Kant, Schlick and Friedman on Space, Time and Gravity in Light of Three Lessons from Particle Physics

Abstract: Kantian philosophy of space, time and gravity is significantly affected in three ways by particle physics. First, particle physics deflects Schlick's General Relativity-based critique of synthetic a priori knowledge. Schlick argued that since geometry was not synthetic a priori, nothing was---a key step toward logical empiricism. Particle physics suggests a Kant-friendlier theory of space-time and gravity presumably approximating General Relativity arbitrarily well, massive spin-2 gravity, while retaining a flat space-time geometry that is_indirectly_ observable at large distances. The theory's roots include Seeliger and Neumann in the 1890s and Einstein in 1917 as well as 1920s-30s physics. Such theories have seen renewed scientific attention since 2000 and especially since 2010 due to breakthroughs addressing early 1970s technical difficulties. Second, particle physics casts additional doubt on Friedman's constitutive \emph{a priori} role for the principle of equivalence. Massive spin-2 gravity presumably should have nearly the same empirical content as General Relativity while differing radically on foundational issues. Empirical content even in General Relativity resides in partial differential equations, not in an additional principle identifying gravity and inertia. Third, Kant's apparent claim that Newton's results could be known a priori is undermined by an alternate gravitational equation. The modified theory has a smaller (Galilean) symmetry group than does Newton's. What Kant wanted from Newton's gravity is impossible due its large symmetry group, but is closer to achievable given the alternative theory.