Spacetime functionalism in GR
The first paper of the special issue by James Read and Tushar Menon provides constructive criticism of Knox’s version of spacetime fuctionalism. Read and Menon show how inertial structure and the operational meaning of spacetime can come apart in some models of GR and in some alternative classical spacetime theories. This divergence, they argue, is problematic for a programme motivated to closely track the operational significance of spacetime. They discuss various ways to modify or amend Knox’s inertial-frame functionalism in order to circumvent the problem. They end with a discussion of the relation between inertial-frame functionalism and the wider dynamical approach and argue that these are largely orthogonal.
Jim Weatherall’s contribution, a straight-on reckoning with two ‘dogmas’ behind the dynamical approach, is thus a welcome contribution to this special issue as it provides important clarification of widely held beliefs within the dynamical approach camp. Weatherall’s paper, which he presents “in reaction to and sympathy with” a recent paper by Read (2020b), identifies the two dogmas as the ideas that, first, the stipulation of spacetime geometry has no implications for the behaviour of matter, and, second, the postulation of what is known as the ‘strong equivalence principle’ is enough to have matter be ‘adapted’ to spacetime geometry. Weatherall questions both of these ideas, and irenically concludes that careful consideration of the details of the relationship between dynamics and geometry dissolves much of the often advertised disagreement between the geometrical and the dynamical approaches.
In his article, David Baker argues that Knox’s inertial-frame functionalism fails to capture the richness of our concept of spacetime and so lacks the generality one would expect from a spacetime functionalist framework. According to Baker, spacetime is a cluster concept: the criterion of playing the role of inertial structure can neither be necessary nor sufficient for calling it spacetime. Admittedly, Knox can easily bite the bullet that her or improved variants of her account will in the end just be valid for a certain sector of spacetime theories. Arguably more problematic, however, is Baker’s follow-up that fundamentality can and is often traded as a central aspect of the spacetime concept—perhaps even of more importance than inertial structure—but is not at all touched by Knox’s functionalism.
A different form of functionalism in GR concerns the status of the energy-momentum tensor in GR: should it perhaps be given a functionalist reading as well, as suggested by Lam (2011) or Read (2020a)? Patrick Dürr’s contribution pursues this question. For this, he appraises functionalist accounts of gravitational energies as opposed to, first and foremost, the eliminativist take on gravitational energy by Hoefer (2000); he arrives at the conclusion that the realist case for gravitational energy via a functionalist account will require substantive modification for it to prove fecund.
Spacetime functionalism in QG
In their contribution, Vincent Lam and Christian Wüthrich follow up on their earlier work having first applied spacetime functionalism to quantum gravity. The main aim of their paper is to distinguish their form of spacetime functionalism in motivation, scope, and implications from spacetime functionalism as it has been advocated in the context of quantum mechanics and GR. Lam and Wüthrich argue that their spacetime functionalism, unlike that in other areas, does not compete with alternative interpretations of the relevant theories. Rather, it articulates and explicates the tasks of physical theorizing in quantum gravity. As such, they conclude, it is perfectly compatible with a realist take on quantum gravity, and even with a realist understanding of GR.
On their part, Michael Esfeld and Niels Linnemann are critical of the extent to which radical claims of spacetime emergence in quantum gravity are ultimately justified. In his contribution, Esfeld likens the current stage of quantum gravity research to the historical development of quantum mechanics and quantum fields throughout which claims had been abundant that the theories necessarily implied the dismissal of local ‘beables’—concrete local things that we can straightforwardly take to be real—and thus the conception of spacetime in any form. Just as the (putative) problem of the non-fundamentality of spacetime in quantum mechanics has been circumvented by Bohmian mechanics, Esfeld believes that the ontological problem so heavily problematised by philosophers of quantum gravity might evaporate after sufficient interpretational work.
Baptiste Le Bihan differentiates the problem of empirical coherence through identifying an epistemological and an ontological component whose difficulties are respectively compared to that of the easy and the hard problem of consciousness. Le Bihan’s differentiation, however, continues: depending on which exact form of functionalism one adheres to, the hard problem is (dis)solved or not solved at all; only the easy problem is straightforwardly solved as suggested by Lam and Wüthrich (2018), or so Le Bihan argues.
Following largely Le Bihan in his distinction between the easy and the hard problem, Linnemann argues that the easy problem (the epistemological problem of empirical coherence) has been overstated by Huggett and Wüthrich (2013) from the start. Secondly, contra both Lam and Wüthrich (2018) and Le Bihan, he seeks to establish that current approaches to QG do not feature a conceptual gap problem worthy of the analogy to the hard problem of consciousness, and that, if they did, functionalism as such could not dissolve it. Linnemann’s analysis seconds Esfeld’s expectation that the conceptual problems of the emergence of spacetime will eventually evaporate by working out that none of the current approaches lacks a codification of diachronicity in its structure—which, as he argues, would be the only clear sign that there is no fundamental spacetime structure in QG in the first place.
While accepting the problem of spacetime emergence and its resolution via spacetime functionalism, Baron points out that the original issue regarding empirical coherence in fact also involves a problem concerning the emergence of ‘entity’, i.e., matter or physical stuff: it is not only important to learn how a notion of beable location arises out of putatively non-spatiotemporal structure but also how the notion of a beable itself emerges. According to Baron, the entity problem might, however, just as well be satisfactorily resolved in a functionalist fashion; at least in the context of a matter-enhanced version of loop quantum gravity (LQG), the matter model of quantum field theory (QFT) can plausibly be seen as functionally realised (namely—and just like in the case of spacetime—by LQG’s spin-network structure). In order to establish his point, Baron makes use of proposals in the LQG community on how the so-called helon model of particles may explain the emergence of entities with charge from modified versions of LQG’s fundamental spin-network structure.
In order to deal with the spacetime functionalism in QG, Rasmus Jaksland—like other contributors—refers to the philosophy of mind. He reads the multiple realisability of the Einstein field equation by different underlying theories postulating different microscopic degree of freedom as a strong case for spacetime functionalism, which is in direct analogy to the central argument in favour of functionalism about mental states. The three theories considered—all of which realise Einstein’s field equation—are Sakharov’s induced gravity (1967), Jacobson’s thermodynamic account of gravity (1995), and various forms of entanglement accounts of gravity. Given how naturally these approaches can account for GR, and thus how generic the emergence of Einstein’s field equation seems to be, however, the recovery of GR is at best a necessary, but definitely not a sufficient condition for the pursuit-worthiness of an approach to quantum gravity, let alone its correctness.
Finally, Thomas Saad’s contribution bridges the gap between space functionalism and philosophy of mind at the level of content rather than just the methodological level: in his essay, he adjudicates whether certain experiences of spatial properties are best accounted for in terms of specific experiential spatial properties (spatial presentationalism) or as functional roles instantiated by suitable spatial properties (spatial functionalism). Saad thus takes functionalism back to the mental. However, in the concrete context he considers, he does not see a clear case for it as being established: whereas the posit of specific experiential spatial properties may lead to the undesirable consequence of spatial properties (currently) not incorporated by physical theories, functionalism about these experiential spatial properties enforces an arguably unacceptable dualism on us—not a path many of us are probably ready to take.