Related: https://eater.net/quaternions
FYI - if you're like me, you just looked at the page thinking it had some links to 3blue1brown videos. Not obvious that those are thumbnails link to interactive video apps. Very cool.
Quaternions and spherical trigonometry
51–53 of 53 posts
Re: Quaternions and spherical trigonometry
#52Earlier quoted context omitted.
To understand spin it's good to consider a gyroscope. when it has a lot of angular momentum there are two stable states for it in a gravitational field: aligned or anti-aligned with gravitation, up or down. in all other cases the gyroscope precesses. a spinor doesn't spin quite like a gyroscope but it is spinning in a sense (after all spin is angular momentum). but just like the gyroscope, you can think of it as havi…
Sounds interesting - would you have a good intro book on spinors you could recommend?
Unfortunately i can't. I've been thinking about spinors and related concepts as a hobby for maybe two years now. But i never found an explanation like mine above anywhere. Good geometric intuition about these things does not seem to be highly valued in physics education so people don't seek it. It turns out you can represent a dirac spinor (as the sum of left and right weyl spinors) extremely well just with your two hands. the dirac matrices simply tell you how to rotate your hands or mirror them (which you can do because you have two!). I should make a video about this actually...
Re: Quaternions and spherical trigonometry
#53Earlier quoted context omitted.
Sounds interesting - would you have a good intro book on spinors you could recommend?
Unfortunately i can't. I've been thinking about spinors and related concepts as a hobby for maybe two years now. But i never found an explanation like mine above anywhere. Good geometric intuition about these things does not seem to be highly valued in physics education so people don't seek it. It turns out you can represent a dirac spinor (as the sum of left and right weyl spinors) extremely well just with your two…
> I should make a video about this actually...
sounds good, I've had a look at a few books but would be good to see something like that