Quaternion Quantum Mechanics [video]
youtube.comScott 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:
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?
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
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.
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
Ok, will rewatch, thanks.
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
I think it's a cool idea, but it's one of many that start with a lattice model of space.
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.
Lee Smolin, Stephen Wolfram and, though I am not an expert, I'm pretty sure many more.
Gerard ’t Hooft has been working on something like that, too.
haven't done the math, myself - are there significant problems with a lattice model of space?
It implies an a priori background structure. Hilbert spaces are usually preferred, as the complex state of a wavefunction kind of implies that representation.
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