Quaternion Quantum Mechanics [video]

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

by miej • 5 years ago

47 14 5 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

wwarner2• 5 years ago

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

miej4• 5 years ago

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

eurasiantiger• 5 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.

bawana• 5 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.

wwarner2• 5 years ago

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

codewiz• 5 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

superjan3• 5 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?

miej4• 5 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

superjan3• 5 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.

Quaternion Quantum Mechanics [video]

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