The conservation of energy and momentum have been viewed as undermining Cartesian mental causation since the 1690s. Modern discussions of the topic tend to use mid-nineteenth century physics, neglecting both locality and Noether’s theorem and its converse. The relevance of General Relativity has rarely been considered. But a few authors have proposed that the non-localizability of gravitational energy and consequent lack of physically meaningful local conservation laws answers the conservation objection to mental causation: conservation already fails in GR, so there (...) is nothing for minds to violate. This paper is motivated by two ideas. First, one might take seriously the fact that GR formally has an infinity of rigid symmetries of the action and hence, by Noether’s first theorem, an infinity of conserved energies-momenta. Second, Sean Carroll has asked how one should modify the Dirac–Maxwell–Einstein equations to describe mental causation. This paper uses the generalized Bianchi identities to show that General Relativity tends to exclude, not facilitate, such Cartesian mental causation. In the simplest case, Cartesian mental influence must be spatio-temporally constant, and hence 0. The difficulty may diminish for more complicated models. Its persuasiveness is also affected by larger world-view considerations. The new general relativistic objection provides some support for realism about gravitational energy-momentum in GR. Such realism also might help to answer an objection to theories of causation involving conserved quantities, because energies-momenta would be conserved even in GR. (shrink)

This paper scrutinises the tenability of a strict conceptual distinction between space and matter via the lens of the debate between modified gravity and dark matter. In particular, we consider Berezhiani and Khoury's novel 'superfluid dark matter theory' as a case study. Two families of criteria for being matter and being spacetime, respectively, are extracted from the literature. Evaluation of the new scalar field postulated by SFDM according to these criteria reveals that it is as much matter as anything could (...) possibly be, but alsoꟷbelow the critical temperature for superfluidityꟷas much spacetime as anything could possibly be. A sequel paper examines possible interpretations of SFDM in light of this result, as well as the consequences for our understanding of the modified gravity/ dark matter distinction and the broader spacetime–matter distinction. (shrink)

We discuss the status of gravitational radiation in Newtonian theories. In order to do so, we consider various options for interpreting the Poisson equation as encoding propagating solutions, reflect on the extent to which limit considerations from general relativity can shed light on the Poisson equation’s conceptual status, and discuss various senses in which the Poisson equation counts as a dynamical equation.

The present paper revisits the debate between realists about gravitational energy in GR and anti-realists/eliminativists. I re-assess the arguments underpinning Hoefer’s seminal eliminativist stance, and those of their realist detractors’ responses. A more circumspect reading of the former is proffered that discloses where the so far not fully appreciated, real challenges lie for realism about gravitational energy. I subsequently turn to Lam and Read’s recent proposals for such a realism. Their arguments are critically examined. Special attention is devoted to the (...) adequacy of Read’s appeals to functionalism, imported from the philosophy of mind. (shrink)

It is widely held among philosophers that the conservation of energy is true and important, and widely held among philosophers of science that conservation laws and symmetries are tied together by Noether's first theorem. However, beneath the surface of such consensus lie two slights to Noether's first theorem. First, there is a 325+-year controversy about mind-body interaction in relation to the conservation of energy and momentum, with occasional reversals of opinion. The currently popular Leibnizian view, dominant since the late 19th (...) century, claims to find an objection to broadly Cartesian views in their implication of energy non-conservation. Here energy conservation is viewed as an oracle, an unchallengeable black box. But Noether's first theorem and its converse show that conservation and symmetry of the laws stand or fall together. Absent some basis for expecting conservation in brains that has a claim on the Cartesian, the objection is circular. An empirically based argument is possible, but is a different argument with little force except insofar as it is rooted in neuroscience. Second, General Relativity has a 100+-year-long controversy about whether gravitational energy exists and is objectively localized. The usual view is that gravitational energy exists but is not objectively localized, though some deny its existence. Without positive answers to both questions, generally applicable conservation laws do not exist: energy is not conserved. This conclusion is startling in itself and a problem for conserved quantity theories of causation. Yet Noether's first theorem applies to General Relativity, which has uncountably many symmetries of its laws and so has conservation laws, indeed uncountably many of them. Many authors downplay these laws due to their quirky properties; some authors even attempt to explain the laws' supposed nonexistence in terms of an absence of symmetries of the geometry, which is a distraction. Thus Noether's first theorem is widely ignored, left uninterpreted, or distorted in relation to General Relativity. Taking the theorem seriously seems possible, however, restoring the conservation of energy, or rather, energies. How do these controversies relate? One sometimes finds claims that General Relativity's supposed lack of conservation laws answers Leibniz on behalf of Descartes. Taking seriously the superabundance of formal conservation laws in General Relativity, however, suggests that General Relativity resists mind-to-body causation. This conclusion can be proven apart from interpretive controversies. The resistance is, however, finite and tends to be swamped by larger world-view considerations. (shrink)