Richard Behiel
Richard Behiel
  • Видео 20
  • Просмотров 1 960 133
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...
Просмотров: 749 348

Видео

Dirac Equation: Free Particle at Rest
Просмотров 38 тыс.6 месяцев назад
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
Просмотров 83 тыс.7 месяцев назад
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)
Просмотров 54 тыс.7 месяцев назад
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
Просмотров 4,1 тыс.8 месяцев назад
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 RUclips channel: ruclips.net/user/DrBrianKeating #physics
The Mass Shell (Relativistic Energy-Momentum-Mass Relation)
Просмотров 24 тыс.9 месяцев назад
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
Просмотров 130 тыс.9 месяцев назад
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)
Просмотров 26 тыс.10 месяцев назад
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
Просмотров 138 тыс.11 месяцев назад
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
Просмотров 224 тыс.Год назад
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
Просмотров 147 тыс.Год назад
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)
Просмотров 103 тыс.Год назад
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
Просмотров 7 тыс.Год назад
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
Просмотров 15 тыс.Год назад
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
Просмотров 28 тыс.Год назад
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)
Просмотров 152 тыс.Год назад
The Beauty of Linear Regression (How to Fit a Line to your Data)
Intro to the Quantum Harmonic Oscillator in 9 Minutes #PaCE1
Просмотров 26 тыс.Год назад
Intro to the Quantum Harmonic Oscillator in 9 Minutes #PaCE1
Structure from Simplicity: A Look at the Mandelbrot Set
Просмотров 2,7 тыс.2 года назад
Structure from Simplicity: A Look at the Mandelbrot Set
A Visual Proof of the Pythagorean Theorem
Просмотров 2,8 тыс.3 года назад
A Visual Proof of the Pythagorean Theorem
A Visual Introduction to the Zernike Polynomials
Просмотров 9 тыс.3 года назад
A Visual Introduction to the Zernike Polynomials

Комментарии

  • @zyme5998
    @zyme5998 2 часа назад

    I clicked on this video having no idea what a spinner is, but the thumbnail made me think you might be talking about what's called a half-spin: en.wikipedia.org/wiki/Spin-1/2

  • @curlyhum1276
    @curlyhum1276 6 часов назад

    here is a thought this equation chained to a few others could prove my assertion: that everything within the whole space room is nothing more then sets or groups of matrices within matrices or as some would say dimensions within dimensions , two off the wall examples, dark energy dark matter, current quantum theory! the other question is , what does that equation look like in Physics? thinking is a chicken feeding a shark, the shark in your brain mind chain, the chicken is the food your brain/mind eats , the food you use determines the outputs you get or want! i f you think on end for days about a single subject your mind at all levels is in a way forced to consider all possibilities you know of? ex, E=MC^2 amazing equation from the solid state to the wave state, you are forced to consider everything this represents with everything you know and what is known? functions within functions in an algorithm that form fractiles scalar waves at the super position edge of space time, some call it perfect symmetry, some thing or some one set this up at some point in past history? this is not a random big bang multiverse , this is engineered by a super technology lightyears from E=MC^2 . the question is what is the relationship between these over layed matrices? think of it in terms of field energy boundaries, within a set of fields how many fields are there? what would the equation look like? The Great Unknown can be known it just take work and faith. .............Sci24

  • @mrhassell01
    @mrhassell01 7 часов назад

    Check Élie Cartan’s work, 1913 or “Spinors and Space-Time” by Penrose. The “square roots” in sections of vector bundles, describe intrinsic angular momentum (spin) of particles like electrons.

  • @MarkSummersCAD
    @MarkSummersCAD 10 часов назад

    Nice video, but what about grunge and disco.

  • @NathanaelNewton
    @NathanaelNewton 12 часов назад

    I'm not sure how i got here but this is really great.

  • @hydromarlon4168
    @hydromarlon4168 17 часов назад

    You are a master teacher and conveyor of ideas

  • @fxy17
    @fxy17 22 часа назад

    2:35 it feels "geometric"

  • @jeffqamoos8746
    @jeffqamoos8746 День назад

    Amazing and highly illuminating. Keep doing this.

    • @RichBehiel
      @RichBehiel День назад

      Thanks, I’m glad you enjoyed the video! Working on the next one now :)

  • @warrenchu6319
    @warrenchu6319 День назад

    I wish I had this video around when I was taking quantum 50 years ago. I had to visualize all of this in my head, not knowing if I was right or wrong. Plus, imagine furiously writing down all these derivations from the blackboard while trying to understand the logic hoping my notes will make sense later on. Well done. ;-)

    • @RichBehiel
      @RichBehiel День назад

      Thanks for the kind comment, and I’m glad you enjoyed the video! :) And I can relate to your experiences writing down derivations from the blackboard 😅 I hope these videos can make physics concepts more accessible.

  • @mikerodix4800
    @mikerodix4800 2 дня назад

    Rotating twice to get back to where you started makes sense if you rotate in the opposite direction like turning up the radio knob

  • @laurenfowler2314
    @laurenfowler2314 2 дня назад

    Incredible video. So well made. Im an undergrad and found this video so interesting and amazing. Thank you

    • @RichBehiel
      @RichBehiel День назад

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

  • @flonker5961
    @flonker5961 2 дня назад

    What video do I need to watch first to be able to understand this one?

  • @RogueElement.
    @RogueElement. 3 дня назад

    2 mins in... And I'm already harrdd😍🤭😈

  • @dillbourne
    @dillbourne 3 дня назад

    14:16 Omg there's no such thing as a particle at rest

  • @witnessprotection4233
    @witnessprotection4233 3 дня назад

    make a harder problem next time.

  • @witnessprotection4233
    @witnessprotection4233 3 дня назад

    done.

  • @witnessprotection4233
    @witnessprotection4233 3 дня назад

    sure. piece of cake.

  • @witnessprotection4233
    @witnessprotection4233 3 дня назад

    you're asking for a point that exists as all points?

  • @witnessprotection4233
    @witnessprotection4233 3 дня назад

    what the fuck is a spinor?

  • @witnessprotection4233
    @witnessprotection4233 3 дня назад

    well i'm pleased you covered existentialism.

  • @witnessprotection4233
    @witnessprotection4233 3 дня назад

    what in the fucking horse fuck is this?

  • @RVeda-vh5on
    @RVeda-vh5on 3 дня назад

    It occurs to me that the surface points of the axis-angle sphere could be identified with the opposite points, rather than of the _same_ sphere, of _one other_ sphere - a slightly different topological object, but one that clearly divides into two classes the rotations whose result is identical in flag space - preserving a clear distinction between the 2 types of continuous incremental path which achieve the rotation. A single 360 degree rotation puts you in the second sphere, and does _not_ close the loop in the dual-sphere space. It is more like the spinor's or lepton's point of view. The 2 covers become 2 different spheres. Which sphere are you in?

  • @whywhy7646
    @whywhy7646 3 дня назад

    Thank you so much for making these videos, they are so good

    • @RichBehiel
      @RichBehiel 3 дня назад

      I’m glad to hear you’re enjoying the videos! Thanks for watching :)

  • @patrickshelton5546
    @patrickshelton5546 3 дня назад

    Oh wait ...there's more than one definition?

  • @exittomenu
    @exittomenu 3 дня назад

    *nods head* Mmhmm yes Indeed

  • @girlkisser
    @girlkisser 3 дня назад

    in the you'd tube. straight up wortching it. and by "it". haha lets just say. my spinor

  • @whywhy7646
    @whywhy7646 4 дня назад

    Wow. This video is so underrated. I only know basic high school physics, and it wasn't that hard for me to follow this video. It was so fun listening to your simple yet detailed explanations of everything

    • @RichBehiel
      @RichBehiel 3 дня назад

      I’m glad to hear that! :)

  • @KingJAB_
    @KingJAB_ 4 дня назад

    Finally someone who acknowledges the possibility to intuit 4D instead of hand waving it as unimaginable

  • @MaNuLaToROfficial
    @MaNuLaToROfficial 4 дня назад

    why this ended up in my recommended i'll never know. i flunked Algebra twice in high school lol

  • @JP-xt6hl
    @JP-xt6hl 5 дней назад

    This is hard. 😂

  • @Tharushi_SM
    @Tharushi_SM 5 дней назад

    Thank you so much for the great content. So, in atoms there’s degenerative orbitals right, where the energy level is the same. And in one of these orbitals two electrons of different spin states exists. Electrons are existing as a standing wave, and now that there’s two electrons in the same energy level, how do they exist? Do they interfere with each other or not ? Thank you.

  • @Tharushi_SM
    @Tharushi_SM 5 дней назад

    7:35 so this is how 2D organisms see the world. And how we see 4D situations.

  • @shmexermeister5701
    @shmexermeister5701 5 дней назад

    52:39 what is that dark spots in colorful line?

  • @WEtOnGTim88
    @WEtOnGTim88 5 дней назад

    ❤ your voice!!! I just subbed because I'm fascinated by science and I can fall asleep listening to you!!Thank you for your energy, nothing is lost!

  • @Nabeel2607
    @Nabeel2607 5 дней назад

    Will there be later videos on the fine and hyperfine structure of hydrogen?

    • @RichBehiel
      @RichBehiel 5 дней назад

      Fine structure yes, hyperfine hopefully someday, after going into second quantization. Part 3 will get into the fine structure, and things that can be calculated with the Dirac equation & first quantization.

    • @Nabeel2607
      @Nabeel2607 5 дней назад

      @@RichBehiel Awesome, I look forward to it!

  • @wolfxlover
    @wolfxlover 5 дней назад

    Hey, I reach out as a University student passioned by learning. My dream is making animations / visuals like you do, but unfortunately, nobody in my CS department does this. I want to join research in Physics, and offer rendering visuals as what I can contribute in exchange for learning more about Physics / more time with Physics professors. Do you think you could give me an explanation on what I can learn in order to develop this as a skill? I would be infinitely grateful if you could provide me with some guidance over this matter. :D Resources or describing your own experience getting into it would be a world of help. Or even just a list of things I need to look at in order to be able to do this. Thanks for your time, if so.

  • @6BWakaWaka
    @6BWakaWaka 5 дней назад

    An amazing presentstion and extremely insightful video, one of the best. Thank you for this!

    • @RichBehiel
      @RichBehiel 5 дней назад

      Thanks for the kind comment, and I’m glad you enjoyed the video! :)

  • @greatestytcommentator
    @greatestytcommentator 5 дней назад

    .. my brain is now broken... thanks.

    • @RichBehiel
      @RichBehiel 5 дней назад

      Welcome to the club 😅

  • @rwshaw1234
    @rwshaw1234 6 дней назад

    Really SUPERLATIVE lesson, Richard. This one is a keeper. Thank you!

    • @RichBehiel
      @RichBehiel 5 дней назад

      Thanks, that means a lot! I’m glad you enjoyed the video :)

  • @joshuapatrick682
    @joshuapatrick682 6 дней назад

    51:59 why do the “strings” in the animation only appear flexible in relation to a relatively small space around the thing to which they are connected. I don’t have a deep enough understanding of physics to understand it but for a layman it seems to be a violation for the point of illustration?

  • @joshuapatrick682
    @joshuapatrick682 6 дней назад

    Finally, someone with deep knowledge of physics who believes that Lorentz Invariance is fallible! That’s refreshing!

  • @SerGio-xs9ss
    @SerGio-xs9ss 6 дней назад

    Is it possible to get this site to play with harmonics ? Thank you.

  • @mahapeyuw5946
    @mahapeyuw5946 6 дней назад

    I find that thinking in images helps me work through. I was watching a different video that mentioned spinors and boom i remembered this one and had to share what i think will help. Think of the flagpole analogy as going round a mobius strip. If this doesn't add up, I'd like to know.

  • @mayanightstar
    @mayanightstar 6 дней назад

    I understand like 7% of the content of your videos but you're funny and your voice is nice so keep it up

  • @reverend11-dmeow89
    @reverend11-dmeow89 7 дней назад

    Thank you foer extending the visuals into Tesseract terrortory. (not a typo, as this maths scares most)

  • @Holonink
    @Holonink 7 дней назад

    sorry , i missed a couple classes, can I borrow someone's notes?

  • @ryangraffius1474
    @ryangraffius1474 7 дней назад

    If (at 6 mins) electrons/positrons live on separate ‘half’s’ of the bispinner, in separate ‘channels’ could it be appropriate to assume that in the special case scenario a Mid/Side transformation of the Dirac impulse can occur? As in doubling and or halving of the magnitude of the impulse? Sum and Difference? As above, so below, if indeed the Dirac is an analogue to the Kronecher Delta?

    • @ryangraffius1474
      @ryangraffius1474 7 дней назад

      As an aspect of statistical uncertainty under a bell curve (facilitated by a M/S transformation) to address the Möbius transformation of the polar coordinates. We may not know where they are, but in the special case we know the highest and lowest (asymmetric balancing) of the magnitudes with respect to alignment with the angular momentum.

  • @bonosmith1113
    @bonosmith1113 7 дней назад

    Idea for future video: If GR is second order (due to Lorentz inv. - like Maxwells) and we know it to be experimentally verified how do we reconcile the “first orderness” of Dirac Eq. ? Ie. How does an electron psi function get altered by gravity? Square Dirac?

  • @Reishira-ln73ks
    @Reishira-ln73ks 7 дней назад

    Study holograms

  • @StoicVision
    @StoicVision 7 дней назад

    "you mind if I put on some white noise? it helps me sleep"