An expanding universe of spinning spheres

TL;DR

This paper introduces a geometric framework on a seven-dimensional manifold of spheres that models spinning particles in an expanding universe, capturing behaviors like Zitterbewegung and photon-like motion.

Contribution

It presents a new geometric construction that models spinning particles and photons in an expanding universe using Finslerian geometry on a manifold of spheres.

Findings

Particles with nonzero mass follow helical paths exhibiting Zitterbewegung.

Massless particles follow straight lightlike paths with aligned spin and velocity.

The model reproduces quantum-like spinning behaviors in a geometric setting.

Abstract

A novel but elementary geometric construction produces on the seven-dimensional manifold of rotated spheres in Euclidean three-space a finslerian geometry whose geodesics are interpreted as the paths of free, spinning, spherical particles moving through de Sitter's expanding universe. A particle of nonzero inertial rest mass typically follows a helical track and exhibits behavior remindful of the phenomenon of ``Zitterbewegung'' of spinning electrons first deduced by Schroedinger from Dirac's relativistic wave equation. Its velocity vector and its spin vector precess about the axial direction of the helix, with their projections onto that direction at all times parallel or at all times antiparallel. Particles of zero rest mass follow straight tracks at the speed of light with their spin vectors parallel or antiparallel to their velocity vectors, thereby replicating behavior of spinning photons predicted by the quantum theory of light.