Abstract
In prior work, we have argued that spacetime functionalism provides tools for clarifying the conceptual difficulties specifically linked to the emergence of spacetime in certain approaches to quantum gravity. We argue in this article that spacetime functionalism in quantum gravity is radically different from other functionalist approaches that have been suggested in quantum mechanics and general relativity: in contrast to these latter cases, it does not compete with purely interpretative alternatives, but is rather intertwined with the physical theorizing itself at the level of quantum gravity. Spacetime functionalism allows one to articulate a coherent realist perspective in the context of quantum gravity, and to relate it to a straightforward realist understanding of general relativity.
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Notes
If one wishes to pursue the issue of ‘spacetime qualia’, similarly to the context of philosophy of mind (where it is sometimes called the ‘hard problem’), then various further standard specifications of functionalism can be invoked in order to solve the issue (see Le Bihan forthcoming). However, we are doubtful that the issue is a genuine one in the spacetime context in the first place, as we have argued in Lam and Wüthrich (2018).
Although we follow common parlance in quantum gravity to speak of spacetime ‘emergence’, it should be noted that although the higher-level entity—spacetime—displays qualitatively novel features, the situation is consistent with a broadly reductive relationship between the fundamental theories of quantum gravity and general relativity. Thus, we accept, as is common in physics and in philosophy of physics, that emergence and reduction are not mutually exclusive. In this sense, the emergence at stake is ‘weak’ rather than ‘strong’ in the distinction popular in philosophy.
Presumably, time in some form or other is also in the wave function monist’s ontology.
We are not aware of being so charged in published work, only in discussions.
At least as things currently stand—see the discussion at the end of Sect. 5.
See Albert (2015, ch. 5–6) and the papers in Ney and Albert (2013). The label ‘wave function realism’ is also frequently used in the literature, but ‘wave function monism’ more specifically underlines the fact that the quantum ontology is only about the wave function on configuration space and nothing else (a single material point in configuration space, the so-called ‘marvelous point’, can be added within the framework of BM, see Albert 2015, ch. 6).
The differences between the contexts of the ontology of QM and the emergence of spacetime in QG—in particular regarding time—have been discussed in Lam and Wüthrich (2018).
See Maudlin (2019).
But sometimes the situation is rather straightforward, as exemplified in the case of wave function monism.
This attitude is nicely captured by Callender (2011, p. 48): “In slogan form, my claim is that metaphysics is best when informed by good science, and science is best when informed by good metaphysics.” How exactly science and metaphysics should engage with one another is of course a difficult issue that goes beyond the scope of this paper.
This does not exclude the fact that GRW, BM and MW—while all accounting for the empirical success of the QM predictive algorithm—can themselves lead to certain different predictions in principle.
The case for the dynamical approach is more convincing for SR than for GR; at best, it seems to collapse into the geometric approach in the context of GR (Read forthcoming).
For more on this distinction as it pertains to spacetime functionalism, see Yates (forthcoming) and Le Bihan (forthcoming).
Knox comments on this tension in her recent Knox (2019).
Of course, as a referee has pressed upon us, the relationalist can circumvent this difficulty by denying that vacuum spacetimes are genuine possible worlds or by claiming that a thoroughgoing empiricist stance makes them uninterested in such worlds. But this response will not carry very far, for two reasons. First, vacuum spacetimes are among the most important spacetimes in GR, scientifically speaking. In fact, many—perhaps most—spacetimes physicists are working on are vacuum spacetimes. If a view on spacetime cannot deal with these exemplar cases, then it can at least not be a candidate for interpreting GR as it is practised by physicists. Second, the fact that there exist gravitational degrees of freedom and that geometry does not supervene on the universe’s matter content and its dynamics is completely general and does not depend on the absence of matter. It is just that this fact can be most vividly appreciated in vacuum spacetimes.
In this sense, the standard geometric interpretation of GR is an interpretation of GR, and there is of course no reason to think that its tenets continue to hold when GR is violated or transcended, i.e., in theories beyond GR.
A referee suggested that at least intuitively, spacetime functionalism in QM and GR is intra-theoretical, taking a stance on what it is that should be called ‘spacetime’, whereas spacetime functionalism in QG is inter-theoretical, concerned with what recovers spacetime and how. Although intuitive, we do not think that this difference is ultimately tenable: in QM and in GR, spacetime functionalism is as much concerned with a reconstruction project of some antecedently characterized ‘spacetime’ from a more minimal structure. This is why we believe that the cases come apart because this reconstruction project is optional in QM and GR, but (presuppositionally, as we admit in Sect. 4) mandatory in QG.
See Huggett and Wüthrich (2013), Huggett et al. (2013), or Huggett and Wüthrich (forthcoming) in the philosophical literature, and Oriti (forthcoming), Rovelli (2011), Rovelli (2004, especially §10.1.3), and Witten (1996) as examples of statements by physicists. We should also note that there has been recent dissent in the philosophical literature by Linnemann and Le Bihan (2019).
There is a strong case to be made for the emergence of spacetime in the context of string theory as well, as is argued by Huggett (2017).
We insist that the illegitimacy here flows directly from our proclaimed naturalism and so is to be understood from the point of view of the considered QG approaches that point to the disappearance of spacetime, for various reasons partly related to the focus on certain physical principles (see Crowther forthcoming for the important roles of principles in QG). It does not imply in any way that alternative QG approaches that retain spacetime in one way or another are illegitimate at this stage.
This crucial point is overlooked in Esfeld (forthcoming).
Indeed, discussing ontological implications of scientific theories may actually lead to a critical attitude towards scientific realism itself (as a good example, see the role of metaphysical underdetermination in QM in van Fraassen 1991).
We remain explicitly uncommitted between realizer and role versions of spacetime functionalism.
In this case, Yates claims that the problem of empirical coherence is not solved. We would insist, however, that it is resolved, as it does not really arise in the first place.
Of course, as we have discussed in Sect. 4, this is also true for the transition from QM to QG, in particular regarding the metaphysical assumption of local beables.
This was also the central difference to the case of wave function monism in QM, where viable interpretative alternatives are readily available—something which is currently not the case in QG approaches without spacetime.
We thank a referee for giving us the opportunity to clarify the dialectical situation as we see it.
However, one could imagine a case where the issue remains underdetermined, that is, a hypothetical QG theory that can be interpreted either in a spatiotemporal or in a ‘spacetime-less’ way.
Of course, spacetime functionalism is not strictly speaking entailed by QG approaches without spacetime and the need to account for the manifest appearance of spatio-temporal features of our world. But spacetime functionalism is a convincing way of reconciling the two and of addressing serious conceptual worries that can be raised this context, as we have extensively argued in our earlier paper (Lam and Wüthrich 2018).
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We wish to thank our audience in Lisbon. We acknowledge support from the Swiss National Science Foundation (Grants 105212_169313 and PP00P1_170460). VL also acknowledges the Agence Nationale de la Recherche under the programme ‘Investissements d’avenir’ (ANR-15-IDEX-02) for partial support. CW also acknowledges partial support from the John Templeton Foundation (Grant 61387). We are grateful to Alberto Corti and David Yates for discussions and comments on earlier drafts. We also thank two referees of this journal for their useful comments.
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Lam, V., Wüthrich, C. Spacetime functionalism from a realist perspective. Synthese 199 (Suppl 2), 335–353 (2021). https://doi.org/10.1007/s11229-020-02642-y
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DOI: https://doi.org/10.1007/s11229-020-02642-y