Spacetime geometry of spin, polarization, and wavefunction collapse

TL;DR

This paper proposes a novel spacetime geometry with 'pointons' to integrate quantum nonlocality into general relativity, leading to new models of fermions, charge, and photon polarization.

Contribution

It introduces a new geometric framework with degenerate metrics and variable tangent space dimensions, connecting quantum properties to spacetime structure.

Findings

Pointons are spin-1/2 fermions satisfying the Born rule.

A new ontological model of photon polarization is developed.

Electromagnetic charge is linked to orientation choices in the geometry.

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 that is endowed with particles which have no distinct points in their worldlines; we call these particles 'pointons'. 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 pointons are spin-$\tfrac 12$ fermions that satisfy the Born rule, where a projective measurement of spin corresponds to an actual projection of tangent spaces of different dimensions. Furthermore, the $4$-velocities of pointons 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 ontological model of photon polarization.