Spacetime geometry of spin, polarization, and wavefunction collapse

Abstract

To incorporate quantum nonlocality into general relativity, we propose that the preparation and measurement of a quantum system are simultaneous events. To make progress in realizing this proposal, we introduce a spacetime geometry where there are no distinct points in the worldlines of dust particles; this new geometry recently arose in nonnoetherian algebraic geometry. We show that on such a spacetime, metrics are degenerate and tangent spaces have variable dimension. This variability then implies that dust particles are spin-1/2 fermions that satisfy the Born rule, where a projective measurement of spin corresponds to the actual projection of tangent spaces of different dimensions. Furthermore, the 4-velocities of dust particles are necessarily replaced by their Hodge duals, and this transfer from vector to pseudo-tensor introduces a free choice of orientation that we identify with electric charge. Finally, a simple composite model of electrons and photons results from the metric degeneracy, and from this we obtain a new realist model of photon polarization.