String theory, loop quantum gravity and eternalism

Abstract

Eternalism, the view that what we regard locally as being located in the past, the present and the future equally exists, is the best ontological account of temporal existence in line with special and general relativity. However, special and general relativity are not fundamental theories and several research programs aim at finding a more fundamental theory of quantum gravity weaving together all we know from relativistic physics and quantum physics. Interestingly, some of these approaches assert that time is not fundamental. If time is not fundamental, what does it entail for eternalism and the standard debate over existence in time? First, I will argue that the non-fundamentality of time to be found in string theory entails standard eternalism. Second, I will argue that the non-fundamentality of time to be found in loop quantum gravity entails atemporal eternalism, namely a novel position in the spirit of standard eternalism.

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Notes

  1. 1.

    For references in the philosophical literature, see e.g. Huggett and Wüthrich (2013), Matsubara (2017), Lam and Wüthrich (2018), Le Bihan and Linnemann (2019), Baron (forthcoming) and Huggett and Wüthrich (forthcoming).

  2. 2.

    This theory of quantum gravity might turn out to be a final theory of everything but it certainly does not have to be so. Certain research programs in quantum gravity are very explicit they are not looking for a final theory but only, more modestly, for a unified account of quantum gravity.

  3. 3.

    This is a rough characterisation. Taking the general theory of relativity seriously implies defining eternalism without using the notions of past, present and future in the following way: all natural things exist independently of their location in the network of spatio-temporal or causal relations.

  4. 4.

    The expression “atemporal eternalism” is already used in the philosophy of religion and refers to the view that God exists beyond time (see e.g. Morris 1991). I will still use this expression as it describes well the content of the position; arguably, there is no risk to conflate the two views.

  5. 5.

    The interest of quantum gravity for metaphysics has been noted on several occasions; see e.g. Huggett and Wüthrich (2013), Muntean (2015) and Norton (2017).

  6. 6.

    Non-locality refers here to the property ascribed to physical systems in response to the violation of Bell inequalities.

  7. 7.

    This of course does not tell us yet what is the right metaphysical interpretation of non-locality. One might argue for instance that it entails priority monism (see Ismael and Schaffer 2016) or, alternatively, a form of coherentism as defended by Calosi and Morganti (forthcoming).

  8. 8.

    See e.g. Huggett (2017), Matsubara (2017, 3-4), Le Bihan and Read (2018) and Butterfield (forthcoming).

  9. 9.

    See Barbour (2001) and Butterfield (2002), Healey (2002), Baron et al. (2010), Le Bihan (2015b) for philosophical discussion.

  10. 10.

    The question of how quantum gravity relates to existence in time is not new. Monton (2006) acknowledging that presentism is inconsistent with special relativity argued that presentism could in principle be recovered from a theory of quantum gravity; a claim that was criticized by Wüthrich (2010). The evidence that Wüthrich is right against Monton is compelling. My goal in this paper is, starting from there, to discuss eternalism and how it fits with the non-fundamentality of time.

  11. 11.

    I am aware that the way I introduce the distinction between these views will sound problematic for many. On the one hand, philosophers of physics may complain that it does not take into account what we learn from General Relativity, in particular that we should avoid any reference to past, present or future entities, using instead the notions of anteriority and posteriority in a reference frame to define eternalism. On the other hand, metaphysicians might argue that we may approach the problem differently, for instance by avoiding reference to existence simpliciter. See e.g. Crisp (2004) and Deasy (2017) for discussion. However, the old-fashioned classification I use is helpful to introduce, as a first go, how we think intuitively of those views.

  12. 12.

    A few philosophers of physics such as Dorato (2006) have argued or expressed the view that the whole debate lacks substance. Following Wüthrich (2012a), I will assume within the scope of this paper that temporal existence is an important and meaningful matter worth investigating.

  13. 13.

    But see Le Bihan (2015a) and Le Bihan (2019) for a defense of the claim that eternalism is consistent with an open future.

  14. 14.

    Another radical option is to replace GR by another theory empirically equivalent to its relevant sector—the set of solutions that could describe the actual world—and that would rely on a different ontology. This is the program behind shape dynamics (see e.g. Gomes et al.2011).

  15. 15.

    For the technically-minded philosopher: I begin by sketching perturbative superstring theory—I will then comment on what might be expected, ontologically speaking, from a non-perturbative M-theory.

  16. 16.

    The ontology of ST sometimes also includes branes which are n-dimensional entities extended through time, giving rise to n+ 1-dimensional geometries. In this two-dimensional field approach, branes are not among the mereological building blocks of the world.

  17. 17.

    Also, one may ask whether the picture actually makes sense in case strings are not interacting, leading seemingly to various disconnected internal spacetimes. This has been pointed out by Keizo Matsubara according to Baker (2016, 10). This is an interesting issue for the two-dimensional approach but not necessarily an unpalatable one. Indeed, it may well be that the actual world is made of causally disconnected islands (see e.g. Bricker2001).

  18. 18.

    There do exist other ontological interpretations of duality (see e.g. Le Bihan and Read 2018). But what matters for our purpose is that, as Huggett (2017) argues, all interpretations start with the claim that we have no reason to identify GR spacetime with one dual background structure alone, barring the road to identifying GR spacetime with any background structure.

  19. 19.

    More technically: “the action is invariant under arbitrary local rescaling of the string metric” Huggett et al. (2013, 254).

  20. 20.

    It could be objected that a non-perturbative string theory might change the fact that the two-dimensional field approach is a natural ontology for ST. It might indeed. However, first we do not have such a theory at the moment, and second M-theory might still be consistent with the two-dimensional ontology, which, after all, is supposed to approximate M-theory. For those two reasons it is worth investigating the ontological consequences of this view.

  21. 21.

    See Norton (2015).

  22. 22.

    Disordered locality remains speculative for two reasons. First, disordered locality has been shown to apply to space, in some models. One should expect disordered locality to apply also to timelike separated events, but this is a conjecture. Second, since we do not have any fully worked out theory of LQG, we cannot exclude that disordered locality in general might be linked to a mathematical artifact with no physical content.

  23. 23.

    For any four-dimensional volume in spacetime, the temporal dimension differs from the three spatial dimensions with respect to several features. To give a simple example, GR is locally special relativistic in the sense that one can always pick a local coordinate system such that at its origin: (1) the metric takes the form of the Minkowskian metric, and (2) the dynamical matter equations remain invariant under Lorentz transformations. This in turns also means that the SR-distinction between space and time is inherited at least locally. But note that our actual world distinguishes space and time in various, and seemingly logically independent, ways: Callender names this feature the “fragmentation of time” (Callender 2017, chap. 6).

  24. 24.

    One might argue that this expression of “surroundings” does not make sense in this context. But if so, then it strengthens the fact that we are not dealing with standard eternalism here. Furthermore, whether this expression does or does not make sense here depends on whether the fundamental LQG structure should be identified to a quasi-space or not. If it is a quasi-space, then it should in principle be possible for this structure to have enough geometrical features to use meaningful quasi-spatial predicates modeled on spatial predicates.

  25. 25.

    The perhaps most famous approach to quantum gravity that, it has been claimed, is consistent with—or even suggests—a growing block interpretation is the causal set theory (see e.g. Rideout and Sorkin 1999, Dowker 2006, Dowker 2014, and Earman 2008, Huggett 2014, Wüthrich 2012b, Wüthrich and Callender 2016, Callender 2017, section 5 for a philosophical discussion). Although, I cannot go fully into detail here, I simply want to point out that in this approach the growth is only local. As Callender (2017, 100) puts it: “[the] ‘birthing’ process is said to unfold in a ‘generally covariant’ manner”. There is no unique way to group together different causal sets that are not causally connected and to take a stance on which of them do exist as of the perspective of a particular causal set. It simply is impossible to quantify over what exists in other causal sequences as from the perspective of a particular causal set in this picture. Therefore, this growing view is not the classical growing block package including the no-futurist component. This view could more adequately be described as a “growing octopus view” since one might think (metaphorically) of all the various causally disconnected growths as octopus’ tentacles extending independently. (Note that the metaphor is not completely accurate since the tentacles should split again and again into novel tentacles.)

  26. 26.

    Wüthrich goes as far as defending that closed timelike curves might be excluded at the fundamental level while nonetheless obtaining at the derivative level (Wüthrich forthcoming).

  27. 27.

    Explaining emergence in terms of reduction might come as a surprise for the reader mainly trained in philosophy of mind or philosophy of emergence since emergence is often defined negatively as an impossibility to reduce a terminological framework to another one. But note that in physics and philosophy of physics, it is common to regard emergence and reduction as consistent tenets since emergence is a broader term (see e.g. Butterfield2011).

  28. 28.

    Braddon-Mitchell and Miller (2019) recently claimed that only the eliminativist interpretation of time emergence is worthy of philosophical discussion. They write:

    Let us distinguish between what we call weakly timeless theories and strongly timeless theories. Weakly timeless theories are theories in which although there is no time at a fundamental level, time, or something very time-like, emerges at a macro level. [...] In what follows we shall not be interested in weakly timeless theories, since although it is an interesting discovery that time is emergent, rather than fundamental, no particular philosophical problems arise from such theories, and it is not really clear that calling these theories timeless is appropriate. (Braddon-Mitchell and Miller 2019, 1808)

    Their claim is puzzling. They merely consider the possible emergence of time within a particular physical theory and do not consider the emergence of a temporal physical theory from a distinct physical timeless theory. Explaining how such an emergence is possible constitutes a highly interesting philosophical issue.

  29. 29.

    For the ease of presentation, in what follows, I will use the expression “fundamental ontology” and refer to entities being more fundamental than other entities, assuming that the word “fundamental” should be interpreted differently depending on whether we are operating under the assumption of the derivative view (then we have a notion of fundamentality which is not identical with mereological composition) or time reductionism (then the more-fundamental-than relation is just logical parthood).

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Acknowledgments

For helpful comments on an earlier draft of this essay, I would like to thank Jiri Benovsky, Annabel Colas, Alberto Corti, Claudio Calosi, Fabrice Correia, Tiziano Ferrando, Vincent Grandjean, Rasmus Jaksland, Niels Linnemann, Cristian Mariani, Keizo Matsubara, Robert Michel and two anonymous reviewers. Special thanks to Nick Huggett and Christian Wüthrich for their invaluable feedback. This work was supported by the Swiss National Science Foundation.

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Le Bihan, B. String theory, loop quantum gravity and eternalism. Euro Jnl Phil Sci 10, 17 (2020). https://doi.org/10.1007/s13194-020-0275-3

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Keywords

  • Eternalism
  • Quantum gravity
  • String theory
  • Loop quantum gravity
  • Fundamentality
  • Emergence
  • Time