A geometric algebra visualizer for particle spin, rotors, spinors, and the Standard Model.
The goal of this project is to make spin less mysterious by showing the geometric structure underneath it. Instead of introducing complex numbers as an abstract extra ingredient, the app uses geometric algebra to show how rotations are generated by oriented planes, how vectors are transformed by rotor sandwiching, and why spin-1/2 states require a 720° return.
Live demo: rotorspin
The home page displays the elementary Standard Model particles in a familiar chart layout. Each particle opens a spin visualization page.
The visualization focuses on three rotation behaviors found in the elementary Standard Model:
| Particle type | Spin behavior shown |
|---|---|
| Quarks and leptons | Spin-1/2 fermion behavior |
| Gauge bosons | Spin-1 integer-spin behavior |
| Higgs boson | Spin-0 scalar behavior |
The broader rule is not “fermions are always spin 1/2” and “bosons are always spin 1.” The broader rule is:
half-integer total spin → fermion
integer total spin → boson