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Spacetime geometry of spin, polarization, and wavefunction collapse
- Source :
- Journal of Geometry and Physics, 2023
- Publication Year :
- 2021
-
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.<br />Comment: 24 pages
- Subjects :
- Physics - General Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Geometry and Physics, 2023
- Publication Type :
- Report
- Accession number :
- edsarx.2103.03743
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.geomphys.2023.105026