Geometrical Constructivism and Modal Relationalism: Further Aspects of the Dynamical/Geometrical Debate

Abstract

I draw together some recent literature on the debate between dynamical versus geometrical approaches to spacetime theories, in order to argue that (i) there exist defensible versions of the geometrical approach; (ii) these versions of the geometrical approach can provide constructive explanations (in the sense of Einstein) of dynamical effects; (iii) light can be shed upon different relationalist views about spacetime which have been articulated in the context of this debate by appeal to the distinction between modal versus non-modal relationalism.

Two Dogmas of Dynamicism

“…He may use terms as he likes, but it is worth emphasizing that this use of "absolutist" is importantly different from its usage in connection with, say, Newton's views on absolute space and time. (See also Read (2019) for a discussion of Acuña in this regard.) quantities that we call "lengths", "angles", etc., as determined by some metric.…”

“…There is also an unresolved (I believe) disagreement about whether there is some salient difference between general relativity and other theories, such as Newtonian gravitation, regarding the status of inertial motion (Weatherall, 2011;Sus, 2014;Weatherall, 2017). Finally, there have been disputes about whether spacetime geometry can provide "constructive explanations" (Brown andPooley, 1999, 2006;Janssen, 2009;Dorato, 2007;Frisch, 2011;Acuña, 2016;Read, 2019); and about whether one can even state matter dynamics without specifying some geometrical background (Norton, 2008;Wallace, 2019).…”

“…In the context of special relativity, conceived as a separate theory from general relativity, he thinks that both views are tenable, but that they are clearly distinct and he prefers the dynamical view. See(Read, 2019) for further discussion of issues that are salient to the debate in special relativity, but which will not concern me in the present article.3 See Baker (2019) andRead and Menon (2019) for critiques ofKnox's view, and (Weatherall, 2019, fn. 40) for a discussion how I see the relationship between my views as discussed there and Knox's.…”

Miracles persist: a reply to Sus

“…In addition, all three parties can be taken to accept the understanding of diffeomorphism invariance presented inPooley (2017, p. 117), for which the salient transformations are those which transform dynamical fields, but not fixed fields. For further details on all these assumed background notions, seePooley (2017) andRead (2016Read ( , 2020b.4 Notably, such a condition does not have to violate the diffeomorphism invariance of the theory in question, for the space of kinematical possibilities ⟨M, g ab , a , Φ⟩ of some theory T , where Φ is a placeholder for material fields, will partition into equivalence classes under diffeomorphisms in which the vector field a is timelike, spacelike, or null. By contrast, fixing a privileges a representative of (some) of the abovementioned equivalence classes, and thereby breaks the diffeomorphism invariance of the theory.…”