The Gravitational Field as Cause
[This post is taken from an early draft of Christopher G. Weaver’s paper entitled “Against Causal Reductionism” now entitled “Fundamental Causation”]
Channeling, to some degree, Bertrand Russell (1912-1913), Jonathan Schaffer (2008) insisted that there is no room for causation in proper scientific practice. Science only requires natural laws and unfolding history (one physical event after the other). He remarked:
…causation disappears from sophisticated physics. What one finds instead are differential equations (mathematical formulae expressing laws of temporal evolution). These equations make no mention of causation.30 Of course, scientists may continue to speak in causal terms when popularizing their results, but the results themselves—the serious business of science—are generated independently.
Considerations such as those in the quoted pericope above quite naturally breed an argument for causal reductionism, the view that obtaining causal relations are not a part of the world’s fundamental structure, and that as a consequence causal facts reduce to (are nothing above and beyond) a species of non-causal facts. For Schaffer would add that if sound scientific practice can proceed without causation, making use instead of natural nomicity and history solely, then causal reductionism is true. Thus, causal reductionism is true.
I find Schaffer’s justification for the claim that praise worthy scientific practice does without causation to be problematic. I would argue that with respect to extremely empirically successful theories arrived at on the basis of sound scientific practice, the notion of causation shows up primitively and indispensably in the respective interpretations of the underlying formalism of those theories. In the present post, I have space only to explore one such scientific scientific theory, viz., the general theory of relativity (GTR).
In GTR, the principle of equivalence (PE) implies that inertial mass just is gravitational mass. What is more, the effects of gravity fade away in coordinizations (or systems of coordinates) that are locally inertial inside some gravitational field, given PE. The evolutions of systems not appearing in gravitational fields are described by the same equations which depict the evolutions of said systems in gravitational fields, provided that the equations are generally covariant (no privileged coordinate system or local Lorentz frame). All of the above indicates that the laws of GTR reduce to those of STR given a flat metric, and that the effects of gravity are not sensed by observers experiencing free fall. We also know from Einstein’s (PE) that gravitation is strongly related to the curvature of spacetime. Einstein’s equation details the relationship, though it says a bit more since it also describes the relationship between the stress-energy tensor (Tab) and the Riemann curvature (R) of space. Famously, the equation also “…relates the spacetime geometry to…matter distribution.”
The gravitational field represented by the Lorentzian metric (gab),
“…interacts with every other one and thus determines the relative motion of the individual components of every object we want to use as rod or clock. Because of that, it admits a metrical interpretation.”
I believe that the best interpretation of Einstein’s equation indicates that the gravitational field causally influences both photons and massive bodies (the causal language was already explicit in the excerpt from Rovelli above). In fact, the Lorentzian metric of Einstein’s equation is commonly interpreted as the field which causally influences objects constraining their movement, determining their relative motions, and even coupling with and influencing all other fields. Moreover, its behavior is quite different from the behavior of other fields since (quoting Hawking) “…it shapes the arena in which it acts”. This gravitational field has also been described as a “causal field” by philosophers of science. Furthermore, gravitation, say the physicists, is that “which affects every particle in the same way.” And this understanding of spatial curvature or gravitation as causally interacting and influencing “matter in relativity, via Einstein’s equation, is regarded as fundamental by itself.” My understanding of the matter is completely consonant with Einstein’s own interpretation of his work, as Pooley commented:
The idea that affine structure plays a quasi-causal role in explaining the motions of bodies figures significantly in Einstein’s criticism of Newtonian mechanics and SR and in his subsequent understanding of GR.
…the fact that it [Newtonian absolute space] acted without being acted upon was held up as problematic [by Einstein]; a ‘defect’ not shared by the spacetimes of GR (Einstein, 1922, 61-62).
So I believe GTR gives us a good reason for believing that causation shows up in correct interpretations of the mathematical formalism of highly successful physical theories.
No doubt the causal reductionist will question my interpretation of the formalism. She will ask, “is it not true that the presence of massive bodies interacts (perhaps causally) with the self-same field?” Is not the famous dictum of John A. Wheeler the claim that “spacetime tells matter how to move; matter tells spacetime how to curve”? Does this not suggest that if there are real obtaining causal relations involved, then the gravitational field causes a material body to behave x-ly, while the material body’s behaving x-ly causes the field to behave y-ly? Does this not breed a circle? Should we not prohibit such causal circles?
I do not find these questions to be very troubling. The gravitational field is present even in the absence of all material bodies, as Harvey Brown noted,
Once it is recognized that gmn is an autonomous field (or fields) in its own right, nothing in Mach’s philosophy implies that its dynamical behaviour or very existence, must be determined by the presence of (other kinds of) matter.
Again, the gravitational field does not owe its very existence to the presence of material bodies (sorry relationalists). Spacetime curvature and geometric structure is prior. I confess to such priority because it’s the very existence of the gravitational field which causally influences the behavior of fields and fundamental particles both massive and massless. I therefore avoid a causal circle since what material bodies influence is the inertial structure of spacetime, not its existence. Oliver Pooley made this clear, the “[i]nertial structure, as encoded in gab, is influenced but not determined by the matter content of spacetime.” So the existence of the gravitational field causally influences particles and fields by constraining their trajectories, and determining their relative motions while the presence of material bodies influences the inertial structure of spacetime.
Carl Hoefer (2009, pp. 703-704) has argued that if GTR implied that there are certain obtaining causal relations, or if it’s best interpretation requires the use of causal notions, the reductionist should not be worried, for GTR is not itself a fundamental physical theory. GTR’s picture of the world is not the quantum mechanical picture of the world, and the thought is that GTR will have to yield to QM in ways that would rub out any attempt to understand the causal activity of the gravitational field as fundamental physical activity. But I could very well argue that in string theory the graviton plays a causal role. I could also argue that in the context of certain string theories, the interactions of branes are best interpreted as causal interaction involving the exertion of causal influence on one another in a way that is not exactly circular or symmetric. Unfortunately, space constraints prohibit me from trotting out such interpretations, but I do believe there remains a promising response to Hoefer’s worry that can be expressed in a sound bite (not really). Look back to my characterization of Schaffer’s argument for causal reductionism. Notice that one of the premises of the argument states that sound scientific practice implies causal reductionism. That premise does not say that such practice must be peculiar to fundamental physical investigation solely. Obviously, sound scientific practice is what physicists leaned on when developing GTR. And GTR is of course an extremely successful physical theory, and that is precisely why any quantum theory of gravity must recover its predictive success. Thus, Hoefer’s complaint should not worry the anti-reductionist about causation.
Causal reductionists will no doubt judge my appeal to GTR to be cheap and shallow. They will insist that the authorities I have invoked are merely describing matters with a particular gloss. Surely we can do without causal talk.
In the absence of both a successful reductive analysis of causation and a correct reductive metaphysical theory of the causal relation, I do not see why we should believe that causal talk in the work of physicists should be understood as redundant and imprecise talk. One cannot dismiss such causal language without providing a worthy proxy or substitute for it. The appropriate substitute arrives at the end of a careful reductive analysis of causal facts and an ontological reduction of the causal relation. The problem is that after a great many years of trying, attempts to reductively analyze and ontologically reduce causation have pretty much universally failed. As two foremost experts on the topic, L.A. Paul and Ned Hall concluded:
After surveying the literature in some depth, we conclude that, as yet, there is no reasonably successful reduction of the causal relation. And correspondingly, there is no reasonably successful conceptual analysis of a philosophical causal concept. No extant approach seems able to incorporate all of our desiderata for the causal relation, nor to capture the wide range of our causal judgments and applications of our causal concept. Barring a fundamental change in approach, the prospects of a relatively simple, elegant and intuitively attractive, unified theory of causation, whether ontological reduction or conceptual analysis, are dim.
I therefore conclude that the direct argument for causal reductionism from sound scientific practice is undercut by a proper understanding of the gravitational field.
* I would like to thank Tom Banks and Aron C. Wall for their comments on an earlier version of this piece. Any mistakes that remain are mine.
 Schaffer (2008, p. 92). See also Hitchcock (2007); and Norton (2007a), (2007b). Bertrand Russell said, “In the motions of mutually gravitating bodies, there is nothing that can be called a cause, and nothing that can be called an effect; there is merely a formula.” Russell (1912-1913, p. 14)
 Zee (2013, p. 258). There are strong and weak forms of this principle for which see Brown (2005, pp. 169-172). Ciufolini and Wheeler (1995, p. 13) discuss three versions of the principle.
 Weinberg (2008, p. 511).
 Misner, Thorne, and Wheeler (1973, pp. 312-313).
 Penrose (2005, p. 459).
 It, of course, says even more than this.
 Wald (1984, p. 68).
Rovelli (1997, p. 194)
 Wald (1984, p. 67).
 Brown (2005, p. 160).
 Hawking (1996, p. 5).
 Hoefer (2009, p. 687), though Hoefer does not believe there is bona fide causation in GTR.
 Hawking and Ellis (1973, p. 2).
 Geroch (1978, p. 180) emphasis mine.
Pooley (2013, p. 541) See Einstein (1916, pp. 112-113)
Pooley (2013, p. 541)
 As quoted by Wheeler and Ford (1998, p. 235), quoting John A. Wheeler.
 Brown (2005, pp. 159-160) emphasis mine.
 And here I’m agreeing (at least in part) with Balashov and Janssen,
“Does the Minkowskian nature of spacetime explain why the forces holding a rod together are Lorentz invariant or the other way around?…Our intuition is that the geometrical structure of space(-time) is the explanans here and the invariance of the forces the explanandum” Balashov and Janssen (2003, p. 340).
 Pooley (2013, p. 541).
 Paul and Hall (2013, p. 249).
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