Richard Behiel
Richard Behiel
  • 20
  • 1 807 200
The Mystery of Spinors
In this video, we explore the mystery of spinors! What are these strange, surreal mathematical things? And what role do they play in physical reality? We'll talk about the algebra of SO(3) and SU(2), and the profound physical implications of spinors, particularly as it relates to spin-statistics and the stability of matter!
Video notes PDFs available for download on Patreon:
www.patreon.com/RichardBehiel
All support is highly motivating and greatly appreciated! :)
Recommended reading: "An introduction to spinors" by Andrew M. Steane: arxiv.org/abs/1312.3824
For a more advanced and comprehensive treatment of spinors, see "Spinors and Space-Time" by Penrose. The homotopy class animations in SO(3) were based on Section 1.5 of that book.
To learn more about the Spin-Statistics Theorem, see "Pauli and the Spin-Statistics Theorem", by Ian Duck and E. C. G. Sudarshan.
Also, check out the wonderful UA-cam series "Spinors for Beginners" by EigenChris! www.youtube.com/@eigenchris
Chapters:
0:00 Intro
3:08 Topology Warmup
9:22 Axis-Angle Representation of 3D Rotations
13:15 Homotopy Classes of Loops in the Axis-Angle Space
22:50 The Algebra of Rotations, SO(N)
33:48 SU(2)
39:35 SU(2) Double Covers SO(3)
49:15 Exploring the Mystery
1:01:20 Superconductivity
1:05:00 Let's get Existential
1:07:50 Conclusion
#math #physiccs #quantum #quantumphysics #spinors
Переглядів: 644 870

Відео

Dirac Equation: Free Particle at Rest
Переглядів 36 тис.5 місяців тому
In this video, we explore the solution to the Dirac equation in a simple situation, an electron or positron at rest in the vacuum of space. Link to "An introduction to spinors" paper, by Andrew M. Steane: arxiv.org/abs/1312.3824 Chapters: 0:00 Intro 0:52 Dirac Equation in Momentum Space 3:58 Why Psi is a Bispinor 5:54 How Psi Varies in Space and Time 8:54 Eigenspinors 10:38 A Brief Look at the ...
Deriving the Dirac Equation
Переглядів 78 тис.5 місяців тому
In this video, we'll derive the Dirac equation, and see where it comes from! :) Recommended reading: Introduction to Elementary Particles, by David Griffiths, Chapter 7. Equations from the videos are available as downloadable PDFs on my Patreon. I'll also be on there to answer any questions you might have. www.patreon.com/RichardBehiel Chapters: 0:00 Intro 0:38 Three Principles for the Dirac Eq...
Relativistic Quantum Waves (Klein-Gordon Equation)
Переглядів 51 тис.6 місяців тому
In this video, we'll unify special relativity and quantum mechanics, to derive the beautiful Klein-Gordon equation! Then we'll explore some of its properties, to see what it can (and can't) tell us about the nature of things. This is part of a video series that's building toward an exploration of the Dirac equation, and then a triumphant return to the hydrogen atom. Thanks for checking out this...
Looking for Dark Matter with LIGO, with Dr. Brian Keating
Переглядів 3,9 тис.7 місяців тому
Hey everyone, thanks for checking out this video! Searching for scalar dark matter via gravitational waves is a fascinating idea, and something we might return to in the future on this channel. Link to the paper by Evan Hall and Nancy Aggarwal: arxiv.org/pdf/2210.17487.pdf Brian Keating's UA-cam channel: ua-cam.com/users/DrBrianKeating #physics
The Mass Shell (Relativistic Energy-Momentum-Mass Relation)
Переглядів 23 тис.8 місяців тому
In this video, we look at the Mass Shell, a way of visualizing the relativistic energy-momentum-mass relation, which is a central concept in special relativity. A good understanding of the mass shell will set us up for our upcoming explorations into relativistic wave equations. Stay tuned for the next videos, in which we will derive relativistic wave equations, explore the four-potential and ga...
Why Relativity Breaks the Schrodinger Equation
Переглядів 128 тис.8 місяців тому
In this video, we look at why the Schrodinger equation is incompatible with special relativity, specifically through the lens of Schrodinger plane waves, and the energy vs. velocity curves for relativistic and classical physics. Stay tuned for the next videos, in which we will derive relativistic wave equations, explore the four-potential and gauge symmetry, and eventually will return to hydrog...
Why e is e (Calculating Euler’s Number)
Переглядів 24 тис.9 місяців тому
In this video, we explore why e (Euler’s number), which appears throughout math and science, in everything from the hydrogen atom, harmonic oscillator, radioactive decay, waves, to Gaussian distributions, compound interest, and all kinds of other things, has the value of 2.71828… It’s a quick and memorably derivation, and I hope you enjoy! :) #math #physics
The Hydrogen Atom, Part 2 of 3: Solving the Schrodinger Equation
Переглядів 132 тис.9 місяців тому
In this video, we explore the solutions of the Schrodinger equation for the hydrogen atom. Thank you to everyone who is continuing on this thrilling adventure into the smallest atom in the universe! For those of you who want to see even more of the mathematical details, here's a wonderful paper on the topic, which I highly recommend: faculty.washington.edu/seattle/physics227/reading/reading-26-...
The Hydrogen Atom, Part 1 of 3: Intro to Quantum Physics
Переглядів 209 тис.11 місяців тому
The first of a three-part adventure into the Hydrogen Atom. I'm uploading these in three parts, so that I can include your feedback in the videos as we go along. Sort of like in a lecture when they stop and ask "Does anyone have any questions?". So please let me know if you have questions! :) Part 2 will solve the Schrodinger equation, deriving the energy eigenstates and eigenvalues. Then we'll...
Complex Numbers in Quantum Mechanics
Переглядів 142 тис.Рік тому
A brief introduction to the use of complex numbers in quantum mechanics. This video is intended mostly for people who are learning quantum mechanics and have some familiarity with things like the quantum harmonic oscillator, or the hydrogen atom, but might have some confusion around what all the complex numbers are all about. I hope this video provides you with an improved sense of familiarity ...
A Quick Intro to Fiber Bundles (Hopf Fibration)
Переглядів 100 тис.Рік тому
Fiber bundles are useful and interesting mathematical structures, with applications in quantum mechanics and other areas of math and physics, but sadly they are tragically underappreciated. In this video, I'd like to spread awareness about the beauty of fiber bundles. Read more about fiber bundles: en.wikipedia.org/wiki/Fiber_bundle Read more about the Hopf fibration: en.wikipedia.org/wiki/Hopf...
The Nature of Gravity, Part 2: Projectile Motion in Constant Gravity
Переглядів 6 тис.Рік тому
This is the second video in The Nature of Gravity, a series which explores the nature and essence of gravity. In this video, we analyze the motion of objects which are thrown, or in freefall, in constant gravity near the surface of Earth. We see how the height of an object will decrease over time, then vectorize that situation into a general equation for parabolic motion in constant gravity, th...
The Nature of Gravity, Part 1: Earth's Potential and Acceleration Fields
Переглядів 14 тис.Рік тому
The first video in a series, in which we will explore the nature and essence of gravity! In this video, we meet the concepts of potential and acceleration, primarily as they apply to the space around Earth. Once familiar with these concepts, we calculate the escape velocity of the Earth, moon, and sun. Links for further study: en.wikipedia.org/wiki/Gravitational_potential en.wikipedia.org/wiki/...
A Meditation on Buoyancy
Переглядів 28 тис.Рік тому
This video explores the fundamental nature of buoyancy, and how it arises from molecular collisions and the weight of stationary water. Along the way we will meet some concepts from vector calculus, which will be useful for understanding buoyancy, and which we will also see again in future videos. Please do not be discouraged if you are seeing some of these ideas for the first time, and are con...
The Beauty of Linear Regression (How to Fit a Line to your Data)
Переглядів 152 тис.Рік тому
The Beauty of Linear Regression (How to Fit a Line to your Data)
Intro to the Quantum Harmonic Oscillator in 9 Minutes #PaCE1
Переглядів 25 тис.Рік тому
Intro to the Quantum Harmonic Oscillator in 9 Minutes #PaCE1
Structure from Simplicity: A Look at the Mandelbrot Set
Переглядів 2,5 тис.2 роки тому
Structure from Simplicity: A Look at the Mandelbrot Set
A Visual Proof of the Pythagorean Theorem
Переглядів 2,7 тис.3 роки тому
A Visual Proof of the Pythagorean Theorem
A Visual Introduction to the Zernike Polynomials
Переглядів 9 тис.3 роки тому
A Visual Introduction to the Zernike Polynomials

КОМЕНТАРІ

  • @isaroo13
    @isaroo13 Годину тому

    What if we are looking at this wrong? The diagram at 18:40 shows the dot moving along the line, but what if it is the dot that moves the line instead? Could the dot be a gravitational center with other dots in orbit, creating a mapping of a sphere when you consider every which way something could orbit something else, that create funky patterns when you connect a line between them?

  • @sh1va444-jw5uk
    @sh1va444-jw5uk 14 годин тому

    nope .. the spinor is more simple

  • @ThirstyB3N
    @ThirstyB3N 16 годин тому

    i'm positive that this has and will have absolutely no relevance in my life

  • @enriquebalpstraffon
    @enriquebalpstraffon День тому

    Looking forward to SEE moving particles!

  • @enriquebalpstraffon
    @enriquebalpstraffon День тому

    Amazing

  • @kreynolds1123
    @kreynolds1123 День тому

    I freqently wonder where particles need 720 degrees of rotation to return to their starting state, can it be possible to model it with a mobius strip. And might this geometry sugest something about real particles, or additional compactified dimentions.

  • @sanjinred
    @sanjinred День тому

    Is it that spinors rotate on the real axis and the imaginary at once? thats why you have to rotate it twice to get back

  • @2013Arcturus
    @2013Arcturus День тому

    Someone who watches TV: "Oh you 'do your own research?' 😏" My research:

  • @Vannishn
    @Vannishn День тому

    59:40 or K=(Z/2Z) where 1=-1 !

  • @DrDeuteron
    @DrDeuteron 2 дні тому

    7:25 I like your approach for a first pass, but but really brought it all home for me is that what you are showing at this time same is Z hat. When we are taught vectors, they tell us “it’s an arrow, it’s a magnitude and direction”, and that is a start, but it is fundamentally wrong. A vector is an L=1 spherical harmonic. The next figure you show is L=0, M=0…that is a scalar. They tell us a scalar is a number. BS. A number lives on the number line, while a scalar lives in the 3D space. Then when we get to tensors, everyone is all wtf? What is it? Well, it’s an L=2 spherical harmonic, something that is an eigenstate of rotations….that has 5 degrees of freedom …and so on.

  • @user-nn4if4tl8b
    @user-nn4if4tl8b 2 дні тому

    A question: in class 2 or higher homotopies, can each separate winding share the same point, yet be distinct loops? Is the collapsed end, around the hole, one or many rings fused into one, all sharing the same points?

  • @plopzzzzzz
    @plopzzzzzz 2 дні тому

    Last chance to buy Silver before it explodes.Cuba banks just crashed,coming to a bank near you!!!!!!🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀🚀Do it Now!

  • @LegendLength
    @LegendLength 3 дні тому

    The fact that complex numbers seem to dictate physics, seems to go along with the idea that the universe is a large 4 dimensional fractal.

  • @springdoctor
    @springdoctor 3 дні тому

    Beautiful. Thanks for putting the spark in it!

    • @RichBehiel
      @RichBehiel 3 дні тому

      Thanks, I’m glad you enjoyed the video! :)

  • @dragonbmgo
    @dragonbmgo 3 дні тому

    Wow. I really love this channel alot, and all the videos 🙂❤️ Physics and maths and chemistry is very amazing! I love this soo muchh ✨️ Especially quantum physics 😌

    • @RichBehiel
      @RichBehiel 3 дні тому

      Thanks for the kind comment! :)

  • @phrygianphreak4428
    @phrygianphreak4428 3 дні тому

    Only two shells? And i thought figuring out how to use three shells was hard enough

  • @WEPayne
    @WEPayne 3 дні тому

    Beautiful !

  • @MRHOTEL-hs7et
    @MRHOTEL-hs7et 3 дні тому

    How would these compare to densley interwoven tesseract torus knots?

  • @Delbzy
    @Delbzy 3 дні тому

    Here at 3am

  • @TreyRuiz
    @TreyRuiz 3 дні тому

    Wow incredible video! The only thing I think you left out is the trick when you hold a Coke can and show that you have to spin it twice to get your arm to reset. If you only spin it once your arm is all negative but if you spin it twice it goes back to positive/normal!

  • @Zhavlan
    @Zhavlan 3 дні тому

    Привет с Казахстана. БОЛЬШАЯ ОШИБКА в измерении Вселенной, чёрных дыр, темной энергии, .. Позвольте господа физики судить о всём этом по результату прямого на 84% опыту: В автобусе, в самолёте выполним опыт Майкельсона-Морли и определяя им прямолинейную скорость. - О таком опыте мечтал ещё Эйнштейн. Но мы возможно будем наблюдать постулаты "Свет это упорядоченная вибрация гравитационных квантов. Доминантные гравитационные поля управляют скоростью света в вакууме". Есть предложение на совместное изобретения ГИБРИД гироскопа из некруглых, ДВУХ катушек с новым типом оптического волокна с «полой сердцевиной с фотоно-замещенной вакуумной зоной», где - свет в каждом плече проходит по 16000 метров при этом, не превышает параметры 0,4/0,4/0,4 метра и вес - 4кг.

  • @vb6database
    @vb6database 3 дні тому

    What a wonderful video. It's such a shame that we don't know more about them.

  • @JAYDELROSARIQ
    @JAYDELROSARIQ 3 дні тому

    VACUIN SUCK ALL AIIR OUT VALVE OPEN PULL 2T AIR TANK STORAGE OPEN AIR PUSHED

  • @SaintTrinianz
    @SaintTrinianz 4 дні тому

    If the white board was space-time and the spinors represent the path of electrons, it makes more sense to me...

  • @GlenSify
    @GlenSify 4 дні тому

    Do not hurt the loop

    • @RichBehiel
      @RichBehiel 4 дні тому

      Do not hurt the loop 🙏

  • @user-dc9rf1sy1m
    @user-dc9rf1sy1m 4 дні тому

    So, God exists?

  • @tens0r884
    @tens0r884 5 днів тому

    "allegedly"

  • @Salmanul_
    @Salmanul_ 5 днів тому

    What physics/maths books are you reading rn?

  • @coffeeicecubes2419
    @coffeeicecubes2419 5 днів тому

    beautiful. thank you so much

  • @dazedream2392
    @dazedream2392 5 днів тому

    sorry i missed that part could you say it again

  • @florianclaaen7535
    @florianclaaen7535 5 днів тому

    Drake Had to do a Double take

  • @myasterr
    @myasterr 5 днів тому

    With all the respect to Grant, this is actually way better that 3b1b in terms of explanatory power. I suspect this kind of all-encompassing approach to give away not only the textbook notion, but all the multi-year experience around the topic is what is badly lacking to push science forward.

  • @stauffap
    @stauffap 5 днів тому

    That an electron in a Stern Gerlach Experiment is either Spin-up or -down isn't mysterious at all if you interpret the spin as an angular momentum. That's how we expect angular momenta to behave in such magnetic fields. The mysterious part then is why the electron has just two spin states and why they have the specific value they have. One way to see that the direction of angular momenta must become directionally quantized is to understand to use the bar magnet model of a spinning electron and realise that it takes energy to change the direction of even a classical bar magnet in a magnetic field. It's as if the bar magnetic is in a potential that depends on the angle to the magnetic field lines. We've seen what quantum objects do in such situations. They get quantized. But since we don't know what exactly is spinning in an electron this seems to be useless to calculate anything. It just makes the directional quantisation in the Stern-Gerlach experiment less mysterious. PS: Of course If you imagine a more more realistic realistic spinning electron, you still get the directional quantisation, but you also get precession. Which adds yet another piece of understanding. Since we know that electrons are precessing from measurements, i find it usefull to think through these cases even though a lot of people keep saying that the electron isn't actually spinning.

  • @bartchen5628
    @bartchen5628 6 днів тому

    woah

  • @scoon2117
    @scoon2117 6 днів тому

    I qas looking up fidget spinners!!!!

  • @LunaLuna-gp2jk
    @LunaLuna-gp2jk 6 днів тому

    is that spaghetti monster

  • @mariakatariina8751
    @mariakatariina8751 6 днів тому

    Spinors are how life creates. Gravity is an illusion, and, materia is an illusion. Mass is an illusion. There is no gravity, no materia, and no mass - other than illusive, reciprocal, interdependent and triune. Mathematics has not proven even the point. Point is merely an assumption, an axiom. There cannot be mass for partly the same reasons as there cannot be point; and as there cannot be lavatanssit without triune duality. One might want to try lavatanssit, to understand. The universe is not expanding, but we are going down the drains. Just look at the galaxies. Going through the drain, through the black sun, to and through the point. Logos (loukkaus, lohkous) was from the beginning, and with the beginning. Of course our brains mirror the universe, even in mathematical sense, as our existence is surfing and emerging on and in the waves of eternity. INRIX

  • @humanwrites5752
    @humanwrites5752 6 днів тому

    Maybe it makes sense if we think of the mirrored effect. I work detangling human tissue and I can feel spun fibres that I have to unhook one way then the other to neutralise. This may explain that everything is a mirrorcoil? Maybe past and future neutralising to present.

  • @KaliFissure
    @KaliFissure 6 днів тому

    Great introduction. Thank you. In playing with manifold I came across the form below. If you'll notice it is toroid like but it has only ONE surface. A single rotation covers the forever and then, after passage through zero/maxima it is reoriented, inverted. The one rotation on one side of temporal manifold, the other rotation on the other. Surface(cos(u/2)còs(v/2),cos(u/2)sin(v/2),sin(u)/2),u,0,2pi,v,0,4pi I have some videos exploring is topology. But it seems like the inversion version of spinor

  • @monkdog007
    @monkdog007 6 днів тому

    Did you quote wu tang?

  • @Tomyb15
    @Tomyb15 7 днів тому

    Really good video. Animations are top notch. But I wanted to say that I feel like when you get to the question "why?" as deeply as you get there towards the end, _everything_ starts to look weird. Just plain rotations in so(3) are kinda weird if you try to think about them abstractly. They just don't really feel weird because we are used to seeing things rotate in 3d. But really it *is* weird that you can apply this transform to a thing that continually and smoothly transforms it and never changes it's shape or size and yet not only does this not make it go through itself or anything "unphysical" but you can stop the transform halfway through to turn it into the opposite version of itself? That's weird, even if it just means turning something around. What I wanna say is that at that point of asking "why?" In a pure maths context, nothing is above the question. If it seems like something isn't weird, it's just our inherent biases telling us otherwise. I also found it very interesting to frame Pauli's principle (and the spin-statistics theorem) as being merely congruent with physics but not a true consequence from our models. It's definitely uncomfortable to think about but undeniable nonetheless. My feeling is that there is some way to "derive" the schrodinger equation and its version in qft from some sort of not-arbitrary first principles that would yield the existence of spinors or spin-like thing as an unavoidable consequence, making the theorem a true consequence of the theory but without having to assume pauli's principle. Having to assume the principle is to me 1000 times more uncomfortable than accepting that spinors exist and give rise to the principle.

  • @mojellajasper1434
    @mojellajasper1434 7 днів тому

    seem quasi almost

    • @mojellajasper1434
      @mojellajasper1434 7 днів тому

      Its like the spinner rotation creates an extra dimension

  • @jeanf6295
    @jeanf6295 7 днів тому

    Another fun related observation : in two dimensions, we have another class of quasiparticle besides fermion and bosons : anyon. This can be linked to the fact that physically exchanging two particles by moving them in two dimension can be done clockwise or counterclockwise. There is a link to be made with Feynman path integrals, by introducing weight factors to classes of paths.

  • @user-hg2sh5lv8b
    @user-hg2sh5lv8b 7 днів тому

    صبح تا شب دروغ میگن این معادلات اصلا درست نیست دروغه

  • @user-hg2sh5lv8b
    @user-hg2sh5lv8b 7 днів тому

    چرا زیر نویس فارسی نداری ویتنامی داری فارسی نداری گاو از تو بهتره

  • @realityisenough
    @realityisenough 7 днів тому

    I lked the pictures

  • @PJRiter1
    @PJRiter1 7 днів тому

    Excellent video! Please do twistors!

  • @ForumArcade
    @ForumArcade 7 днів тому

    Your intro is way too late for me, I fell headfirst into existential philosophy as a teenager and never made it back. Because there is no going back. Much like the singularity at the core of a black hole, all paths merely lead deeper in. God time and space and possibility and consciousness and experience and the fact that anything exists at all are such wonderfully stimulating topics of inquiry.

  • @Frank-ie8dh
    @Frank-ie8dh 8 днів тому

    There is nothing mysterious about spinors. He is right about it being the square root of geometry, they are called rotations in geometric algebra by half angles. And yes, they have physical significance

  • @ghazad1660
    @ghazad1660 8 днів тому

    as an art student, i'm clicking off. I don't want to have to change carrees cause of one youtube video.