Octonions and the Standard Model

Paul Schwahn and I have come out with a new paper about octonions and the Standard Model: • The Standard Model gauge group from the exceptional Jordan algebra It builds on things I’ve discussed here, but it goes further. Let me explain a bit. A bit is just a binary alternative: 1 or 0, true or false. That’s how it works in classical logic. We could also have a ‘trit’, meaning 3 alternatives. In quantum physics we instead have qubits and qutrits. Qubits and qutrits are usually described using complex numbers. The algebra of observables of a qubit is the Jordan algebra , consisting of self-adjoint complex matrices. Similarly, the algebra of observables of an qutrit is the Jordan algebra , consisting of self-adjoint complex matrices. We can also study systems with more than 3 alternative ways to be. They work the same way, using the Jordan algebras with But we can also do quantum mechanics using other number systems! The options have been mapped out, and the largest allowed number system…