9 ай бұрын
Жыл бұрын
Жыл бұрын
Жыл бұрын
Жыл бұрын
Жыл бұрын
4 жыл бұрын
4 жыл бұрын
Пікірлер
@gabitheancient7664 19 сағат бұрын
heyyy do you use manim to make your videos? I'm planing of making a video on my own and I love the way you specifically do animations so I'm curious
@PissyKnish 20 сағат бұрын
This is Satanic.
@ワドゥリト Күн бұрын
Your ability to make me laugh at my own ignorance is unparalleled.
@onajejones3259 Күн бұрын
something just tickles my elementary particles in my quarks, hearing "Electromagnetism as a Gauge Theory"
@KipIngram Күн бұрын
1:00:24 - And NOW you're going to shove electromagnetism in by hand. Because that's what it's going to take to force local phase symmetry. And that is something of a miracle - it feels miraculous to me that the whole gauge approach works. But it IS something new - it wasn't latent in the theory to start with. I think the real fundamental lesson here is that local phase invariance is simply required, and we are compelled to do whatever it takes to enforce it - the corresponding physics will be there. And that seems like the only explanation for the huge success that gauge theories have proved to be.
@KipIngram Күн бұрын
I think the salt grain analogy is poor. That really has nothing to do with the dynamics of particular particles. I agree with you, though, that the "backward in time" bit is also misleading - we just PERCEIVE time flowing in a particular way, and we can't perceive it the other way. We perceive what the electron solution is doing forward in time, and we perceive what the positron solution is doing forward in time. The whole backward in time thing is just a way of "regarding the math," and not really a very useful one. The positron does something "opposite" to the electron, that's all. You might convince me to think of it (a little) as a "negative energy" solution, because you can get energy to show up in that exponential, and it can carry the sign as well as anything else can. But when an electron and positron annihilate, you get double the energy, not zero energy, so that's misleading too, really. I think it's best to not try to put any such simple-minded interpretation on it.
@KipIngram Күн бұрын
The existence of electric and magnetic fields isn't weird at all. It's an inevitable consequence of the existence of even a single conserved quantity in nature. Not some particular conserved quantity, but ANY - so long as there is something, anything, conserved, we have to have these fields. So that's the answer to your question "Why is electromagnetism a thing." I don't stay up at night over that anymore. Basically, it's impossible for them NOT to be a thing. The same line of reasoning explains why there's space, too. It also arises from the existence of any arbitrary conserved quantity. Most of the things you take as your starting point here are in fact consequences of conservation.
@KipIngram Күн бұрын
Just one comment on your presentation style. In some places you have words in your narrative that kind of go like so: "Hmmm, how should we do this... Oh, I know - let's do this." And then you carry on. But you just could NOT have made a video this long without a script - this is not something you just coughed out on the spur of the moment. Given that, those words come off as ever so slightly phony. Staged, so to speak. It would have felt more natural and authentic to me if you had just systematically moved through the logical progression, without the feigned moments of thought. The little chuckles also seem kind of contrived and pre-planned. Good coverage of the material overall. I do wish you'd spent more time on the physical side of things, in addition to the math.
@tomgraupner171 2 күн бұрын
I hope for "Weak Force as a Gauge Theory" to come up next. That would be wonderful
@tondog54 2 күн бұрын
The SU(2) and SO(3) stuff was always so arcane for me until this video. Good stuff 👍👍👍👍
@PAULGORDON-ki5zj 2 күн бұрын
Thanks!
@RichBehiel 2 күн бұрын
Wow, that’s very generous! Thank you Paul! :)
@noobjsooo6093 2 күн бұрын
That was much more easier than those which i already had watched. That's amazing.
@RichBehiel 2 күн бұрын
I’m glad to hear that! :)
@rojopantalones9791 2 күн бұрын
I don't know what it is about this video in particular, but I often find myself here. I'll get a little stoned and put it on to help me fall asleep, only to end up attempting to visualize all the math involved. I figure out something new every time, like being able to "see" the math that explains time as its own dimension. I don't know the more basic calculus to explain exactly what it is I'm seeing, but it certainly made sense at the time lol. Something about axes of rotation beyond the degrees of freedom we experience in 3D physical space allowing space to move up into it, like how disparate points on a planar graph can both be solutions to an unbroken function by lifting off the plane and into 3D space, rotated 90° from the plane we're more used to working within. This is just a wonderful video for engaging my mind and challenging it. As I learn more math, I find myself with a deeper understanding of this subject and more questions to find the answer to.
@MontoyaMatrix 3 күн бұрын
I must be a good boy, or God might give me a Spinor Tap.
@ultrio325 3 күн бұрын
I think I see why people study this for years in uni now...
@thomastheiner5780 3 күн бұрын
Can’t wait for the follow-up videos on how this! This is one of those exciting topics I can just kinda feel has deep implications I’m not smart enough to grasp yet lol.
@jijuanzheng4790 3 күн бұрын
complex number isn't mandatory in QM, it just a simpler way of computation tool comparing to matrix, we can use matrix with real values only to do the same job as i, so in fact it just mean that quantum world is very geometric and i is a need to do rotation in geometric world
@GoodBaleadaMusic 3 күн бұрын
It's like a omni gyroscope so reality orients at points. We would just phase into instant destruction without it. I dunno i did mushrooms last night.
@JCrustii 4 күн бұрын
what if we spin the row of positives and the row of negatives infinitely fast and then sent a positive/negative through it?!?
@tomgraupner171 4 күн бұрын
Please allow one question, Richard. @21:31 there are 2 solutions of the Dirac Eqn. As this is a linear eqn, I might create solutions as a linear combination (superposition). But that would mean that I could measure one partical once as an electron and once as a positron and - - - this sounds wrong and weird. Where is my fault?
@dunravin 4 күн бұрын
"spacetime" huh. Is this really just 4 number lines and isn't it limiting to think of them as time, x, y, z? Time is a reciprocal of energy, it's only connection to space is through space's reciprocal matter, energetic events (of matter) to the nth power over time describes frequency but time here is still just a gauge stick of some other arbitrary cyclic energetic event. Okay you need four number lines to do the maths tricks then why not use area squared like two intersecting planes perpendicular to each other. This way time is liberated and free to be the reciprocal of energy and not some silly distortion of space. Using area squared instead of "spacetime" you can still describe boxes and spheres etc, I am four dimensional, I have a left and right side and a front and back side with a central axis. If I observe a box I can describe it in terms of x, y, z but from the box's point of view it has the same left and right sides, front and back sides and a central axis. The revelation here is WE DON'T NEED THIS SPACETIME NONSENSE. It's wrong and if you think it's not wrong you're looking at it all wrong.
@roodog1 4 күн бұрын
2:08:00 I took a class on general relativity as a junior in undergrad, and we had a final project that we could choose. I choose to derive the action integral for space time. The process of building the lagrangian density and then doing WAY too many integration by parts to move the variation term around has brought back many memories, and actually makes this derivation pretty mellow to follow. I imagine it’s the same process for any complicated Lagrangian. It’s so cool when something I learn in school shows up in a random KZbin video a year later.
@loveless-savage 4 күн бұрын
50:15 This is an absolutely crazy lore drop
@danielwalker5682 4 күн бұрын
Superb video. I am an engineer just wanting to master spherical harmonics, but this makes me want to go further. Thank you.
@RichBehiel 4 күн бұрын
Thanks, I’m glad you enjoyed the video! :)
@EMPP81 4 күн бұрын
With life pounding and pounding at the moment, I'm glad I can watch this video for the second time during Christmas. It's a masterpiece of no comparison, that gives me so much Joy such that I can postpone driving my car into a brick wall at 200km/h. Maybe I will just finish my physics phd instead. The beauty of it is worth living to see as much progress in the field that you can possibly absorb.
@RichBehiel 4 күн бұрын
Wow, that’s quite a comment! I’m glad you found so much joy in this video. Please don’t drive your car into a brick wall. I know life can be hard. The progress in physics is exciting. It can also be helpful to look forward to upcoming space missions, as an incentive to stick around and see what the future brings. I’ve used that trick before. We’re living in exciting times. I definitely resonate with you though. Just a few days ago, I got dumped by my girlfriend of three years. We had been living together for a year. I was convinced she was the one, and was saving up for a beautiful ring. But she recently moved 2-3 hours away to start her PhD, and we started to drift apart, with the distance. So we figured I should move in with her, keep our relationship going, and so I found a way to shift to more of a remote role at work, packed up my apartment, and was all set for the move. She was on board with all this, also excited to pick up where we left off. But, she had a last-minute change of heart. I don’t entirely fault her for that. Our lives just sort of diverged, I guess. But it’s weird now to be living in our old apartment, alongside the old things of hers that she didn’t take with her, realizing I’m in that category too. You know, when moving, you have to decide what to take with you, and what you no longer need. It’s not great to be in the category of no longer needed. I didn’t see that coming! To make matters worse, I already sold my bookshelf, as I was preparing to move. So now I’ve got books all over the floor. An unintended metaphor, I guess. The one silver lining is that when you’re at your lowest, it becomes most clear what you have to do. And no, it’s not driving into a brick wall, though I fully understand the temptation. In my case, I have to pick the books up off the floor and put their equations in the computer and share them with the people of the internet. In your case, it sounds like you have to finish your physics PhD. If you’re watching physics videos during Christmas, then I do believe you have the spirit and character required to complete that PhD! And the world will be better off having you in it, with your advanced knowledge of physics. We need more people like you.
@EMPP81 4 күн бұрын
@RichBehiel Wow, that's very tough as well. We might be able to figure out the fundamental equitations of physics, the equations of love are a completely different cookie to crack. But don't worry, I'm not really going to drive into a brick wall. It was more an expression of how hard live can be, but if you don't experience the super hard part, you cant enjoy life's best. Thanks for your kind reply. Live is suffering, but we are in it for the great and beautiful moments. The piece of art you put here on youtube is one of them. Thank you for that. Despite everything, a merry Christmas and all the best for the new year.
@tomgraupner171 4 күн бұрын
if there will ever be a poll for the best physics video here on the tube: IT'S THIS !!! Thank you so much for your hard work.
@RichBehiel 4 күн бұрын
Thanks for the kind comment! :)
@RVeda-vh5on 4 күн бұрын
16:38 With every morning coffee I recall your elegant (and eye-opening) proof that 3D rotations are multiply (in particular, 2-ways) connected. Traditional Costa Ricans have typically lived long and well on little. Nothing exemplifies their basic, economic and practical approach to life better than their coffee maker, for which one picture says it all: cdn.shopify.com/s/files/1/0669/0435/9171/files/chorreador_600x600.jpg?v=1698774064 When my cup is full I naturally place another cup beside it and shift them together so that the second cup catches the remains of the still-running coffee stream. You can easily visualize the path that stream takes, from the center of the first cup to the center of the second. (In a previous post I mentioned this 'two-cup' topology as an alternative mapping of the 3D rotation space, one that actually maps the two versions of the 'same' rotation onto two distinct points). I still am struck that this 'split personality' of rotation state seems to come only when the state is considered not in isolation but rather in its continuous connection, either with past time (its 'path' or loop) or with neighboring space (those amazing Hines 'belt trick' animations). Also by the fact that some particles have lepton, some boson character, and the things (like 'massness' vs. 'force-mediator-ness') that seem to come with that. Oh well: 'Whatever you think, it's more than that'. That seems certain. One can either despair or rejoice over that; the latter seems the more fruitful course.
@pelasgeuspelasgeus4634 5 күн бұрын
Euler formula is simply wrong. One side is the exp function which tends to infinity by definition and the other side is a sum of trig functions each ranging from -1 to 1, ie it's finite. So how can they be equal. Also, the derivation from Taylor series is erroneous because that series is validated for real numbers. Is iθ a real number?
@schrod-f1s 5 күн бұрын
This is one of the best videos I've ever seen in my life. This video probably summarizes an entire course in relativistic quantum mechanics. It showcases such deep fundamental beauty and elegance in the logic and belief in the symmetries that blossom into concrete physics reality . It's just beautiful in every sense of the word
@RichBehiel 5 күн бұрын
Thanks for the kind comment, and I’m glad you enjoyed the video! :)
@schrod-f1s 5 күн бұрын
@@RichBehiel appreciate you man
@panchgo5620 6 күн бұрын
Turns out i hate school but love learning this stuff on my own time. Thanks for teaching 😊
@RichBehiel 5 күн бұрын
Thanks for learning! :)
@fernandohadad 6 күн бұрын
At 07:00, where you prove Euler's formula using Taylor series, I wanted to share an elegant alternative proof that reveals the deep geometric meaning behind this formula. By defining f(θ) = e^(i·θ) and examining its derivative f'(θ) = i·f(θ), we can write f(θ) = u(θ) + i·v(θ) where u and v are real functions. This leads to a simple system of differential equations: u'(θ) = -v(θ) and v'(θ) = u(θ). Combined with the initial condition f(0) = 1, these equations show that u(θ) = cos(θ) and v(θ) = sin(θ), proving that e^(i·θ) = cos(θ) + i·sin(θ). What makes this proof particularly illuminating is that f'(θ) = i·f(θ) shows us that at each point, the rate of change is perpendicular to our position in the complex plane (since multiplying by i rotates by 90 degrees) - precisely the behavior we expect in circular motion. This deep connection between complex numbers and rotational motion helps explain their natural emergence in quantum mechanics, where wave functions and phase relationships are fundamental to describing quantum states.
@Simplecrow7584 6 күн бұрын
Enrolled into KZbin University class for the night!
@rayanchtt 6 күн бұрын
same here!
@PhysicssperspectiveTamil 7 күн бұрын
Part 3 please.
@PhysicssperspectiveTamil 8 күн бұрын
Make that 3rd video soon, please.
@AbdiPianoChannel 8 күн бұрын
In my world positive attracts positive
@RichBehiel 4 күн бұрын
🙏
@Waltonruler5 8 күн бұрын
Watched this when it first came out, but I've been working my way through more physics and math content. Coming back to this now, im wondering why A transforms as it does with a local phase transformation. I understand that it *can*, that adding a gradient of a scalar field leaves the Faraday bivector unchanged, and I understand this is the desired behavior to preserve local phase symmetry of the Lagrangian, but is there some deeper source of the four-potential that would dictate its transformation under a local phase change?
@RichBehiel 8 күн бұрын
That’s a great question! :) There are different ways of thinking about it. My favorite way is to imagine what kind of a mess would be created by a local phase transformation in psi, if A didn’t exist. Well, as you alter the time derivative and spatial gradients of the wavefunction, you’d be creating a whole energy-momentum four-vector field of a mess. It’s precisely that mess that makes it so surprising that local phase symmetry should be a thing. At first glance it seems like this should not be a thing, because it would require modifying the laws of physics, modifying the vanilla Dirac equation that comes from relativistic energy-momentum considerations. And the simplest modification would simply be to suppose that there exists a four-vector field which can be transformed in a complementary way to psi, so that it can soak up the energy-momentum mess, and restore balance to the universe. So that’s the electromagnetic four-potential A. This way of thinking is very mathematically elegant, but it leaves us wondering why A should exist at all, and for that matter where local phase symmetry comes from. And that’s a very complicated question. In my upcoming video, Superconductivity and the Higgs Field, we’ll go one level deeper than the phase symmetry of electromagnetism, seeing how it’s embedded in the electroweak gauge group. That still won’t answer your question, frankly no good answer yet exists, but it’ll add some context.
@eventyonwhite686 8 күн бұрын
you just blew my mind with those tasty intuitions man <3
@AndreaCalaon73 10 күн бұрын
Dear Richard, let me be very cheeky and "reveal" to you why QM needs spinors/complex variables ;) It is straightforward, no mysticism needed. First a short premise that you already know: In the algebra that everyone should be using, i.e. geometric algebra, a spinor is a simple geometrical/algebraic entity (probably the simplest multi-vector): an un-normalized rotor, i.e. the combination of a scalar and a bivector (a plane in my mind). Rotors rotate things of any dimension, and in any space (like 3D or 4D-spacetime). They act bilaterality, on the left and on the right of the operand, with half angle each time. This is why spin 1/2 is purely a geometrical fact, not at all specific to QM; and it applies identically in standard mechanics. Here the reason for spinors in QM: The spinor variable in the Pauli and Dirac equations describes two things at the same time: 1) the orientation of the spin plane, 2) the probability density. The other free parameter in the spinor is the zitterbewegung phase, which is an "unused" part of the rotor rotation. (For the Dirac’s spinors there is an additional parameter, the angle beta, the meaning of which is still debated). 1) The spinor variable of QM rotates a reference plane, precisely the "mystical i" that appears explicitly in the equations, to the orientation of the particle spin plane at each point in space. 2) Since the spinor is an unnormalized rotor, its norm can be used to encode the probability density. Actually, it must encode the square root of the probability density, since the rotor has to be used twice on its operand. In geometric algebra the squaring is done with the geometric product (what else?), but for the "complex world" one must use the complex multiplication by the conjugate (without geometric algebra there are always pointless complications). As David Hestenes says: "The Schrödinger equation describes an electron in an eigenstate of spin". Best of luck Richard! Your channel is fantastic!
@superslayerguy 10 күн бұрын
I’m just watching this so I feel smarter :) no good stuff though, I dropped out of college but I love shit like this I know it will all gel over the years, thank you for taking the time to put this highly technical and well explained lesson :)
@RichBehiel 10 күн бұрын
Thanks, I’m glad you appreciate the video! :)
@eqwerewrqwerqre 11 күн бұрын
Bro i understood like 90% of this! Finally! I'm one semester into grad school and I'm finally beginning to unlock the real information in all these crazy KZbin lectures. Thanks for making banger videos every time man <3
@RichBehiel 11 күн бұрын
Awesome, I’m glad to hear that! :)
@mohaimin2785 11 күн бұрын
Is it normal that I don't understand it as an 12th grader, cuz I've been trying to understand it for a week now @@RichBehiel
@ArchibaldPrime 12 күн бұрын
Y'know what? I think i can fall asleep to th-
@Most_Trustworthy_Weasel 12 күн бұрын
Chris Langan does
@phlebas-uq6fv 12 күн бұрын
This is absolutely superb stuff! Would it be possible for you to share just one or two examples of the manim (I'm assuming) code you are using to render this? Would be a lovely starting place for my own explorations to get a better feel for these spaces.
@RichBehiel 11 күн бұрын
Thanks, I’m glad you liked it! :) I use matplotlib in Python. As of my last video, I started posting Python codes to my Patreon. There are some SU(2) flag animations codes on there, and one of these days I’ve been meaning to clean up and post the squiggly loop codes too. But I’ve got to finish my next video first, hoping to post it before the end of the year.
@phlebas-uq6fv 11 күн бұрын
@@RichBehiel Great! Will find the patreon - thanks
@NebMunb69 13 күн бұрын
Oh man. I really thought this was a video about those after-image, rainbow looking blobs you see when you close your eyes
@johndeer-he5de 13 күн бұрын
You appear to be a decent human, unlike myself. I appreciate you explaining everything as you go for those that have difficulty in comprehension of complex concepts
@fade1racecarpeek 13 күн бұрын
Need a 3rd part... but ur the goat
@minanovkiril 14 күн бұрын
just give me visualised spaces. the words are shit. just put the math into visual physics and it will work. this will counterintuitivelly explainnthe math as well. the texts are just fuzzy bs
@L.DOT.P. 14 күн бұрын
That was amazing thank you so much!!
@CombFilter-vo4gk 14 күн бұрын
Complex numbers seem to me to be a fudge. They appear when you get a solution that makes a function equal zero when at no point does the function equal zero.