Really great video. I was struggling through the math of spinors earlier this year and the inability to contract loops in Special Orthogonal / "SO(n)" manifolds came up. This is a very nice visualization.
I am by far no physics expert (still an undergraduate), but I saw a really interesting video about "Geometric Algebra" with which spinors and Clifford Algebras in general can be neatly explained.
Absolutely fantastic: the stop motion animation, the explanation, all absolutely phenomenal. I have a degree in a field related to QM and this is truly one of the best explanations for the existence of anyons.
Wow !! I was part of the research group that actually made one of the first experimental detection of anyon and your video is one of the best explanation so far. My thumb is not big enough to encourage you for more content like this one.
What an amazing video!!! Everything looks perfect, the way you're presenting the video, the explanation, the content and basically everything in the video and the background music as well. Keep up the good work :)
Topology and the Dirac Belt trick are nice. But if you already algebraic know that F(x,y)=w*F(y,x) is a rotation, it might be a shorter leap to assume that to switch the parameter twice you should and end at the original value. So it can be only rotation by a multiple of 180 degree.
Great video! Do you know an easy explanation on why two transformations corresponding to two homotopic paths in configuration space must transform the state in the same way, i.e. lead to the same final wavefunction? That's the only thing I didn't quite get.
I think it's the implicit assumption that the configuration space models _all_ properties that would cause classic observables to be indistinguishable. So, it follows directly from the construction. If you added something to it, like, say, the proper time experienced by a particle during the exchange makes a difference, then you can exchange then with one particle moving slowly and the other moving rapidly in a round-about path, and this difference would not be modeled by your configuration space.
So you absolutely can consider the situation in which the phase is path-dependent, but that amounts to effectively introducing "extra physics" into your system. Like for example a magnetic field could produce this effect. But the absolute bare bones of the physics is probed by the homotopy classes of curves in configuration space - that's what leads you to the discovery of bosons/fermions/anyons. You may well have forgotten even asking this question - sorry for being incredibly slow!
I like the animation style. It's very approachable with low barrier to entry. It's not as much work to create as full computer-generated graphics, but it streamlines the presentation as compared to classic chalkboard use.
Hello Love your video so much Can you please say what is the name of physics section where you use homotopy Is it particle physics?or may be u can refer to some books or papers
It's a new insight for me that having three spacial dimensions (plus some notion of time in which the wave function can evolve and positions can change) is enough to show that indistinguishable particles can only have two possible things happen to the wave function when they undergo an exchange. Now I already understand that _spin_ arises as a quantum property due to the properties of Minkowski space-time; in short, composing pure boosts will result in a combined boost vector _and_ a rotation. So, how does this effect, inevitable with three dimensions alone, play into that? More later when I have time... Thanks again for making the video.
To be honest I'm not really sure how this picture would work with special relativity and the spin-statistics theorem! If you read anything more about this let me know!
Very refreshing multimedia presentation! If you had a negative integer/probability, would(n't) the square = (absolute value) probability of Not happening/ p = non-occurrent potential. P.s. Your perspective on configuration-space, combinatorically relalted to hermitian topologies (paraphrasing, I imagine and hope) is interestingly parametric in terms of algebraic reciprocality. P.p.s. If we extend our integer understanding of wave-functional exchange-paths as an operad of symmetric reciprocation governed by temporal angular moment (wth +- 1 being unit vectors); thus a function of periodic isometry exponentially grows over time, allowing any asymmetry to potentiate significant differentials compared to our idealized, possibly narrow/special equations (like trying to sum the sequence from only a few samples). Question: What do you think, if not too far out, about complex/real-integer fermionic analogues outside the typical mass/time discretized 3-flavour 2-d scalar spectrum of leptons?
The “Pac-Man” topology of the half sphere in configuration space is the same topology as a torus. That might help some people, because then you can buy a donut or bagel and mess around with it and some string to understand better.
This was beautiful! I love the stop motion animation style, and your explanation was so clear! Amazing video, I hope you make many more!
This is the start of something amazing :)
Really great video. I was struggling through the math of spinors earlier this year and the inability to contract loops in Special Orthogonal / "SO(n)" manifolds came up. This is a very nice visualization.
I am by far no physics expert (still an undergraduate), but I saw a really interesting video about "Geometric Algebra" with which spinors and Clifford Algebras in general can be neatly explained.
@@lvl3tensorboi929 Can you share the link. Thanks
@@williamnelson4968 I believe its mentioned in this YT video:
th-cam.com/video/60z_hpEAtD8/w-d-xo.html
@@lvl3tensorboi929 Great. Many thanks!
This is phenomenal. I learned about the mathematical basis of fermions but this explanation is so much better.
What a beautiful video! Thank you for the clear explanations! The past videos are great also!!! Love them!
Absolutely fantastic: the stop motion animation, the explanation, all absolutely phenomenal. I have a degree in a field related to QM and this is truly one of the best explanations for the existence of anyons.
This is absolutely mind blowing, such an elegant and accessible proof! Love it, brilliant stuff mate!
Wow !!
I was part of the research group that actually made one of the first experimental detection of anyon and your video is one of the best explanation so far.
My thumb is not big enough to encourage you for more content like this one.
Great video. Will definitely use this for reference when explaining anyons.
Great vid, found two years later. Nicely done
What an amazing video!!! Everything looks perfect, the way you're presenting the video, the explanation, the content and basically everything in the video and the background music as well. Keep up the good work :)
this was fantastic! please make more!
great stop motion!
Excellent. Verry impressed.
very nice explanation, congratulations!
This was fascinating and yet easy to understand, even though I nevertheless feel smoke coming out of my ears.
great video, just found that funny that the first thing came to my mind when I saw your channel picture was Marlboro Cigarettes.
Topology and the Dirac Belt trick are nice. But if you already algebraic know that F(x,y)=w*F(y,x) is a rotation, it might be a shorter leap to assume that to switch the parameter twice you should and end at the original value. So it can be only rotation by a multiple of 180 degree.
Great video :)!
Great job dude your channel gone viral soon!!!!!!
Great video! Do you know an easy explanation on why two transformations corresponding to two homotopic paths in configuration space must transform the state in the same way, i.e. lead to the same final wavefunction? That's the only thing I didn't quite get.
I think it's the implicit assumption that the configuration space models _all_ properties that would cause classic observables to be indistinguishable. So, it follows directly from the construction.
If you added something to it, like, say, the proper time experienced by a particle during the exchange makes a difference, then you can exchange then with one particle moving slowly and the other moving rapidly in a round-about path, and this difference would not be modeled by your configuration space.
So you absolutely can consider the situation in which the phase is path-dependent, but that amounts to effectively introducing "extra physics" into your system. Like for example a magnetic field could produce this effect. But the absolute bare bones of the physics is probed by the homotopy classes of curves in configuration space - that's what leads you to the discovery of bosons/fermions/anyons.
You may well have forgotten even asking this question - sorry for being incredibly slow!
I like the animation style. It's very approachable with low barrier to entry. It's not as much work to create as full computer-generated graphics, but it streamlines the presentation as compared to classic chalkboard use.
This is a masterpiece 😀
Hello
Love your video so much
Can you please say what is the name of physics section where you use homotopy
Is it particle physics?or may be u can refer to some books or papers
It's a new insight for me that having three spacial dimensions (plus some notion of time in which the wave function can evolve and positions can change) is enough to show that indistinguishable particles can only have two possible things happen to the wave function when they undergo an exchange.
Now I already understand that _spin_ arises as a quantum property due to the properties of Minkowski space-time; in short, composing pure boosts will result in a combined boost vector _and_ a rotation.
So, how does this effect, inevitable with three dimensions alone, play into that?
More later when I have time...
Thanks again for making the video.
To be honest I'm not really sure how this picture would work with special relativity and the spin-statistics theorem! If you read anything more about this let me know!
This is FANTASTIC! ✌️
"He's not Fred, I am!" ... nice addition 👌
Very refreshing multimedia presentation!
If you had a negative integer/probability, would(n't) the square = (absolute value) probability of Not happening/ p = non-occurrent potential.
P.s. Your perspective on configuration-space, combinatorically relalted to hermitian topologies (paraphrasing, I imagine and hope) is interestingly parametric in terms of algebraic reciprocality.
P.p.s. If we extend our integer understanding of wave-functional exchange-paths as an operad of symmetric reciprocation governed by temporal angular moment (wth +- 1 being unit vectors); thus a function of periodic isometry exponentially grows over time, allowing any asymmetry to potentiate significant differentials compared to our idealized, possibly narrow/special equations (like trying to sum the sequence from only a few samples).
Question: What do you think, if not too far out, about complex/real-integer fermionic analogues outside the typical mass/time discretized 3-flavour 2-d scalar spectrum of leptons?
So the inability of lines to tangle in 4D is the reason that there are only 2 types of particles. Weird.
1mil subs 2 years from now
I invest
Truth.
The “Pac-Man” topology of the half sphere in configuration space is the same topology as a torus. That might help some people, because then you can buy a donut or bagel and mess around with it and some string to understand better.
Subd 🤙🏽
My grams flew 'half of a plane' back to base in NAM.
LHC was a waste of money.
You're right, science and technology are a waste, you can go back to hunting and gathering, I'll catch up
Do you know where the World Wide Web came from?