Abstract

Earman and Ruetsche ([2005]) have cast their gaze upon existing no-go theorems for relativistic modal interpretations, and have found them inconclusive. They suggest that it would be more fruitful to investigate modal interpretations proposed for "really relativistic theories," that is, algebraic relativistic quantum field theories. They investigate the proposal of Clifton ([2000]), and extend Clifton's result that, for a host of states, his proposal yields no definite observables other than multiples of the identity. This leads Earman and Ruetsche to a suspicion that troubles for modal interpretations of such relativistic theories "are due less to the Poincaré invariance of relativistic QFT vs. the Galilean invariance of ordinary nonrelativistic QM than to the infinite number of degrees of freedom of former vs. the finite number of degrees of freedom of the latter" (577-78). I am skeptical of this suggestion. Though there are troubles for modal interpretations of a relativistic quantum field theory that are due to its being a field theory—that is, due to infinitude of the degrees of freedom—they are not the only troubles faced by modal interpretations of quantum theories set in relativistic spacetime; there are also troubles traceable to relativistic causal structure.