Deflating Spacetime: A Dynamics-First View of the Spacetime Manifold

TL;DR

This paper proposes a novel dynamics-first perspective on the spacetime manifold, viewing it as a pattern codification of matter's behavior, supported by new mathematical tools for analyzing various spacetime theories.

Contribution

It introduces a dynamics-first view of the spacetime manifold, developing mathematical tools to compare different spacetime codifications based on their fit to dynamics and kinematics.

Findings

Developed mathematical tools for spacetime analysis.

Proposed a competition framework for spacetime codifications.

Established criteria for judging spacetime models based on dynamics fit.

Abstract

What, if anything, can help us explain the dynamical behavior of matter? One may be tempted here to appeal to the laws of nature, or to the world's geometric structure, or even to the smooth topological structure of the spacetime manifold itself. Some think, however, that the metaphysics involved in such explanatory strategies is excessively spooky. Indeed, some opt to reverse the arrow of explanation, putting dynamics first. For instance, one can use Lewis's Best Systems Analysis (BSA) to view the laws of nature as merely being codifications of certain patterns in the dynamical behavior of matter. Similarly, one can use Huggett's Regularity Relationism to achieve an analogous view of the world's geometric structure. At present, however, there is no such dynamics-first view of the spacetime manifold itself. This dissertation puts forward such a view: The spacetime manifold is merely a codification of certain patterns in the dynamical behavior of matter. This dissertation develops powerful mathematical tools for investigating and negotiating between a wide variety of spacetime settings for a wide range of spacetime theories. From here, a competition between different spacetime codifications is invoked analogous to the competition between different law-like codifications in Lewis's BSA. Whereas the BSA judges law-like codifications based on their balance of simplicity and strength, spacetime codifications are to be judged by how well they fit the theory's dynamics and kinematics.