Counterfactuals in the Initial Value Formulation of General Relativity

Abstract

<jats:title>Abstract</jats:title> <jats:p>How precisely to understand and evaluate counterfactuals can be an intricate issue. The aim of this article is to examine a new set of difficulties for evaluating counterfactuals that arise in the context of the dynamical spacetimes described by the theory of general relativity (GR). The initial value formulation provides us with a methodology to pin down the specific combination of features of the theory at the origin of the difficulties, namely, non-linearity and certain non-local aspects (typically captured by ellipticity at the analytical level), in particular when combined with the global and/or quasi-local character of physical quantities in GR. Finally, we connect the philosophical question about counterfactuals with concrete applied physical issues in GR about extracting meaningful predictions by constructing appropriate initial data sets, leading us to question the very suitability of the Cauchy approach to fully account for the explanatory power of the theory. 1Introduction2Maudlin’s Recipe3The Initial Value Problem of General Relativity4Conformal Strategies for Solving the Constraints5Non-linearity and Ellipticity at the Heart of the Difficulties6Relativistic Infection and Possible Worlds7Perspectives</jats:p>

Causation and the conservation of energy in general relativity

“…The answer is not so simple. As Curiel ([2015]) and Jaramillo and Lam ([2021]) argue (see also (Vassallo [2019])), coming up with a good way of evaluating counterfactual statements in GR is a rather tricky issue in part because it is not clear how to make sense of nearby possibilities when comparing different spacetimes, in part because of the complexity of the initial value problem in GR. In addition to these difficulties, some might argue that counterfactual theories 'produce' more causation than what one might expect in the context of GR.…”

The general-relativistic case for super-substantivalism

“…One is that approaches (such as Salmon’s and Dowe’s), based on conserved quantities, aren’t directly applicable to GR: the status of conservation of energy and momentum—as the two quantities standardly taken to be chiefly relevant—is controversial (Curiel, 2000 ; Dürr, 2020 ; Hoefer, 2000 ). Alternative accounts of causality, based on counterfactuals (such as Lewis) fare little better: in GR, one faces principled difficulties with regards to evaluating counterfactuals (Curiel, 2014 ; Jaramillo & Lam, 2019 ). GR poses a third problem for causality simpliciter: certain exotic spacetimes (see e.g.…”

Laws beyond spacetime

“… 23 The dynamical nature of spacetime within general relativity creates difficulties for Maudlin’s procedure for evaluating counterfactuals, which can be precisely specified in terms of non-linearity and ellipticity within the framework of the initial value formulation (Jaramillo and Lam, 2021 ). …”