Quaternion Quantum Mechanics [video]

codewiz 4 years ago |

Scott Manley's explanation of the ISS accident also introduces quaternions as a coordinate system for objects in space that solves the gimbal lock problem and has other desirable algebraic properties:

https://www.youtube.com/watch?v=dDBt9rZhMb4

superjan 4 years ago |

I recall from quantum physics classes a long time ago that some elementary particles are not identical to themselves 360 degrees rotated. You need a 720 rotation for that. I recently learned that quaternions have that same property. Would there be a relation?

miej 4 years ago | |

yep, this exact thing is discussed in the later part of the video. it's used to hypothesize a qm interpretation where the complex components could actually be more physically interpretable as (quaternion-based) rotations of the kleinert crystal model

superjan 4 years ago | | |

When was that then? I saw the spin animation, she did not refer to it then … although I was baking cookies at the same time so I might have missed a remark here or there.

miej 4 years ago | | |

vaguely a combination of 12:02-ish with 48:26-ish. my understanding was the general idea of the spin animation was proposed to be localized and manifest to some region of the kleinert crystal roughly corresponding to a given particle. so basically an internal torsion co-located with the phonon behavior that defines the paricle in that framework

superjan 4 years ago | | |

Ok, will rewatch, thanks.

adamnemecek 4 years ago |

Reasoning about space and time is just so much nicer in geometric algebra. There's a new cool community on geometric algebra https://bivector.net/

The founder (Steven De Keninck aka enki) gave a talk at Siggraph2019 https://www.youtube.com/watch?v=tX4H_ctggYo

You should join the discord https://discord.gg/vGY6pPk

wwarner 4 years ago |

I think it's a cool idea, but it's one of many that start with a lattice model of space.

bawana 4 years ago | |

what other models start with a lattice assumption of space? I have been working on the math for a a model of space that is just a lattice, bosons are a vibration on the lattice, hadrons are twists on the lattice, gravity is stretching/compression of the lattice.

wwarner 4 years ago | | |

Lee Smolin, Stephen Wolfram and, though I am not an expert, I'm pretty sure many more.

leephillips 4 years ago | | |

Gerard ’t Hooft has been working on something like that, too.

miej 4 years ago | |

haven't done the math, myself - are there significant problems with a lattice model of space?

eurasiantiger 4 years ago | | |

It implies an a priori background structure. Hilbert spaces are usually preferred, as the complex state of a wavefunction kind of implies that representation.

miej 4 years ago | | |

so i think that's actually part of what I found notable about one of the posed hypotheses nearer the end of the video - the complex nature of the wavefunction essentially gets transformed into a 'more intuitive' lattice node space-like rotation within the Kleinert elastic crystal model. which, as someone who spent a short time 'getting used to' qm, seems very tempting.

plus, dont Hilbert spaces assume they are infinitessimally detailed (ie: complete)? which seems like it could lead to potential collisions with set-theoretic geometry, eg possibly some potential for a physical manifestation of the banach-tarski paradox, which would clearly violate conservation laws