Space-time Constructivism vs. Modal Provincialism: Or, How Special Relativistic Theories Needn't Show Minkowski Chronogeometry

TL;DR

This paper challenges the orthodox view of space-time geometry in relativity, advocating for a constructivist approach that considers multiple geometries and emphasizes dynamical details over fixed geometrical assumptions.

Contribution

It introduces a constructivist perspective on space-time theories, arguing against the assumption of a unique geometry and highlighting the importance of dynamical details in relativistic field theories.

Findings

Constructivism applies to all local classical field theories.

Orthodox space-time realism assumes a unique geometry, which is often inadequate.

Massive scalar gravity exemplifies the limitations of the orthodox view.

Abstract

In 1835 Lobachevski entertained the possibility of multiple (rival) geometries. This idea has reappeared on occasion (e.g., Poincar\'{e}) but didn't become key in space-time foundations prior to Brown's \emph{Physical Relativity} (at the end, the interpretive key to the book). A crucial difference between his constructivism and orthodox "space-time realism" is modal scope. Constructivism applies to all local classical field theories, including those with multiple geometries. But the orthodox view provincially assumes a unique geometry, as familiar theories (Newton, Special Relativity, Nordstr\"{o}m, and GR) have. They serve as the orthodox "canon." Their historical roles suggest a story of inevitable progress. Physics literature after c. 1920 is relevant to orthodoxy mostly as commentary on the canon, which closed in the 1910s. The orthodox view explains the behavior of matter as the manifestation of the real space-time geometry, which works within the canon. The orthodox view, Whiggish history, and the canon relate symbiotically. If one considers a theory outside the canon, space-time realism sheds little light on matter's behavior. Worse, it gives the wrong answer when applied to an example arguably in the canon, massive scalar gravity with universal coupling. Which is the true geometry---the flat metric from the Poincar\'{e} symmetry, the conformally flat metric exhibited by material rods and clocks, or both---or is the question bad? How does space-time realism explain that all matter fields see the same curved geometry, given so many ways to mix and match? Constructivist attention to dynamical details is vindicated; geometrical shortcuts disappoint. The more exhaustive exploration of relativistic field theories (especially massive) in particle physics is an underused resource for foundations.