Science. Funding for this work was generously provided by the Formal Epistemology—the Future Synthesis grant from the Institute of Philosophy of the Czech Academy of Sciences under the Praemium Academicum programme.

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    Vera Matarese

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Matarese, V. Loop Quantum Gravity: A New Threat to Humeanism? Part I: The Problem of Spacetime. Found Phys 49, 232–259 (2019). https://doi.org/10.1007/s10701-019-00242-6

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