Entanglement and the quantum spatial continuum

The non-locality of entangled systems provides more evidence that the spatial continuum of quantum particles is not classical. We assume that physical quantities take Dedekind real numbers in a topos for their numerical values. This means that the quantum spatial continuum is isomorphic to R-D(E-S (M))(3), where R-D(ES(M)) the sheaf of Dedekind real numbers in the topos Shv(E-S(M) of sheaves on the state space of the quantum system. In such a continuum, a single particle can have a quantum trajectory which passes through two classically separated slits and two particles in an entangled condition stay close to each other in their quantum space and hence Einstein locality is retained.