Pauli Spinors: Just Geometry, Not Quantum Magic!

This video presents the idea that Pauli Spinors are the result of geometry rather than quantum mechanics, and that they have a simple and visualizable geometric interpretation!

// Timestamps

00:00 - Intro & Foreword
01:47 - Summary of Geometric Algebra
06:33 - Plane Bisectors
09:24 - What Pauli Spinors Are
17:32 - Synopsis & Outro

//Music

Music by C418
Download the music on Bandcamp:
Stream the music on Spotify:

Music by Vincent Rubinetti
Download the music on Bandcamp:
Stream the music on Spotify:

#geometricalgebra #maths #mathematics #physics #geometry #spinor
#spinors #spin #quantumphysics #quantummechanics

[michaeldfarmer]

I’m a vehement supporter of adopting geometric algebra as the consensus approach to teaching and researching physics and engineering. Thank you so much for sharing your knowledge in this accessible way! It’s people like you who will give the next generation access to this incredible tool. 🙏🙏🙏

[chrisjager]

I wish I had learned Geometric Algebra before Relativity, QM, Maxwell's Equations.

[TymexComputing]

I remember from adv. physics that there were some Dirac spinors - not necessarily Pauli spinors but it doesnt matter how you call it - more important is how it behaves :)

[douginorlando]

Geometric Algebra requires hours of teaching and examples to get an intuitive feel. It does look like a powerful branch of math to understand/model any real world system that deals with angular momentum or torque (both mechanical and in EM fields/radiation). I see the value and concur with other commenters who want geometric algebra to be included up front in college level STEM.

[ckpioo]

amazing!, this could definitely play a part in my "pocket universe" (a simulation of a universe where i can control physics)

[TheOneMaddin]

I thought spinors are pretty easy things, being elements of the spin group which double covers the orthogonal group. But I get confused if people introduce these bases.

[scottychen]

This is excellent . The proclaimed principle itself could be considered nothing other than the use of vectors to speak of the Minkowski - state of the quantum particle system in question . …

The use of this kind of Moduli space in the sense of a PDE has many meanings associated to it : so an excellent video.

To clear up the confusion one may have surrounding such a thing .

[KaliFissure]

Great video. 👍

I came across this form in my explorations and it seems like it is prefect for spinors.
A radially symmetric single sided closed surface. A symmetric Klein bottle.
The two regions are joined at a point of catastrophe. Joining minima and maxima.

Surface(cos(u/2)cos(v/2), cos(u/2)sin(v/2), sin(u)/2), u, 0, 2pi, v, 0, 4pi

And notice that 2pi only covers one region, that one needs 4pi to complete the surface. Electron half spin. We see an electron, for 360° but INSIDE the electron, on the other side of time/infinity is a positron to balance it. So 720° total. 🖖

[Globbo_The_Glob]

Cool vid, love GA. Mind sharing some reseoruces for the link between the "quantumness" and geometry you mention around 14mins?

[millamulisha]

Connections to quaternions and how to explain bispinors? Octonions maybe?

I know there’s some connection between SU(2) and SO(3), is there a similar ‘trick’ to connect SU(3) to SO(4)?

Great video, new to learning geometric algebra. Thanks! 🙏

[roneyandrade]

Really want to start getting my PhD now

[strict_asianbroccoli]

is this related to mohrs circle for stress and strain at all???

[chuckaway]

Not done with the video, but isn't plane based geometric algebra just the exterior algebra of the dual space?

[BingoDan]

Q. What is the difference between left spin and right spin?
A. The direction in which the particle is moving in relation to the field in which it moves.
Magnetism is spiral.
Put the cork on the screw it spins in one direction.
Take the cork off the screw it spins in the opposite direction.
There is only one cork.

[Miparwo]

Your content gets hidden below the subtitles.

[TheOneMaddin]

Are you allowed to use the minecraft background music in your video?

[anywallsocket]

The lack of symmetry of your rotating circle is triggering but thanks otherwise

[EricDMMiller]

Let's go all the way and apply this reasoning to physics. What is being bisected?