Space-time Philosophy Reconstructed via Massive Nordström Scalar Gravities? Laws vs. Geometry, Conventionality, and Underdetermination

Abstract

Klein-Gordon gravity, 1920s-30s particle physics, and 1890s Neumann-Seeliger modified gravity suggest a "graviton mass term" *algebraic* in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is invariant under the Poincaré group but not the 15-parameter conformal group. It thus exhibits the whole Minkowski space-time structure, indirectly for volumes. Massive scalar gravity is plausible as a field theory, but violates Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide: matter sees a conformally flat metric due to universal coupling, but gravity sees the rest of the flat metric (on long distances) in the mass term. What is the `true' geometry, in line with Poincaré's modal conventionality argument? Infinitely many theories exhibit this bimetric `geometry,' all with the total stress-energy's trace as source; geometry does not explain the field equations. The irrelevance of the Ehlers-Pirani-Schild construction to conventionalism is evident given multi-geometry theories. As Seeliger envisaged, the smooth massless limit yields underdetermination between massless and massive scalar gravities---an unconceived alternative. One version easily could have been developed before GR; it would have motivated thinking of Einstein's equations along the lines of his newly reappreciated "physical strategy" and suggested a rivalry from massive spin 2 for GR (massless spin 2, Pauli-Fierz 1939). The Putnam-Grünbaum debate on conventionality is revisited given a broad modal scope. Massive scalar gravity licenses a historically plausible rational reconstruction of much of space-time philosophy in light of particle physics. An appendix reconsiders the Malament-Weatherall-Manchak conformal restriction of conventionality and constructs the `universal force' in the null cones.

References in corpus (10)

• Resummation of Massive Gravity
• The (pseudo)issue of the conformal frame revisited
• Some remarks on the notions of general covariance and background independence
• On the emergence of Lorentzian signature and scalar gravity
• Minkowski space-time: a glorious non-entity
• Permanent Underdetermination from Approximate Empirical Equivalence in Field Theory: Massless and Massive Scalar Gravity, Neutrino, Electromagnetic, Yang-Mills and Gravitational Theories
• Global weak solutions to the Nordström-Vlasov system
• Gravity's Scalar Cousin
• Local spinor structures in V. Fock's and H. Weyl's work on the Dirac equation (1929)
• Massive Nordström Scalar (Density) Gravities from Universal Coupling

Cited by in corpus (5)

• Einstein's Physical Strategy, Energy Conservation, Symmetries, and Stability: "but Grossmann & I believed that the conservation laws were not satisfied"
• Kant, Schlick and Friedman on Space, Time and Gravity in Light of Three Lessons from Particle Physics
• Would Two Dimensions be World Enough for Spacetime?
• Space-time Constructivism vs. Modal Provincialism: Or, How Special Relativistic Theories Needn't Show Minkowski Chronogeometry
• The Field-Theoretic Approach in General Relativity and Other Metric Theories. A Review