#science #physics #ideas The Biggest Ideas in the Universe | 14. Symmetry

#science #physics #ideas The Biggest Ideas in the Universe | 14. Symmetry 77,680 viewsJun 23, 2020 Sean Carroll 154K subscribers The Biggest Ideas in the Universe is a series of videos where I talk informally about some of the fundamental concepts that help us understand our natural world. Exceedingly casual, not overly polished, and meant for absolutely everybody. This is Idea #14, "Symmetry." Different manifestations of symmetry are at the heart of much of modern physics, so it's worth looking at how we should best characterize it. That's leads us into the mathematics of group theory. My web page: http://www.preposterousuniverse.com/ My YouTube channel: https://www.youtube.com/c/seancarroll Mindscape podcast: http://www.preposterousuniverse.com/p... The Biggest Ideas playlist: https://www.youtube.com/playlist?list... Blog posts for the series: http://www.preposterousuniverse.com/b... Background image by Sylvia Cordedda at DeviantArt: https://www.deviantart.com/c-91/art/N... #science #physics #ideas #universe #learning #cosmology #philosophy #math #grouptheory #symmetry 164 Comments rongmaw lin Add a comment... Sean Carroll Pinned by Sean Carroll Sean Carroll 1 year ago As noted by "markweitzman's wannabe a theoretical physicist school," I was wrong to say that O(n) is the direct product of SO(n) and Z_2. That's true when n is odd, but when n is even it's a "semidirect product." https://www.youtube.com/watch?v=yCxacFBLHIY&lc=UgxJ8yI8fMwI7n2XMsF4AaABAg&ab_channel=SeanCarroll 32 mironmizrahi mironmizrahi 1 year ago Hi Sean, I am a big fan of your work and a Patreon supporter of Mindscape. I wanted to express my deep gratitude to you for doing these videos. They fill a massive gap I have had for ages where the 'usual' lectures (by your and many others) have been too high level and a proper physics course too detailed and time consuming. I am sure there are many others like me, who are not laymen but also not able or willing to study physics at a university. Yet we are fascinated by physics and want to learn as much as we can. If anything, I wish there was more math in these videos:). But they have been, nevertheless, something I eagerly await every week. I sincerely hope you will continue until you are done even if the whole Covid situation improves markedly. 19 Dr10Jeeps Dr10Jeeps 1 year ago Dr Carroll is informative, articulate, and engaging. Thank you for doing these sessions! 31 Valdagast Valdagast 1 year ago "4 does not equal 6" was the one thing I really understood in this video. 56 pedro pablo garcia herrera pedro pablo garcia herrera 1 year ago Excellent video. You have given me a new understanding of mathematics, about how it arises etc, and made me see the connections between fundamental concepts that I would not have appreciated before. For all that, thank you very much! 9 Paul C. Paul C. 1 year ago Thanks again Prof. Carroll, for another great video. Although I watch all of them twice, and I consider myself a scientist (Chem & Biol), some of the Maths involved does leave me feeling way out of my depth; sorry to say. But of course, I appreciate that you have a very wide range in the audience, from very basic level maths, up to full math-geek level. But every episode is always interesting and well worth watching. 7 Alex Tritt Alex Tritt 1 year ago I love how we’re finally at Nöther’s theorem after 14 episodes starting with conservation laws. It’s full circle. 6 Klaudia Wawrowska Klaudia Wawrowska 1 year ago Amazing content! Thank you so much for these videos, you have done an amazing job at explaining complex ideas in the simplest way possible. Jeff Wheeler Jeff Wheeler 1 year ago (edited) I love this series! You do such a great job at explaining complex topics at a down to earth level, Sean. I always enjoy when you take an abstract concept that I "learned" in college and put it in language that actually makes me understand all of the formalism that was taught in the classroom. Can't wait for the next video. :) 1 0x63 0x63 1 year ago Thank you for making these videos! I've never intuitively understood Noether's theorem and principle of action until now, fascinating example Mark Deslauriers Mark Deslauriers 1 year ago (edited) Thank you for these videos Dr. Carroll. I wish that you were my professor when I took quantum mechanics. No knock on who taught my course at BU, but I really love how you explain concepts and I really like your manner. I just love this stuff and I'm learning so much and find myself laughing at your wonderful comments and asides. jyre Heffron jyre Heffron 1 year ago you really present these complex concepts fluently and comprehensibly... so much fun to see pieces of understanding creating mega-structural outlines... 1 Christopher Christopher 1 year ago Sweet Notability skills, Dr. Carroll! You're the best and this series rules. 1 Remus Gogu Remus Gogu 9 months ago I really love how you explain complex things with such great clarity 🤗! I do remember many years ago when I did not have access to internet and such great teachers, how impossible was the thought that I would one dat be able to understand these things 🕺 tepsoram tepsoram 1 year ago Excellent series and very much appreciated. One small quibble about today's video: It is misleading to say that finite groups are "classifiable" (25:30). The finite simple groups have, indeed, been classified but non-simple finite groups (especially those of prime power order) are so numerous, it is hard to imagine ever obtaining a classification, at least up to isomorphism. 1 RD2564 RD2564 5 months ago (edited) Beautiful concepts, appreciate you Sean taking the time to educate us mere mortals on these concepts which have been important to science in the past century. KAĞAN NASUHBEYOĞLU KAĞAN NASUHBEYOĞLU 1 year ago Thank you so much Prof.Carroll. Great physics series. 1 Perry Whan Perry Whan 1 year ago This series is just the greatest. Thank you, Dr. Carroll. Akami Channel Akami Channel 10 months ago This is so helpful. I've watched many lectures and read several textbooks that have group theory in them and everything I saw just assumed that I knew some of these basic groups. I was always wondering why it is called SO2 etc. R C R C 1 year ago I just want to thank Sean Carroll again for these videos. As they get more and more complicated, I am encouraged to learn more and more. The goal for me is to become a more educated viewer and reader of science journalism so that hopefully those journalists can feel confident in producing videos and articles of more subtle and nuanced areas of active research in physics. Stelios P Stelios P 1 year ago (edited) Oh i m going to love this one. I cannot wait to get off work to check this out. As always, thank you Dr. Caroll :) 2 RooRaaah Crumbs RooRaaah Crumbs 1 year ago I look forward to these with impatience, thank you so much! 2 Vancouver Terry Vancouver Terry 1 year ago (edited) I can't thank you enough for what your videos are doing for me, Prof Carroll. I am an intellectually-active 70-year-old who needs to dig up and dust off some math and physics I learned and half-learned almost 50 years ago as I need them now in a model I have constructed. For me, your detailed, thoughtful, example-filled videos are tremendously valuable because not only do they solidly develop the fundamental ground, they also are a one-stop-shop for updating one's knowledge of some things, for example entropy or quantum physics. It certainly is great getting the clear views you give about the present understandings, terms, and some of the histories to getting there. You're leaving something of significant value on the internet with your videos, both for new learners and for re-learners, as well as for anyone who wants to verify if their current understanding is still sound. Your videos are truly a bang-on job of spreading out the field in front of people and explaining it in crystal-clear detail as you do it. Many superlatives, Sir! Thank you very much! 1 mandar khadilkar mandar khadilkar 1 year ago Euler was just amazing person and his theorems and many corollaries are awesome. 2 Kafiristanica Kafiristanica 1 year ago This series is so good, thank you very much Sean 11 WriterBlocks WriterBlocks 1 year ago (edited) interesting. I have some experience with human anatomy and we have to use special language to describe physical locations of specific body parts in relative environments. I see now why math is needed to describe reality, because of how relative it is. 1 David Sardarov David Sardarov 8 months ago admire Mr.Sean Carroll every time I listen to his lectures. I hope all of this material will be stored for the future and available to everyone just like today. Truly amazing topics and remarkable person by doing all this work. You can't get it in this form anywhere else at any Educational facility - they don't teach you like that. A great way of doing it Mr.Sean Carroll! Mot Mot Mot Mot 1 year ago I have a question from a previous video and I apologise for not bringing it up in your earlier video. Why is it that within a black hole, where even light can’t escape, the gravitational effects of whatever is within the black hole can still be observed outside the event horizon? Why aren’t those effects “hidden” from observers outside the event horizon? Ahsan Rubel Ahsan Rubel 1 year ago You are the teacher I always missed.. thank you dr Shen Carroll... Jon Wesick Jon Wesick 1 year ago Thanks for your thorough explanation. You filled in a few gaps left over from grad school. Rahul Jain Rahul Jain 1 year ago "It's a reflection of the fact that there's some symmetry there." Indeed :) 20 Steve White Steve White 1 year ago I'm not sure I totally got all of that but it was amazing, especially the very end :) BZ BZ 1 year ago Superb as expected for the normal people. The math is complicated and I had to look some stuff up (trauma doc so no math normally) but you give it in a way that makes sense. PLEASE keep this coming. 1 Cooldrums777 Cooldrums777 1 year ago OK. So I have a BS in NucEng and an MS in EE. This is the first video in the series where I really need a homework set assignment to help me understand the details. I'm starting to think I owe the good professor a tuition payment !!!!!!!!! 4 Paul Frischknecht Paul Frischknecht 1 year ago In other words, symmetry is another word for universal quantification or law (of nature) . It basically says that some equation or "invariant" applies for all things from a certain set (a set of some geometrical transformations for example, or all points in spacetime). In other words, it is just a way of saying "no matter what (you do)/where/when... something is always true". For specific applications, you need to define the invariants you are interested in and the set you are quantifying over... Imager Imager 1 year ago (edited) Great video! Is it possible to get a copy of your notes? What teaser, next time ... will come together and tell us something about the fundamental laws of nature. NightWng120 NightWng120 10 months ago Learning where the SU(2)×SU(3)×U(1) comes from was pretty rad. Thanks science man brocoli brocoli 1 year ago if you had labeled the sides of the triangle with arrows and allowed flipping individual arrows, you'd get a bigger symmetry group too John Długosz John Długosz 1 year ago at the end, you mentioned rotations in space and translation in time as leading to conservation laws. That begs the question on what happens if you perform a rotation in spacetime . After all, we're taught that changing inertial reference frames due to velocity is performing just such a rotation. mandar khadilkar mandar khadilkar 1 year ago (edited) Dr Sean, why are Mathe things bad? I love when I can see equations and proofs. It makes so much sense. 1 nemuritai nemuritai 1 year ago (edited) I am familiar with the 1D complex plane (real and imaginary), but what does a 2D, 3D, 4D etc. complex plane look like and how many phases are there? Traruh Synred Traruh Synred 1 year ago One common confusion on Quora is the confusion between the symmetry of the eqn. the lack of symmetry of the solution (such as 'our' world). The simplest is how can things change when 'physics' is time independent. You might want to explain that sometime! aspeoijmda aspeoijmda 1 year ago (edited) Hey Sean! What do you think of chemist Peter Atkins' theory of where the symmetry of the universe and conservation laws came from? His theory: in the beginning, there was nothingness. Now, this nothingness has perfect time symmetry and space (translational and rotational) symmetry. By Noether's Theorem, this implies it has conservation laws of mass-energy and momentum (linear and angular). And thus that explains all conservation laws exhibited by the universe today. Moreover, the nothingness had 0 mass-energy and 0 momentum, and the universe today does too. (If we sum up the positive mass-energy of stuff, it cancels out with 'negative energy' due to gravity. If we sum momentums of galaxies, they sum to 0.) Thus the theory is that indeed in a physical sense, there is still nothing! So there is no problem of how something came from nothing at all! Out of nothing, nothing still remained! (It just changed 'form', for some reason) Atkins' theory is elaborated in his book Conjuring The Universe. acac acac 1 year ago The Biggest Ideas is like Sean's unending desire to teach people stuff, minus the requirement to grade papers. :D 2 Skorj Olafsen Skorj Olafsen 1 year ago This presentation of groups at 11:50 has always seemed needlessly confusing. To me "operations" (or just functions) are just a different order of thing from numbers or triangles. A group is a set of entities, plus one operation that when performed on any element of the set gets us to some other element of the set. When people start talking about a set of operations, it gets confusing. Maybe try to explain this using any other sort of group than a set of functions? With any other operation than "functional composition"? Everybody has an intuition for addition, very few have an intuition for something as abstract as "the act of functional composition". Shalkka Shalkka 1 year ago I don't know what it would feel like to live in a complex vector space so I don't know that my experience mismatches that. Argument from lack of imagination is not very convincing and I have tried to give more embodied meaning to such mathematical concepts as imaginary numbers. For example in spacetime metrics difference squared can be negative which would mean that the underlaying amount is complex. So it seems plausible for me that time is imaginary space and distance is imaginary time. There is a difference between not knowing whether that is the case and knowing that is not the case. Afterall I can't just declare that "particles are obviously the nature of reality" just because the ordinary human experience is very particlelike vs wavelike. 1 Family Guy Family Guy 1 year ago Your teaching explanations I get! Thx. Supertraced Supertraced 1 year ago In the discussion of Noether's theorem, you say that S(AC) is the conserved quantity, but I would think this quantity would depend on the choice of ε and would be infinitesimal anyway. Would the value of the conserved quantity then end up being S(AC)/ε or (for those squeamish about infinitesimals...) d S(AC(ε))/dε (where C(ε) is the starting point after the small shift using the symmetry with parameter ε)? Engin Atik Engin Atik 1 year ago I burst out laughing: "We live in a real world, did you ever see anyone giving complex coordinates?" Better than Descartes' convoluted proof of reality of existence. 3 David Hand David Hand 1 year ago Is the e- field at each point in space a single complex value or a set of 4 complex values? I've heard of this 4 component electron field to account for spin and anti-matter, but it doesn't make sense to me for each of those values to be independent and orthogonal. If they were orthogonal, I don't see any reason for positrons and electrons to annihilate. If four values are needed, there must be some bound applied to those values, right? That doesn't seem orthogonal. How are these values coupled to the photon field? What makes the difference in charge? Is there some way to encode spin or charge in one complex-valued field? Wayne K. Massey Wayne K. Massey 1 year ago Looking forward to the upcoming video that covers quaternions and octonions. 3 William Mc guinness William Mc guinness 1 year ago Sean,I'm not qualified in any scientific joundra but am interested, as I believe that you study time what would a model of the universe look like if time was slowing down. I think you would enjoy that David Hand David Hand 8 months ago It seems like symmetries are all about throwing information away. With the triangle, if you include the labels of the vertices in your object, they aren't symmetric anymore. So when we say there's a symmetry, what we really mean is that there are variables/information that disappear under some form of evaluation. For example, if we have some F(x) = x^2 where x is a real number, and we can only measure or know F, but we are promising anyway that x could be negative, we just would never know it. It gives two solutions for x for every value of F, there is a binary degree of freedom in F. Knowing that continuous symmetries underlie the gauge fields and their corresponding bosons, is it correct to say that the forces of nature exist not because there are internal degrees of freedom at each point in space, but because those degrees of freedom are immaterial at some level? For example, Psi being "squared" (PsiPsi*, not PsiPsi) when observed disposes of the phase, but we suppose that Psi is, in fact, complex anyway. It has a degree of freedom, but our form of evaluation obscures it. Therefore, we can relate symmetries to entropy. Entropy is literally a measure of hidden degrees of freedom. For example, we can measure only the P, V, and T of a gas, but there are actually several degrees of freedom for each molecule, an unfathomable number. The domain of states is far larger than the range of our measurement, and that is the entropy of each {P, V, T}. The difference in degrees of freedom for the quantum gauge fields is much, much smaller, but it still seems appropriate to assign each of the fields an entropy, right? I don't think it matters very much because it would seem that the entropy would be a constant; there are never more or fewer components to each of those fields, and their macrostates (the observed or manifest boson particles) are similar or identical to one another. What we measure is typically reducible to a number of binaries: was there a particle here or in this state or wasn't there? My instinct is that every binary hides the same number of variables. Thus, there would be no gradients of entropy and therefore no work to extract from it. Unless, of course, we consider the expansion of space to be the creation of these new hidden degrees of freedom, in which case entropy would be made to increase through the expansion. That's kind of interesting, maybe. 1 Charles Steinbruegge Charles Steinbruegge 1 year ago If a map from the original triangle onto itself counts as a symmetry, why doesn't a 360 degree rotation about the x or y axis count as a symmetry? Brad S Brad S 1 year ago Dr Carrol, thank you so much! Bohan Xu Bohan Xu 1 year ago this Feynman way of intuitively understanding neother theorem should be mentioned in every relevant class. it's a shame that this is the first place I heard it (no disrespect to Sean Carroll's wonderful class of course)...given i'm a second year grad student Jimmy Snyder Jimmy Snyder 1 year ago Just a nitpick, but with one exception, those pairs of points (at t = 29:30) on the circle are not antipodal. aresmars2003 aresmars2003 1 year ago Great introduction in 1 hour! 1 terrypussypower terrypussypower 2 months ago If I was suddenly as smart as Sean Carroll, I’d be very happy! Well, for a while at least…! 1 David O'Neill David O'Neill 1 year ago How are symmetries and conservation applied in non-euclidean spaces? Aren't there aspects of the Riemann curvature tensor that challenge Noether's theorem? Loz Shamler Loz Shamler 1 year ago Energy is conserved, but it becomes "more useless" eventually ending up as background heat. (I think). Does this imply there is some underlying asymmetry? Mark Callaghan Mark Callaghan 1 year ago My chemistry degree and knowledge of group theory really helped here 7 Anonymous Anonymous 1 year ago Q: These symmetry groups, they were the same ones used to prove Fermat's Last Theorem (In ellipses), right? 1 Stormy Mangham Stormy Mangham 7 months ago I would be working at CERN if Sean Carroll had taught me physics in high school. Unfortunately, I got a public education system slave mill monkey and ended up digging ditches my entire life. John Długosz John Długosz 1 year ago Note: in Noether , the 't' and the 'h' are not the English digraph for the fricative /ð/ (or /θ/). They are separate sounds. [ˈnøːtɐ] /ø/ is somewhat like "heard". Ever-learning-Will Ever-learning-Will 1 year ago So in your discussion on O(2), why is there only one flip symmetry? In the case of the triangle, you had three flip symmetries, and it didn’t matter that you could generate the other two from 1 flip and rotations. Following suit, I would think there would be infinitely many flips in O(2), parameterized by the angle of the axis around which you flipped. 1 protoword protoword 1 year ago As always - exscelent! John Długosz John Długosz 1 year ago The way I explain why it's so important to physics: Symmetry and Group Theory is the formalism of "compare and contrast". That is what you want when you go to consolidate and organize all your observations: "This is just like That, in the following ways..." and describing patterns separate from the types features and relationships forming the patterns. 2 Dinesh Kumar Dinesh Kumar 1 year ago U(1) is the rotation in complex plane right. Then how is the SU(n) rotation different from U(1) Rotation? 1 Go Away Go Away 1 year ago Ive always hated "imaginary" numbers (and the terms "real" and "imaginary"). If we could start again and take a fresh look at it, I think we'd call "complex numbers" just "2-dimensional numbers". That would have prevented me from looking at the number i so skeptically in all those math classes. We would write complex numbers as just (2, 3) rather than "2 + 3i". jmmahony jmmahony 6 months ago (edited) 29:34 flipping a circle does not flip "antipodal" points generally. Gilbert Anderson Gilbert Anderson 1 year ago (edited) 36:45 COME ON SEAN, DON'T LEAVE US HANGING. What are the alternatives to real or complex ? ( For "real" problems. I'm assuming you're not talking about the integers.) stick109 stick109 1 year ago Love this series! However, your proof of Noether's theorem is not convincing. You can't say that two infinitely close trajectories have exactly the same action (well, maybe you do, but you didn't show that), so you can only say they differ by infinitely small amount dA. But then the whole argument falls apart, and you don't get conservation, you get rate of change dA/dx (partial derivative), which is not infinitely small or zero. mandar khadilkar mandar khadilkar 1 year ago I am going back 30 years in my Engineering Maths days. Higher maths for electromagnetic waves, thermodynamics and applied mathematics.... Optical fibers 1 R K R K 1 year ago Love the floating head symmetry EarlWallaceNYC EarlWallaceNYC 1 year ago Lov'in the details. I enjoy the way you give just enough details to push my knowledge, with going "over the cliff". Nice job. Thanks. And your said..."I predict that next week...". Yeah, yeah yeah. Let's see :-) 1 Harry Heck Harry Heck 1 year ago If you had a New York accent I would think you had got Alan Alda to dub over your voice. Good video, I think I need to watch each one of these 14 vids about a thousand times and I might fully catch on. markweitzman's wannabe a theoretical physicist school markweitzman's wannabe a theoretical physicist school 1 year ago (edited) Professor Carroll, what you write at 31:30 O(n)=SO(n)xZ_2 is correct only when n is odd, for n even it is incorrect - see: https://math.stackexchange.com/questions/29279/why-is-the-orthogonal-group-operatornameo2n-mathbb-r-not-the-direct-prod I guess this is similar to what Zee talks about in his group theory book that technically its not U(N)=SU(N) X U(1) but rather SU(N)/Z_N x U(1) = U(N) - Group theory in a Nutshell for Physicists p. 253 2 Boris Petrov Boris Petrov 1 year ago Symmetry discussion and Noether's theorem remain a mystery to me ;-(( markweitzman's wannabe a theoretical physicist school markweitzman's wannabe a theoretical physicist school 1 year ago For further info on symmetry in physics see my playlist: Symmetry and Group Theory in Physics: https://www.youtube.com/playlist?list=PLrYjnFgP8e0mt4oVaA_FGIdaXkE4-hbSz Nichael Cramer Nichael Cramer 1 year ago My apologies, but I’m going to be a bit dense here. In the discussion of the symmetries related to the equilateral triangle it was repeatedly stated that the “members of symmetry groups” were the operations on the triangle (I.e. the various Rotations, Flips, Identity...) However, when discussing Z, the integers, it appears “members of the symmetry group” were the elements being operated on (I.e the integers themselves). OK, so what am I missing here? Robin Betts Robin Betts 1 year ago I don't understand why SO(3) is 3 dimensional... any rotation of the sphere onto itself can be expressed with only 2 [0-2pi) real numbers ( theta, phi.. longitude, latitude)? Pritam Karmakar Pritam Karmakar 1 year ago The biggest ideas in the universe: Applied Mathematics 1 Michael Terrazas Michael Terrazas 1 year ago Your definition of a radian was actually its reciprocal 1 radian = 360 degrees / 2 π 3 imperatoreTomas imperatoreTomas 1 year ago Thank you for this David Crabtree David Crabtree 1 year ago (edited) Heisenberg and Noether most scinctlty describe nature's dance. The drive toward simplicity via Symmetry Conservation, vs. the conflicting clumsy uncertain left foot of Heisenberg. The asymmetry is vital even though the drive to simplification, the cancelling process, cleans up most of the slop. The slop left? Us John Długosz John Długosz 1 year ago Be sure to see 3blue1brown for "lockdown math" on understanding powers of e. 3 Change Gamer Change Gamer 1 year ago (edited) ANoether great video! 24 Milligram Milligram 1 year ago (edited) 10:20 looks like a category. 16:00 Abelian groups have more requirements than commutativity. You need closure, associativity, an identity element, and each element require an inverse element. 34:30 lol I wondered if you'd conveniently stop at three dimensions! ;D 1 AlwaysDisPutin AlwaysDisPutin 7 months ago 1:00:00 So what if S(AC) is conserved? When are you going to show that S(AC) = momentum or energy? disliked Crypto Brian Crypto Brian 1 year ago (edited) Someone’s been watching BG videos lol , when u stop learning u start dying 2 Matt Black Matt Black 1 year ago Thanks Sean i'm going to smoke a jay and unpack this , shame i don't have any LSD in these trying times. 2 Haleem Muhammad Haleem Muhammad 1 year ago Are spinor symmetric? My palm is a spinor. Is it symmetric? Werner DePauli-Schimanovich Werner DePauli-Schimanovich 1 year ago very good, but please do not mix up the greek epsilon with the elementhood in set theory. i am axiometric set theorist and hate that therefore. the possible worlds and the incompleteness are trivial for logicians. look into my book "gödel: a life of logic". Roger Bee Roger Bee 5 months ago Yep... symmetry... got it.... thanks. Erik Dahlgren Erik Dahlgren 1 year ago what a cliffhanger! 1 schel sullivan schel sullivan 1 year ago Things that can be cut or sliced into two symmetrical sides don't count? teflontelefon teflontelefon 1 year ago That escalated quickly. South Coast South Coast 1 year ago These videos send me to sleep every night Apsteronaldo Apsteronaldo 7 months ago Does the word Nerd derive from Noether? apper cumstock apper cumstock 1 year ago Guess the interrelationships of these "ideas" is going to be revelead soon? Michael Sommers Michael Sommers 1 year ago (edited) Q: What's purple and commutes? A: An Abelian grape. 18 Renaud Kener Renaud Kener 1 year ago Listen the video, take a break, listen again, take notes... Richard Redic Richard Redic 1 year ago I try to like Eric Weinstein. I wish Dr. Carroll would teach him how to explain personal ideas to others. Rachel Rexxx Rachel Rexxx 1 year ago I dig the electric sheep still in the back Rachel Rexxx Rachel Rexxx 1 year ago Radians: wherein you can be radical in your 30s and 60s. Martin Popplewell Martin Popplewell 1 year ago You can add another dimension, making 12 changes to the triangle. You do that by adding another dimension which represents the action of reducing the triangle from a 2D shape to a 1D shape thus: A-------B-------C, B-------A-------C, C-------B-------A etc, with ABC, ACB, BAC, BCA, CAB and CBA, you can then flip or rotate to the same yet upright - making 18, then you can drop down another dimension to 0-dimensions and show: .A, .B and .C - which makes 21 representations of different triangles. This is how you think in 3D instead of 2D and thus observe 4D matter instead of 3D matter. It also unlocks 100% brain use too or should I say that is how you begin to use 100% of your brain. The consequence of 100% brain use is complete awareness of any single point and all its connecting points. AnarchoAmericium AnarchoAmericium 1 year ago ** YouTube viewers frankly lookup Group Theory videos ** 2 Graham S Graham S 1 year ago I don't understand any sentences that contain the words "Lagrangian" or "Hamiltonian" which makes following this hard. I can't figure out what these words might mean from the videos, from wikipedia or any texts purporting to explain what they might mean. What are these things? Tapani Linnaluoto Tapani Linnaluoto 1 year ago (edited) The Integers sounds like, err, a .. group .. from the 1960s. Jaime Lopez thurén Jaime Lopez thurén 1 year ago Professor Abel? #science #physics #ideas The Biggest Ideas in the Universe | Q&A 14 - Symmetry 32,014 viewsJun 28, 2020 Sean Carroll 154K subscribers The Biggest Ideas in the Universe is a series of videos where I talk informally about some of the fundamental concepts that help us understand our natural world. Exceedingly casual, not overly polished, and meant for absolutely everybody. This is the Q&A video for Idea #14, "Symmetry." A mixture of abstract thoughts about the integers, what it means for dimensions to be complex, and how we know if a theory has topological defects. My web page: http://www.preposterousuniverse.com/ My YouTube channel: https://www.youtube.com/c/seancarroll Mindscape podcast: http://www.preposterousuniverse.com/p... The Biggest Ideas playlist: https://www.youtube.com/playlist?list... Blog posts for the series: http://www.preposterousuniverse.com/b... Background image by Sylvia Cordedda at DeviantArt: https://www.deviantart.com/c-91/art/N... #science #physics #ideas #universe #learning #cosmology #philosophy #math #grouptheory #symmetry 58 Comments rongmaw lin Add a comment... Tom Howard Tom Howard 1 year ago I'm enjoying these videos. Just want to make two points. 1) The symbol for the quaternions is H, named after Hamilton. The Q is used for rationals. 2) In describing the topology of SO(3), you should be identifying antipodal points rather than reflections. If you identified reflections you'd end up with a manifold with a boundary. 15 Colby Nye Colby Nye 1 year ago As always, thank you for continuing this series! Extremely informative and it's much appreciated! 14 Amaar Quadri Amaar Quadri 1 year ago Great video! It's surprising how much of particle physics comes down to group theory and topology! (Although I'm sure there's lots of other stuff you haven't gotten to yet) 5 Kobev3li Kobev3li 1 year ago Hey Dr. Carroll ! Thank you for the video, and thank you for all you are doing for the field of physics !!! 5 beamfunk beamfunk 1 year ago Love this web series. What presentation tools are used for this series? I am trying to do something similar for my classes next year. 5 Roman Travkin Roman Travkin 1 year ago 50:33 It is the antipodal involution (the reflection around the center) that you should divide the 3-sphere to get SO(3) (which also happens to be topologically the same as a 3-dimensional real projective space) Stephen Schaefer Stephen Schaefer 1 year ago Tricky stuff, but fun! Thanks for the explanations. 1 Athanasios Giannitsis Athanasios Giannitsis 11 days ago Thanks to this video, first time ever I understood what is the physical interpretation of "symmetry breaking". Feel grateful Mgenth bjpafa Mgenth bjpafa 1 year ago Congratulations to descend to basics, and especially presenting views that arev obviously your doctrine or understanding. Symmetries (SSYm) are a menace to the many worlds...Thank you icesrd icesrd 1 year ago Thank you Dr. Carroll. Another excellent Q&A... please keep'm coming!!!! 1 Nathaniel Gregg Nathaniel Gregg 1 year ago (edited) You can think of the symmetry group of the triangle as all the ways to relabel the vertices so that the edges connect the same endpoints. So if A is connected to B, it has to stay that way after the relabeling. For a triangle, any way to rearrange the labels will keep the connections the same, but that’s not true once you have a square instead. This way of imagining it can help you compute the symmetry groups of more complicated things like a cube. 2 4L3PH4 4L3PH4 1 year ago Brilliant lectures. Thank you. 1 Kobev3li Kobev3li 1 year ago The only thing that would make this video better is if it was x10 longer !!! Thank you so much Dr. Carroll, this series is very much appreciated. 1 Daniel Karbach Daniel Karbach 1 year ago (edited) Is it coincidence that, if you had rotated the first around x' (rather than x), you'd end up with the second? I mean, does rotation in transformed coordinates relate to rotating in the original space in reverse order? Traruh Synred Traruh Synred 1 year ago It seems to me a symmetry of moments can be defined by your non-symmetric squigle. Pick a point, draw tangent, add perpendicular to tangents and compute moments of this object. They will come out the same regardless of how you rotate, flip or translate. I guess this is saying the 'shape' is invariant, right? Shpongle Shpongle 1 year ago Love this series. Keep going bruh 2 Paul C. Paul C. 1 year ago (edited) Hi Prof. Carroll. Thanks again for another great Q & A. And you are dead right - you gave way too little information near the end, for us in the Non-maths group, to follow. These are HARD going for some of us. But I keep coming back for more. And BTW, does the Higgs Boson have Anti-particle ? Thanks again. David Hand David Hand 1 year ago Suddenly I don't understand how SO(2) or U(1) are symmetries anymore. If I multiply by e^iO, I don't have the same value anymore. That's not symmetry. Why am I wrong? Also, when rotating in 3D, don't you regain associativity or something by rotating about the current axis, like x' instead of x? nemuritai nemuritai 1 year ago 'Photons are real-valued, electrons are complex-valued'. This is is so interesting, I hope the link with charge is elaborated in future videos. you tou you tou 1 year ago I can listen to Sean for hours 1 aresmars2003 aresmars2003 1 year ago (edited) 16:00 SO(3) - 3 angles - like pitch yaw, and roll! https://en.wikipedia.org/wiki/Aircraft_principal_axes#Principal_axes Or just think of pointing your camera in space - azimuth (compass) and altitude (above horizon), and third angle tilt camera up away from real up. 4 Michael Schnell Michael Schnell 1 year ago It would be great if there were means to jump over the current answer to a question and skip to the next (in case I am rather save with some of the questions). jjm319 jjm319 1 year ago This is for fun (scifi) but i looking up monopoles i found this website describing what engineering with monopoles would look like including how the density and mass of a monopole would interact with matter. https://www.orionsarm.com/eg-article/48630634d2591 Alex Tritt Alex Tritt 1 year ago Quarternions are H, since Q is taken for rational numbers, and Hamilton (of Hamiltonian fame) first came up with them. 1 D T D T 1 year ago thanks dr.carroll i dont understand much but i watch to feel smart 14 Jo Allen Jo Allen 1 year ago Maybe this is a controversial opinion, and maybe I'm just traumatized by undergrad, but not even Sean can make group theory exciting. 2 BRDRDRDAT BRDRDRDAT 1 year ago The symbol for octonions is H for Hamilton, who discovered them. 2 BRDRDRDAT BRDRDRDAT 1 year ago Better to say "group product" than "group multiplication" MohPK MohPK 1 year ago Thank your for making these 2 Potonicml Potonicml 1 year ago (edited) The truth of the matter is, science plays its part well, and they should be glorified for getting humans this far, however, they are either clearly ignorant or lying to you when it comes to the fabric of space/time.. Just imagine 5th dimensional geometry bleeding down into the 3rd dimension, this is why space increases by the way.... also imagine that energy can be compacted... density... based on material geometry, energy refracts inside and fluctuates in every part of it but can't get out which is why they create fields! since they're all trying to go towards the path of least resistance they end up folding in on them selves and the same happens to the other side, they want to tear them selves apart but can't because the space is stuck and is super positional! like a rusting pipe! every time matter moves it moves the fabric of space depending on its density and properties and geometry and then you realise how resistance is everything! Mass IS Resistance on this dimension because it's from the 5th like bubbles of oil in water! EVERYTHING IS MOVING FASTER THAN LIGHT WHICH IS WHY LIGHT IS EASY TO SEE IN TIME! THE TRICK IS SLOWING THE PARTICLES DOWN WITHIN OUR REFERENCE FRAME BY USING GEOMETRY! Robin Betts Robin Betts 1 year ago Ahhh, thank you so much for answering my question.... Cooldrums777 Cooldrums777 1 year ago Oh boy. This video demonstrates why I majored in engineering and not physics Rick Harold Rick Harold 1 year ago Rock on. Thanks! Valdagast Valdagast 1 year ago Wait... I'm supposed to understand everything in the normal videos? ... Will there be a test? Mgenth bjpafa Mgenth bjpafa 1 year ago (edited) Spontaneous symmerty breaking and unbroken subgroups. Reiner Wilhelms-Tricarico Reiner Wilhelms-Tricarico 1 year ago why is it called "spontaneously" broken symmetry? D T D T 1 year ago i watch in hopes your vocabulary will seep in 2 Stumpy Mason Stumpy Mason 1 year ago I think I'm gonna fail this subject.. Jeffrey Anwar Jeffrey Anwar 1 year ago thank you Mgenth bjpafa Mgenth bjpafa 1 year ago Least but not the least, learn topollogy if you want to rise... Charles Dinolfo Charles Dinolfo 1 year ago what do think of pierre marie robitaille ? 1 SalmonBoa420 SalmonBoa420 1 year ago I was hoping he was going to say something outlandish and then say jk 😆😅 2 Emiliano Corcino Emiliano Corcino 1 year ago Why so(6)=. To Sl(4) 1 Christopher Carson Christopher Carson 1 year ago 39:29 * Eric Weinstein has left the chat * 1 Too Crash Too Crash 1 year ago 🤤 Andrey Bashkin Andrey Bashkin 1 year ago Uno, uno, uno! Kevaaalahh Kevaaalahh 1 year ago Symmetry/yrtemmyS 2 Rex Mundi Rex Mundi 1 year ago I don't do this, but hey, first. 2 AP Computing AP Computing 1 year ago First. I'll come back and watch this later. 1 Ryan Cole Ryan Cole 1 year ago Hi, this is the first comment. 1