I read an interesting and thought-provoking paper: “Causation and the conservation of energy in general relativity” by Sebastián Murgueitio Ramírez, James Read, and Andrés Páez (forthcoming in The BJPS[1]).
The paper is about the apparent problems the general theory of relativity (GR) presents for Phil Dowe’s conserved quantity theory of causation (CQTC). The authors examine the challenges more carefully and comprehensively than I have seen before, and they argue that they can be given a successful response. The authors leverage some recent work on GR models, and I think they make a good case (a caveat: I do not know most of the cited physics literature, so I’m not in a position to critique some of the details of the discussion). Below I give a brief summary of the paper and my thoughts about it. Following that, I add some further reflections about the philosophical status and value of the CQTC.
Dowe’s theory describes causal phenomena in term of entities called causal processes and their interactions (in this respect it was a successor to Wesley Salmon’s earlier mark-transmission causal process account). Causal processes are worldlines of objects that possess (instantiate) conserved quantities such as energy or momentum and causal interactions happen when processes intersect and exchange CQ’s. The problem is that while this picture fits intuitively with many familiar physical phenomena (picture a collision scenario described in the framework of classical mechanics), it runs into obstacles in the context of GR, where conservation laws are difficult to find. While there are other, more purely philosophical, objections to Dowe’s approach, this problem has been viewed as acute. This is because Dowe describes his theory as resulting from an “empirical” analysis of what worldly causation is: one that proceeds by examining our most successful scientific theories (see Dowe, 2000, Ch.1).
The authors look in turn at two ways GR poses a problem: those relating to the difficulty of defining global (integral) conservation laws and local (differential) conservation laws. Summarizing quickly: in the first case, global conservation laws can only be defined in certain special spacetime models that don’t reflect the character of actual spacetime; in the second case, proposed local conservation laws are seen as “pathological”: a proposed analogue to a conserved total energy cannot be defined in a coordinate-independent way, and it cannot be uniquely defined in any case (one can choose from an infinite number of possibilities).
The authors put these challenges into the form of an argument and then formulate responses. Note that given the way the argument is framed, it can be defeated if the CQTC works in at least some GR-based examples: it need not be applicable to all scenarios (in the final section, the authors give an example of a case which remains hard to analyze using the CQTC).
I won’t discuss the responses in too much detail (see sections 4 and 5 of the paper). But an important thrust of their strategy is to argue that the supposed unrealistic and/or even “pathological” assumptions that are necessary to justify conservation laws are not different in kind from the pragmatic steps actually taken by scientists when creating and using models to get useful results in the framework of GR.
When it comes to integral formulations, one can theorize that our spacetime contains fields that approximate the symmetries needed for conservation (“almost” Killing” fields can yield “almost” conserved quantities). Another avenue they explore is the notion, already employed by physicists, of an asymptotically flat spacetime. Even though this does not describe actual spacetime, it is an idealization used for models of relatively isolated sub-systems, and CQ’s can be defined in this context.
For local formulations, the authors focus on a widely discussed conservation law that derives a gravitational stress-energy pseudo-tensor that balances out the tensor associated with energy from matter fields. The problems here are that the notion cannot be interpreted in a coordinate-independent way, and also that there are mathematically an infinite number of such pseudo-tensors. But these are not viewed as deal-breakers when it comes to applying the idea pragmatically to analyze a particular system of interest. The authors also consider and reply to a number of objections relating to utilizing this kind of somewhat unusual CQ in Dowe’s theory; importantly they show that the exchange of such a quantity has featured in physicists’ analysis of interactions of massive objects.
In the concluding section, the authors also include a brief sketch of why finding an alternative causal theory in place of the CQTC would be difficult (in a GR context) if it is one that relies on counterfactuals.
I think the paper makes a good case, because the focus on actual modeling practices (including their many idealizations) fits with Dowe’s stated intentions of appealing to both scientific “methods” and “results” in formulating his account (Dowe, 2000, 7). GR may be a theory where modelers of specific systems face particularly difficult technical challenges to get practical results, but idealization is ubiquitous in physics (the notion of a perfectly isolated/closed system is of course itself an idealization), and if more coaxing is needed to define CQ’s in GR compared to other physical theories, this still does not amount to something different in kind. Given this, I concur that GR-based objections to the CQTC are not decisive.
—————————————————————————-
With this said, I do think that this discussion provokes further thoughts about the philosophical value of the CQTC.
Let me present my bottom-line view first. The conserved quantity theory of causation is actually not best thought of as a theory of causation. It is, instead, an approach to modeling causation in the context of physics. It differs from other kinds of models in that it foregrounds causation, where many or most physical models leave causal notions in the background. For example, I may model a collision problem in mechanics by estimating initial conditions, and making an assumption about elasticity. Then I calculate final conditions (either as a prediction, or just as part of a description of this system of interest). I might say nothing about causation. But if one is asked to explain the final conditions in terms of the initial conditions and Newton’s laws, then causation is likely to enter into the discussion (at least implicitly). The appeal to the notions of causal processes and their exchange of conserved quantities is an explicit way to formulate a causal explanation. And the fact that exchanges of conserved quantities do enter into our thinking in how interactions work across physical models makes the formulation a sensible and helpful one.
But this is an approach to causal modeling, and it stands along side other approaches in the sciences. Mechanistic causal models, in the context of biology in particular, are popular and have received much attention from philosophers of science. A more abstract approach that uses difference-making relations to model causation (such as those that use structural equations and directed graphs to depict systems) is very popular and can be applied across a variety of sciences. Note that all of these approaches employ idealization to get off the ground.
From the perspective of Dowe’s project, this conclusion is perhaps disappointing. Dowe himself did not emphasize modeling practices or idealization, and his goal is clearly to present a theory of what causation is. While he emphasizes the difference between his project and other kinds of philosophical investigations of causation (particularly conceptual analysis), and limits the goal to what is contingently the case in our world (rather than a matter of metaphysical necessity), it is still an ambitious project. But if idealized causal models inform us about the true nature of causation, they do so only indirectly and imperfectly. This is a similar situation we face when asking what science tells us about the ontology of objects or properties, or about the metaphysical character of laws.
So while it is good news is that we can perhaps say GR provides no reason to reject the CQTC, and the approach is coherent and useful, the bad news is that the idealized, model-based context is telling us that it should not be taken too literally as a theory of causation.
Finally, though, on a more positive note, viewing the CQTC as an indirect, imperfect representation of causation doesn’t mean it tells us nothing at all about the nature of causation. Its conceptual consistency and usefulness in the context of our most universal sciences may be seen as evidence for the existence of a metaphysical theory with some similar characteristics. And in fact, I think this is the case. But that is a story for another time.
[1] Update: a link to the published paper is here.
Reference
Ramírez, Sebastián Murgueitio , Read, James Alexander Mabyn, and Paez, Andres. 2023. Causation and the Conservation of Energy in General Relativity. The British Journal for the Philosophy of Science. https://doi.org/10.1086/727030