◉ Particles
Particles as topological defects (torus knots) in the electromagnetic field. Spin, statistics, and particle spectra emerge naturally from the geometry of these confined photon trajectories.
Key Result
Exchange of two T(1,1) seats → π phase → half-integer spin (Finkelstein–Rubinstein theorem)
Core Concepts
Spin-½ from Topology
Exchanging two T(1,1) seats on the Hopf atlas picks up a phase of π. This is the topological origin of half-integer spin. Finkelstein–Rubinstein theorem applied.
Fermi–Dirac Statistics
Follows from the FR phase. Identical topological particles cannot occupy the same seat. The Pauli exclusion principle is a theorem, not a postulate.
The Electron
The electron is T(1,1): the simplest stable torus knot with one winding in each direction. Its mass, charge, and spin all follow from T(1,1) geometry.
Antiparticles
An antiparticle is the topological mirror of its partner: T(p,q) ↔ T(q,p) with opposite orientation. Pair production is topological bubble nucleation.
Spin–Statistics Theorem
Integer-spin particles commute (boson), half-integer anti-commute (fermion). Derived from the FR phase and Hopf atlas exchange.
Particle Spectrum Skeleton
The allowed T(p,q) with gcd(p,q)=1 give the particle spectrum. Mapping to known particles: T(2,3)=proton, T(3,2)=neutron, T(1,1)=electron.
Mass Hierarchy
Why is the muon 207× heavier than the electron? The mass hierarchy of leptons and quarks from torus knot geometry. Open investigation.
Quark Model
Quarks as fractional-winding knots confined by the knot lattice. Colour confinement from the topology of the S³ lattice.