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. 🙏🙏🙏
Could not agree more, and have felt this way ever since I discovered geometric algebra. At least after I got over the anger of never having had it taught to me in school.
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 :)
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.
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 .
The paper in the description has a brief mention of that, and also this video th-cam.com/video/Zk6YnJpbhOo/w-d-xo.html by one of the paper's co-authors.
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.
Something that's not actively promoted is that there are different definitions of spinors. One is a "classical spinor," which is an element of a spin group as you said. That's the rotor in this video. Another is an element of a minimal left ideal, called an "algebraic spinor." That's when you multiply the rotor by the projector, which is equal to the bisector times the projector. The last, and least used (because it's only truly valid in 3 dimensions), is the "operatorial spinor," which is an element of an even subalgebra.
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. 🖖
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! 🙏
This algebra (the APS: G(3) ) is isomorphic to complexified quaternions, and the even subalgebra of the APS is isomorphic to quaternions! SU(2) is the "double cover" of SO(3), which basically means that for every transformation element in SO(3), there are two elements in SU(2) that represent the same transformation. There, unfortunately, is no trick to connect SU(3) and SO(4). They are both their own things! Glad you liked the video!
@@EccentricTuber I’m reading this paper, ‘Some recent results for SU(3) and Octonions within the Geometric Algebra approach to the fundamental forces of nature’ by Lasenby. Some interesting stuff in there. Maybe you can make more sense of it than me. 😅
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.
"The direction in which the particle is moving in relation to the field in which it moves." No, that has nothing to do with spin. Where did you get that idea from? Spin is related to _angular_ momentum, whereas the direction into which a particle moves is simply related to _momentum_ itself. "Magnetism is spiral." What is that supposed to mean? And what does all of that have to do with corks?
@@BingoDan936 You didn't answer any of my questions and ignored my corrections. Typical, like a true crackpot. "Magnetic Spiral Fields." Again: What is that supposed to mean? "Particles, like photons, follow the spiral magnetic field." That contradicts almost everything we know from at least 100 years of experiments with electromagnetic fields and photons. Get an education!
@@Miparwo I understand, don't worry. I was just proposing that maybe a solution is to read the subtitles but then pause the video so you can temporarily turn off subtitles to be able to see the slide better. In the future I'll try to not take up the whole slide.
There's a short quiz to test your retention/understanding: quizwithit.com/start_thequiz/1723220806250x216672769950089200
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. 🙏🙏🙏
Could not agree more, and have felt this way ever since I discovered geometric algebra. At least after I got over the anger of never having had it taught to me in school.
Oh we cooking! TY my guy 👨🍳
@@ImaGonnar 🍽️🍷🫡
I wish I had learned Geometric Algebra before Relativity, QM, Maxwell's Equations.
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 :)
Dirac spinors (Righthanded & Lefthanded Weyl spinors) are basically the relativistic equivalent of Pauli spinors :)
Ah, Memes, Minecraft music, and Math. the holy M trinity. subbed
simple and insightful explanation
Well put & explained my boy
Wonderful man. Thanks
amazing!, this could definitely play a part in my "pocket universe" (a simulation of a universe where i can control physics)
Minecraft music! Nice!
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.
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 .
Damn math goblins.
Cool vid, love GA. Mind sharing some reseoruces for the link between the "quantumness" and geometry you mention around 14mins?
The paper in the description has a brief mention of that, and also this video th-cam.com/video/Zk6YnJpbhOo/w-d-xo.html by one of the paper's co-authors.
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.
Something that's not actively promoted is that there are different definitions of spinors. One is a "classical spinor," which is an element of a spin group as you said. That's the rotor in this video. Another is an element of a minimal left ideal, called an "algebraic spinor." That's when you multiply the rotor by the projector, which is equal to the bisector times the projector. The last, and least used (because it's only truly valid in 3 dimensions), is the "operatorial spinor," which is an element of an even subalgebra.
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. 🖖
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! 🙏
This algebra (the APS: G(3) ) is isomorphic to complexified quaternions, and the even subalgebra of the APS is isomorphic to quaternions! SU(2) is the "double cover" of SO(3), which basically means that for every transformation element in SO(3), there are two elements in SU(2) that represent the same transformation. There, unfortunately, is no trick to connect SU(3) and SO(4). They are both their own things!
Glad you liked the video!
SU(3) and SO(4) are quite different groups. But SU(2)×SU(2) has a double cover over SO(4) in a similar way.
@@EccentricTuber I’m reading this paper, ‘Some recent results for SU(3) and Octonions within the Geometric Algebra approach to the fundamental forces of nature’ by Lasenby. Some interesting stuff in there. Maybe you can make more sense of it than me. 😅
@@millamulisha Funny you bring that up! I've actually been reading it myself! Maybe I'll make a video eventually 🤙🤙
is this related to mohrs circle for stress and strain at all???
No, sorry
❤
Really want to start getting my PhD now
@@roneyandrade6287 Same, but alas: money 😭
@EccentricTuber holy hecks, that's so me. Big L for us non privilege people 😢
@@roneyandrade6287 Maybe someday for both of us!
what happened to Nyrþik?
That's a good question! It's just not a good language. I made it while I was first learning to conlang, so it has tons of flaws.
Not done with the video, but isn't plane based geometric algebra just the exterior algebra of the dual space?
It's related, but it's the Clifford algebra "extension".
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.
"The direction in which the particle is moving in relation to the field in which it moves."
No, that has nothing to do with spin. Where did you get that idea from? Spin is related to _angular_ momentum, whereas the direction into which a particle moves is simply related to _momentum_ itself.
"Magnetism is spiral."
What is that supposed to mean? And what does all of that have to do with corks?
@@bjornfeuerbacher5514 Yes. Magnetic Spiral Fields.
Particles, like photons, follow the spiral magnetic field.
@@BingoDan936 You didn't answer any of my questions and ignored my corrections. Typical, like a true crackpot.
"Magnetic Spiral Fields."
Again: What is that supposed to mean?
"Particles, like photons, follow the spiral magnetic field."
That contradicts almost everything we know from at least 100 years of experiments with electromagnetic fields and photons. Get an education!
Your content gets hidden below the subtitles.
@@Miparwo That's a bummer, maybe turning off subtitles temporarily is the way to go, then?
@@EccentricTuber for non english speakers, telling apart different english accents is difficult, and reading the subtitles is necessary.
@@Miparwo I understand, don't worry. I was just proposing that maybe a solution is to read the subtitles but then pause the video so you can temporarily turn off subtitles to be able to see the slide better. In the future I'll try to not take up the whole slide.
this is more of a youtube issue than anything
The lack of symmetry of your rotating circle is triggering but thanks otherwise
Lol it's called "I can't be bothered to learn proper animation techniques"
@@EccentricTuber What's funny is how GA has seen a renaissance of use in animations due to its simplicity
Are you allowed to use the minecraft background music in your video?
😂
Let's go all the way and apply this reasoning to physics. What is being bisected?
@@EricDMMiller The angle between the spin axis and the spin direction, as demonstrated in the video with a and c