Title: Space-time Constructivism vs. Modal Provincialism: Or, How Special Relativistic Theories Needn't Show Minkowski Chronogeometry,
Abstract: In 1835 Lobachevski entertained the possibility of multiple (rival)
geometries. This idea has reappeared on occasion (e.g., Poincaré) 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,
Nordström, 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 Poincaré 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.