The Relevance of Irrelevance: Absolute Objects and the Jones-Geroch Dust Velocity Counterexample, with a Note on Spinors

James L. Anderson analyzed the conceptual novelty of Einstein’s theory of gravity as its lack of “absolute objects.” Michael Friedman’s related concept of absolute objects has been criticized by Roger Jones and Robert Geroch for implausibly admitting as absolute the timelike 4-velocity field of dust in cosmological models in Einstein’s theory. Using Nathan Rosen’s action principle, I complete Anna Maidens’s argument that the Jones-Geroch problem is not solved by requiring that absolute objects not be varied. Recalling Anderson’s proscription of (globally) “irrelevant” variables that do no work (anywhere in any model), I generalize that proscription to locally irrelevant variables that do no work in some places in some models. This move vindicates Friedman’s intuitions and removes the Jones-Geroch counterexample: some regions of some models of gravity with dust are dust-free, and there is no good reason to have a timelike dust 4-velocity vector there. Eliminating the irrelevant timelike vectors keeps the dust 4-velocity from counting as absolute by spoiling its neighborhood-byneighborhood diffeomorphic equivalence to (1, 0, 0, 0). A more fundamental Gerochian timelike vector field presents itself in gravity with spinors in the standard orthonormal tetrad formalism, though eliminating irrelevant fields might solve this problem as well. keywords: absolute object, general covariance, dust, spinor, parametrized ∗History and Philosophy of Science Graduate Program, 346 O’Shaughnessy, University of Notre Dame, Notre Dame, Indiana 46556 USA email [email protected]