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 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.

Friedman and Some of His Critics on the Foundations of General Relativity

“…These theories suggest two main challenges to Friedman's analysis. The first and most trenchant is implicit in the particle physics approaches to gravitation theory and in the work of Pitts (2016aPitts ( , 2016bPitts ( , 2018. This is the view that the equivalence principle is eliminable, and therefore unnecessary for the development of Einsteinian gravitation.…”

The principle of equivalence as a criterion of identity

“…The aspiring eliminativist is motivated by a counterfactual: if Einstein had not developed his gravitation theory in 1915, particle physicists would have 20 years later and without the help of the equivalence principle. The eliminativist account, which is suggested in the work of a number of twentieth-century figures and which is implicit in the recent work of Pitts ( 2016a , b , 2018 ), is fleshed out with the help of the massless spin-2, and to a lesser extent massive spin-0 and spin-2, theories of gravity. 16 These research programs assume the framework of relativistic field theory and a “graviton” field, and from these and other assumptions recover versions and relatives, both close and distant, of Einstein’s field equations.…”

“… See Pitts (2016a, b, 2018 for details and for a near-exhaustive list of the original research papers.17 For example, in massive spin-2 gravity, immersion in a homogeneous gravitational field and uniform acceleration are not identical in their effects. The difference between gravitational effects and inertial effects is observable only in experiments sensitive to the graviton mass term in the gravitational field equation, that is, only if one looks carefully enough to observe the influence of the mass term on inertial effects.…”

“… 16 See Pitts ( 2016a , b , 2018 ) for details and for a near-exhaustive list of the original research papers. …”

“…The difference between gravitational effects and inertial effects is observable only in experiments sensitive to the graviton mass term in the gravitational field equation, that is, only if one looks carefully enough to observe the influence of the mass term on inertial effects. See Pitts ( 2016a , b , 2018 ) for details.…”