Paul Schwahn (npub1zz2…9mhx) and I met here and started talking about math. We did a lot of work here on Mastodon, trading posts. Eventually we found a new way to understand the symmetries of the best theory of particle physics - the so-called 'gauge group of the Standard Model'. And now our paper on this is out!
This group is well-known but still mysterious. It seems random! But we may have found a clue.
In quantum physics we often talk about qubits. But we also talk about qutrits, where a quantum system has 3 alternative ways to be, instead of just two. We can also study systems with more than 3 alternative ways to be.
Qubits and qutrits are described using complex numbers. But we can also do quantum mechanics using other number systems. We understand the options, and the largest allowed number system for this purpose is called the 'octonions'.
A weird thing is that the octonions can describe qutrits, but not quantum systems with more than 3 alternative ways to be.
So, there's something special about octonionic qutrits - and it turns out that every symmetry in the gauge group of the Standard Model is a symmetry of an octonionic qutrit!
Now, not every symmetry of an octonionic qutrit is a symmetry of the Standard Model. But those that do have a simple description. They are those that restrict to give symmetries of an ordinary qutrit sitting inside the octonionic qutrit... and an ordinary qubit sitting inside that!
All this suggests an intriguing connection between the Standard Model and quantum information, where the octonions lie in the background, but we mainly see the complex numbers.
https://arxiv.org/abs/2606.15235
John Carlos Baez
npub1nf…3nqe4
2026-06-16 10:11:58 UTC
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2026-06-16 10:11:58 UTCEvent JSON
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"content": "nostr:npub1zz2mah7y6j4nld7dwedl7eh0yph4swkkv88spuvh0urq32xgz3ws459mhx and I met here and started talking about math. We did a lot of work here on Mastodon, trading posts. Eventually we found a new way to understand the symmetries of the best theory of particle physics - the so-called 'gauge group of the Standard Model'. And now our paper on this is out! \n\nThis group is well-known but still mysterious. It seems random! But we may have found a clue. \n\nIn quantum physics we often talk about qubits. But we also talk about qutrits, where a quantum system has 3 alternative ways to be, instead of just two. We can also study systems with more than 3 alternative ways to be.\n\nQubits and qutrits are described using complex numbers. But we can also do quantum mechanics using other number systems. We understand the options, and the largest allowed number system for this purpose is called the 'octonions'. \n\nA weird thing is that the octonions can describe qutrits, but not quantum systems with more than 3 alternative ways to be.\n\nSo, there's something special about octonionic qutrits - and it turns out that every symmetry in the gauge group of the Standard Model is a symmetry of an octonionic qutrit!\n\nNow, not every symmetry of an octonionic qutrit is a symmetry of the Standard Model. But those that do have a simple description. They are those that restrict to give symmetries of an ordinary qutrit sitting inside the octonionic qutrit... and an ordinary qubit sitting inside that!\n\nAll this suggests an intriguing connection between the Standard Model and quantum information, where the octonions lie in the background, but we mainly see the complex numbers.\n\nhttps://arxiv.org/abs/2606.15235",
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