Across several posts, I have outlined how a causal process theory can provide an attractive ontology for phenomena described by the natural sciences, from quantum physics to biology. An exception, mentioned in a recent post, is that I haven’t had much to say about the spacetime of general relativity (GR). This topic is complicated by the fact that GR and quantum physics are not reconciled. I expressed optimism about approaches to quantum gravity that incorporate causation in their foundation, and in particular I gave a shout-out to Causal Set Theory (CST).
A new paper, “Causal Theories of Spacetime”, by Sam Baron and Baptiste Le Bihan, explores the idea of formulating a causal theory of spacetime, specifically using CST as its basis. This was very welcome to me, since CST, developed by physicists, gets only occasional attention from philosophers.
The paper begins by discussing and pointing out the problems with an earlier form of causal theories of spacetime, which sought to identify spacetime structure with causal structure. For various reasons this type of “identity” theory is set aside (see section 2). The most important problem here is that space-like separated events have a spatio-temporal relation that cannot be readily identified with a causal one.
Next (section 3), the authors explore the idea that spacetime structure has a more indirect foundation in causality (a “non-identity” causal theory of spacetime). Here they use CST for a framework. Causal sets are, roughly, locally finite elements organized by a relation obeying partial order. A partial order relation provides an arrangement of precedence that can be viewed as minimally satisfying our notion of a causal structure. The promise of CST is that one can view it as a fine-grained underlying structure that maps appropriately onto features of a spacetime manifold that, in turn, is seen as its “zoomed-out” approximate counterpart. Things get even more interesting when this “kinematics” is supplemented by a “dynamics” that describes how set elements give birth to new ones, growing the causal network (I’ll return to this below). I’ll note here that while there are ongoing efforts to develop CST in a distinctively “quantum” direction, the initial ideas, and the only ones discussed here, are essentially classical.
The authors develop their non-identity causal theory of spacetime by looking at how relations in the causal set structure can be said to “ground” spatio-temporal relations. The connection between time-like separated events and underlying causal structure is fairly straightforward. But also, in contrast to the identity theory, we can say that spacelike relations between events can be “grounded” in the fact that while there is no (and cannot be any) causal connection, they still derive from the same total causal structure and the character of their relation is due to the details of their common ancestry in that structure. There are many more details in the discussion that look to make this more precise (section 4).
The authors go on to (in section 5.1) further develop the notion of grounding in terms of mereology – the spatio-temporal relations are seen having appropriate elements of the underlying causal structure as parts. This fleshes out the mapping relation described in CST.
In their section 5.2, the authors go on to talk about the interpretation of causation that is inherent in causal set structure in section 5.2. This is where I disagree with their approach.
The authors begin by first pointing out that (obviously) a causal notion used for present purposes cannot itself make any essential references to spacetime. They point out, for instance, that the causal process theories of Wesley Salmon and Phils Dowe assume a spacetime context. After also pointing out that David Lewis’ counterfactual approach to causation uses a similarity relationship between possible worlds that defines these as spatiotemporal, they assert that “It would thus appear that the usual approaches to causation are unavailable options for understanding causation in the context of the non-identity theory (p. 18)“. This is a bit quick of course. There are a lot of ideas about causation out there, and my preferred version of causal process theory, to be sure, does not place processes in spacetime (otherwise, it could not fit with quantum mechanics).
They decide the best tool for the job is James Woodward’s intervention/manipulation approach. I think this is a mistake. This approach can be applied only because the authors invoke added metaphysics which is not itself causal, and this misses the point if the goal is to describe how spacetime emerges from a causal foundation. Further, the way CST dynamics is described by its formulators suggests a very different concept of causation.
On the first point: interventionism offers ideas that underpin a method for investigating and modeling dependence relationships; it is not a theory of causation per se. The sort of relationships it describes are “difference-making” ones, where a special kind of counterfactual, describing a change in one variable, is determined to make a difference to another variable. As the authors note, since “intervention” is itself a causal notion, the approach makes no pretense toward describing or defining what causation “is.” Further, the approach makes essential use of counterfactuals, which are obviously not part of the actual world’s ontology.
The use of interventionist counterfactuals in the present context can be justified, according to the authors, if the arrangement of causal set elements has been endowed with a modal structure that would support an assessment of how things could have been different. Since the interventionist approach to causation cannot itself provide this, the authors use the fact that causal set structures can be thought of as subject to a governing law – specifically the law of sequential growth that describes CST dynamics. Given such a law, that describes the dependencies between elements, one can apply interventionist modeling to these law-governed relations.
Here’s my objection. The authors posit that this law, while unusual due to its non-spatiotemporal setting, can otherwise be thought of as a viable physical law. But note that one also needs to assume a realist (non-Humean) metaphysical interpretation of lawhood to provide the necessary modal structure. There is a long history of ideas about this, and all are controversial. But, in any case, the end result will still be an interpretation of “causal” set theory dynamics where causation plays no necessary fundamental role.
The authors anticipate criticism along these lines. But I think it can be sharpened by noting there is an alternative that is a better fit. To set the stage, I want to highlight the emphasis CST theorists place on causal set dynamics as a “growth” or “birthing” process. They also speculate that the ongoing “becoming” of new elements can provide a fundamental basis for the passage of time. These discussions invoke a notion of productive causation. Existing causal set elements literally produce new ones.
Causal process theories and mechanistic approaches to scientific explanation are examples of approaches that implicitly embody a version of productive causation (e.g., interactions between objects produce change). Other examples come from metaphysicians who construct theories of causation based on dispositions/causal powers: powers possessed by objects (or their combinations) produce change. Note these approaches do not rely on comparing counterfactual scenarios – causation is rooted only in actual structures. Along these lines, I think a modified causal process theory, removed from a spatio-temporal setting, can be formulated to “breathe fire” into the formalism of CST dynamics.
The way I would sketch it is as follows: Each causal element is endowed with dispositions (or “propensities”, given their probabilistic nature) toward producing a new one. These dispositions follow the mutual manifestation model: when a set has multiple members, the specific manifestation is a collective result of these inherent causal powers working together (these are “non-local” properties of the elements). The dispositional profile of the set is altered by a manifestation, setting the stage for the next one.
Developing an account along these lines will be philosophically contentious, but the advantage is that it provides a real causal ontology for a causal theory of spacetime.
Reference
Baron, S., & Le Bihan, B. (2023). Causal theories of spacetime.
Noûs, 1–23. https://doi.org/10.1111/nous.12449