Spacetime geometry of spin, polarization, and wavefunction collapse

Charlie Beil

doi:10.1016/j.geomphys.2023.105026

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arXiv · 2103.03743

Spacetime geometry of spin, polarization, and wavefunction collapse

Charlie Beil

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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.

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Charlie Beil. 2021-01-18. Spacetime geometry of spin, polarization, and wavefunction collapse. https://doi.org/10.1016/j.geomphys.2023.105026

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