Indeterminism in General Relativity

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One of the perennial philosophical questions is whether our world is deterministic. If we believe that physical theories tell us what the world is really like, we may just as well ask if these theories are deterministic. It would be desirable if determinism was a feature of the theory's formalism - we could just look at it and settle the issue right away. But this is not so: determinism is a feature of what the theory describes, and so we need to know what exactly the theory says about our physical reality, i.e. we need to have our theories interpreted.In the case of general relativity (GR), it seems at first sight that we have a good grip on what the theory says about the world (at least much better than in the case of quantum theories). Nevertheless, the question of GR's determinism is not yet settled. On the one hand, there are general issues with the notion of determinism in spacetime theories. First, how to find a plausible definition of determinism (Butterfield 1989, Earman 1986, Melia 1999), which both (i) does justice to clearly (in)deterministic toy examples (Melia 1999, Cudek 2023a), and (ii) is sufficiently independent of our metaphysical commitments (see Earman and Norton 1987). Second, how to understand the relation between the theory's models and the possible situations these models represent: for conflicting views on this, see Weatherall 2018, Fletcher 2020 and Belot 2018. This, in turn, is closely related to the vast topic of symmetry and structure (Dewar 2022 is a recent overview). These two issues will preoccupy the first two chapters of my thesis. On the other hand, there are issues specific to GR, which seem to pose a threat to any plausible account of determinism. First, there are well-known examples such as spacetimes with closed time-like curves or naked singularities (for more examples, see Earman 1995 and Doboszewski 2019).But the question of whether these anomalies are genuinely physically possible, and thus a threat to determinism, remains open (Earman 1995, Manchak 2011). Second, a significant strand of contemporary cutting-edge research in GR investigates formal prerequisites for a certain appealing formal criterion for determinism (namely, inextendibility of maximal future Cauchy development of given initial data). Recent results seem to suggest that, quite surprisingly, the value of the cosmological constant plays a significant role in establishing this criterion (see Dafermos and Luk 2017 and Kehle 2022). The third and fourth chapters of my thesis will discuss the philosophical significance of these results.In my doctoral project, I shall seek to gather these loose threads together, and investigate the possibility of a unified account of determinism in the context of GR. The sections on definitions of determinism, the relationship between determinism and modal metaphysics, and the representation of possibilities by models, will expand on my previous work (Cudek 2023a, 2023b). The conclusion of this project should be relevant not only to philosophy of physics and our general understanding of relativity theory, but also to metaphysics, epistemology, and general philosophy of science.My intended method for addressing the research questions set out above combines: (a) expertise in the philosophical literature covering the issues of: determinism in physical theories (with an emphasis on spacetime theories), modality in physics, and the relationship between the formalism and the interpretation of a theory, with (b) technical proficiency in graduate-level GR, and familiarity with contemporary research in mathematics of GR. Thus, my research method will involve both standard philosophical methodology of reading and reviewing papers, attending discussion groups and seminars, as well as covering any relevant technical material by auditing graduate classes in mathematics or physics departments, or through self-study.