I love that Sean Carroll took the time to explain the equations. He's right: we don't need to solve them, but we can handle them, understand them, and see their usefulness. Bravo!
you don't need to solve them ? what ? the point of mathematics is either obtain numeric or analytic solutions. that's the whole point - their "usefulness". and i reserve the right to believe you when you claim to "understand" them
@@hamidmazuji Yes, you are right. I should have been clearer. I should have said, "Among the audience are people like me who aren't professional physicists or mathematicians but who value this work. We appreciate seeing and understanding the equations even if we can't or don't want to do the 'working out' of them." And I 100% support the idea of reserving belief until proof.
i apologize for being so blunt. at 47:15 he provides a great example of a solution for the energy momentum tensor for stars and planets. i would have liked to see other examples, such as a particle in an accelerator
I explained this with a simple prop without any complicated gobbledygook or idiom just revelation And relativation ... water.....hermetic ... enertia ie. gravity or GRAVITY flux.... ground effect ie .. boundary effect .. shear plain ...friction frictionless principle of least action ... water has atributes and modes !!!!!.... hence its suface tension makes water bead up ..... no mater what height that you drop water from it will return to as long as you do not introduce impedance.....ie .. flow stream... stream line .....😎 slick as a bic A dynamo dose not have an active resistance it is passive as in I must introduce energy by converting the mass of a standing colom of water next too an arc/parabola of the same height ... and have a pendulum for least time.. and as above so below pendulum dual aparatus as water is like a yo yo . ..ctrinity .BIG G little g .... tesseract . Torus .... figure 8 but1 ...top down and sideways . Maximum mode minimum not maximum minimum mode
A freaking 5 year old could do Relativity... you all been hoodwinked ... hornswoggled ....bewitched...bamboozled gypped..... corn-fed ... ignorance is bliss 😊 who thought... you thunk ....about think...bet you can't hear tone deff .... sweet devotion Chandra ....soma mantra ...
This is the kind of lecture people have been expected from a professor who knows how to communicate the difficult concepts in physics. I have to praise Prof. Sean Carroll for NOT backing down to the publisher crooks who want to get rid of all equations (I am sure they would prefer to print money instead of books if they are allowed to do so). If you talk about science without equations, it is like talking about investment without money or literature without words. Mathematics is what nail down the concept so that at the end of the day you know what you have learned. For those who really understand the subject, it is a joy to be able to explain difficult equations using language that laymen could understand. Keep it up, Prof. Sean Carroll. If the audience could understand your video, they would have no problem in buying your book too. People are expecting more of the same kind to come in the future.
This is crazy. I’ve been trying to understand the math behind this for over 40 years. This is the closest I’ve ever gotten. I’ll need to listen again, and again, and take notes. Dr. Carroll, I can’t thank you enough. Oh, and I ordered the hard cover.
It's beautiful how Sean explains things in a simple fashion. This is art. Ever since I read his books, he has inspired me to learn more, know more, understand more in ways in which I never knew I can. He is one of the best science communicator out there, surpassed only by the great Carl Sagan. Sean I loved your explanation and will continue watching your videos, gaining insights, and continue to be inspired from your work. Thank you for such a brilliant session. Hoping to see more from you.
@@shantanulokhande3730 You're welcome, no apology necessary, we all use words whose meanings we have extracted incorrectly from their contexts. A similar thing happens in regard to pronunciation. I remember reading 'Persephone' and in my head hearing it as per-seh-phone and being amused to hear it pronounced per-seh-phony, i.e. correctly. lol.
Sean Carroll is the best presenter Physics has!!! And all the great scientists would thank him for that-- make it simpler for the masses to understand!!
Sean Carrol is by far the best communicator I have heard in high- level physics. The formulas in this are over most people's heads but do not hesitate to look at Carroll's other lectures, he always brings some good information for every level of viewer.
@@Tore_Lund Do you mean the many worlds interpretation of quantum mechanics? That is quite a different thing from the multiverse - either one of these or even both could potentially be real at the same time. I get the impression that he is agnostic on the multiverse - it might be true or it might not, but there's nothing suggesting that it must be, but on the other hand there are very good reasons to believe in the many worlds interpretation of quantum mechanics. Schrodinger's equation of quantum mechanics is the most successful equation there is for how the universe works and it already contains the so called "many worlds" (aka superpositions - e.g. Schrodinger's cat being both alive and dead). The many worlds interpretation is the simplest one - to just believe what the equation says; it's all the other interpretations that try to somehow make those superpositions/worlds disappear when a measurement is made, for example by adding an additional rule saying that the wavefunction somehow collapses, because many people are uncomfortable with the idea that all those possibilities could be real.
One of the biggest things that kept me out of physics as a career was the math I thought I could never ever get down. Sean absolutely makes the math digestible and makes its application seem so easy to follow. Wish he was my high school math teacher; I might just have become a physicist!
This was absolutely riveting for me! I mean, a good portion of it went a bit over my head, but I _got_ enough of it for this to really be enjoyable! Thanks!
Three cheers for Dr. Carroll. In this lecture, he displays all the finest qualities of an excellent teacher. He presents some of the knottiest issues in physics in an understandable, non-threatening way. He shows great respect for his listeners by liberally tossing around some very complex equations, carefully explaining each one. I'm just a bohunk Georgia boy, but I never miss Dr. Carroll's lectures, and indeed, often find myself viewing them a second and third time.
Perfectly digitally rendered on the Kindle version if you can't get your hands on the hard copy. He is a genius in explaining a difficult subject, a deeper understanding of space and time that can only be had by going through the concise formulation.
Extremely brilliant as always. Sean explains so much better. I understood way better and will be looking forward to more lectures from Sean. The univers is just beyond incridible
Wow this was phenomenal. I've been casually following modern pbysics since college and have never seen an approachable explanation of GR before that actually follows the math. Sean Carroll is a national treasure.
after listening to Sean I think now 50 times, all different lectures. The picture in my head becomes more and more complete. I am not a mathematician (like Einstein lol) I do kind of get it now, I remember that a long time ago I set myself a goal that if I get the change I would try to understand Einstein's theories. And I feel that I am getting there, so thx Sean and You Tube. And now I think I will order your book.
Still stunned by how good this lecture is. The way Sean intersperses history and his use of graphics to communicate an idea works really well. Whatever it is you’re doing Sean, please don’t stop. Request, if I may be so bold, I’ve been trying for a couple of years to understand how Planck solved the, at the time, 40 year old Blackbody problem problem but to no avail. An explanation of how he solved it without using any of the nomenclature, words, ideas, or concepts that came into being post 1900.
Danke! With those YT videos Ri contributes to global, individual knowledge by providing very interesting subjects which are very well prepared and thus easy to follow.
"Your channel is something very very special. Top 3 on RUclips for this type of programming in my opinion. It boggles my mind almost as much as the information you provide in the shows, how you only have half a million subscriber’s. I feel like I’m getting in early on a community with the potential to reach 10 million subscribers or more. Just fantastic ground breaking work you’re doing here my friend. I’m honored to be a part of it. I will be making donations to the channel going forward. Thank you for what you’re doing from Canada. 🙏💫🇨🇦🍻"
What a nice surprise! In the middle of an introductory GR class right now :). I Definitely need to get this book! Riemann a student of Gauss. Oh that wouldn't be intimidating at all! :)
So, in a nutshell, the equation presented in Slide 2 predicts Black Holes, gravity waves, and much more. Brilliant! Thank-you. We'll be wrestling with some of this for a long time.
Since you're including the math I'll check out the book. I don't always understand the math, but I do like to see it in hopes one day I will finally get it.
Thank you to Sean. He has put these ideas clearly and freely into the public domain I understand why it is so complicated and has been difficult for people to make use of it I appreciate that some people devote a lot of time and study to make use of it Maybe this is artificial intelligence and not the first. Something we create that s smarter than we are Brilliant
Thank you to Sean for using a good microphone! I love The Royal Institute's videos, but most of these remote ones have painfully terrible audio, so I quickly lose my motivation to watch them, this one, not so much!
Great to see him back in the RI. I wish other scientists would dare to show the real math behind these concepts. If you keep hiding them, things will never change. Bold move to explain the Riemann tensor in less then 53 minutes 😃
Sean Carroll makes me feel that Mathematical Physics, Tensor Calculus and GTR are not that difficult at all. I wish my professor in physics class made me feel that way, years ago! 🙂
I knew most of the parts of this talk, but this is the best joining up of the dots that I've seen. Excellent! (My only quibble is the use of the can of worms that is the twin paradox, but it's tricky!)
1. I'm a traditionalist... I prefer seeing c or c squared explicitly in relativity equations, rather than ”oversimplifying” by setting c=1 as Sean did in this video. 2. The minus sign in the Minkowski ”pythagorean” equation can be eliminated by subtracting the negative term(s) from both sides of the equation. (That moves the negative term from the right side of the equal sign to a positive term on the left side, so that all the terms are positive.) This leads to a truly pythagorean equation. (With the minus sign, it's actually a hyperbolic equation, not pythagorean.) With a bit of algebraic manipulation, you can arrive at a pythagorean equation where the hypotenuse of the right triangle is the speed of light c, and the other two sides of the right triangle are an object's velocity through 3-dimensional space and the object's rate of aging. The interpretation of the equation is that everything -- including light, and including you & me -- is traveling through 4-dimensional Minkowski spacetime at the same speed c that light travels through 3-dimensional space. That ”speed of everything” has the aroma of a fundamental equation... one that I wish I'd been taught when I was young.
It'd be a good idea to learn to take c=1 to fully understand relativity. You can certainly swap the proper and world-time to make the equation exactly pythagorean if form (a "mixed" coordinate form or my-space-their-time metric) but this doesn't change anything. Note: It is true that the tangent vector to any world-line norms to the speed of light, but extending this to the light itself is, well a little bizarre, as there is no proper time affine parameterization of a null curve.
@@kylelochlann5053: 1. How does setting c=1 help one ”fully understand” relativity? Isn't it just a convenient choice of unit that makes the equation look simpler, but obscures an important piece of physics information? 2. I don't see why you're quibbling about “extending“ it to include light. The implication of the equation is that light doesn't age... all of its travel in 4D spacetime is confined to 3D space. Objects age more slowly as their speed through 3D space increases, and the limit is zero aging as an object's speed through 3D space approaches the speed of light.
@@brothermine2292 No, it's the exact opposite. Relativity understood through the causal structure of the gravitational field is deeply illuminating as to what is going on. Setting c=1 is measuring time in terms of length. If you take a graduate level (or advanced undergrad) textbook you'll see that distance, time, mass, energy, and electric charge are all measured in meters (or the length units of your choice). For example understanding time dilation and the clock effect and properties of black holes is an entirely different experience when understand in the context of spacetime foliation and distances along world-lines, and experience that is more clear and in alignment with common sense.
@@kylelochlann5053 : I guess we disagree on what it means to ”fully understand.” Choosing a convenient scale factor can make some relationships easier to see due to limitations of human cognition, but that simplification has a cost. I would conjecture that an AI (or augmented human mind) would be able to see those relationships as clearly without the crutch of setting c=1, and I would call this a fuller understanding. It's the advanced math tools (differential geometry, etc) that offer a deeper understanding, not setting c=1.
@@brothermine2292 Setting c=1 has nothing to do with scale factors and is emphatically not a scale factor. It is a fundamental shift in the meaning of the equations. Instead of explaining this, which you're clearly not understanding, explain to me how it is that given two clocks, one of which remains and rest and another taken on a journey around campus come back reading different elapsed times? What is happening to the clocks?
A very well put together lecture for everybody to understand. My biggest aim is to give people the chance to compete in events who never did good at school or sport. This is a very good general knowledge lecture and so are a lot of the other lectures from The Royal Institution.
I can describe all this in 5 words; It's all Greek to me! For some reason I just love reading about things like this even if I understand none or very little about it...
Thank you for the excellent explanation. Now I know the problem with our current physics. We have built on a foundation that doesn't quite match observations of nature. Newtons postulates. The solution is going back and refining Newton's postulates to be more accurate descriptions of nature. Fyi, Walter Russell has already done this.
Thank you! You provided the most comprehensive, most intuitive explanations for one of the most iconic and complex equations: Einstein Field Equations! 🙂
Well done prof. Carroll! I like your simplification way through GR. I think that the geometrical meaning of Ricci's tensor and scalar should be better explained (in general). Possibly as the first "Taylor terms" (constant and first linear term) of the expansion of the "curvature state". Probably Geometric Algebra could help. I think that the full Riemann's tensor is unnecessary and cumbersome. Have a beautiful day!!
37:25 You're not quite a member of the last generation who had to calculate these tensors by hand. A few years ago I learned tensor algebra at a German university from a stern Russian professor who still made us calculate these entries by hand during exams. It was in the context of continuum mechanics instead of General Relativity, but it's still the same kind of mathematics with Einstein's summation convention and stuff. Believe it or not, some of what I learned in that course is still useful to me, as I keep impressing some of my colleagues at work with it every now and then by finding neat solutions with it. :)
Thanks for that well explained connections we should plant into our brains now. It is very inspiring and leads to dive into the math more manually than just accepting the theory.
It's really amazing lecture. And it's very important how to correctly to interpret Einstein's equations in GR. We can see also: Rethinking the Formal Methodology (II): Cognitive Content of Relativity (On the Centenary of General Relativity)
Thank you for making this so understandable. Even though I may not be able to do the math or even want to do the math. Understanding how it all works and what the math is trying to say. I can now appreciate the strugle that is going on in the world of physics. Maybe my theory of ST1 dimention and the TS1 dimention entertwined together beeing respocible for the quantum foam that we expolor today and will show up one day described by the math. Then prove I was right all along. This is a fun ride. Thank you.
Hello Sean, I like how you try to explain quantum theory, I have an opinion that it's on the right track, however it is somewhat different from how I understand creation to be. First of all though I must explain that I've never attended university and have no formal qualifications. Although I have attended a 3 year training programme in Maori arts & culture graduating in 1982, and for the past 40 years I've been studying The Urantia Book, which aligns with our Maori culture, history and teachings. The universe of universes (current creation) is not an infinite plane, a boundless cube, nor a limitless circle, it certainly has dimensions. The laws of physical organisation prove the whole vast aggrregation of force-energy and matter-power functions ultimately as a space unit; as an organized and co-ordinated whole. The observable behaviour of material creation constitutes evidence of a physical universe of definite limits and order. The successive space levels of creation (the evolving master universe) constitute the major divisions of pervaded space, total creation, organized and partially inhabited or yet to be. If the master universe were not a series of elliptical space levels of lessened resistance to motion, alternating with zones of reletive quiescence, it would conceive that the cosmic energies would be observed shooting off on an infinite range of straight line paths into trackless space, and creation would not form, but would instead continually fly apart, and that is not observed as happening, ever the universe of universes whirl, always swinging onwards through the great circuits of space... (The Urantia Book, Paper 12 The Universe of Universes, pg 128)
WAIT A MINUTE: at 7'07" you show 'ma', but in the previous equation I only saw "m" (small m). Now, I spent dozens if not hundreds of hours learning about both quantum mechanics and astrophysics, but I am totally ignorant about math and shivers in fear when I see an equation. But, now I feel I am ready to take a dive (well, actually I am ready to dip my toe in the water, but, whatever.) So, I was interested to discover this lecture and I thought: this is exactly what I need, a Virgil who takes me by my hand and patiently teaches me to understand. But then, bang, you pulled the rug under my feet. Where is "m" and where did "ma" comes from? Are they the same thing?
I love that Sean Carroll took the time to explain the equations. He's right: we don't need to solve them, but we can handle them, understand them, and see their usefulness. Bravo!
you don't need to solve them ? what ? the point of mathematics is either obtain numeric or analytic solutions. that's the whole point - their "usefulness". and i reserve the right to believe you when you claim to "understand" them
@@hamidmazuji Yes, you are right. I should have been clearer. I should have said, "Among the audience are people like me who aren't professional physicists or mathematicians but who value this work. We appreciate seeing and understanding the equations even if we can't or don't want to do the 'working out' of them." And I 100% support the idea of reserving belief until proof.
i apologize for being so blunt. at 47:15 he provides a great example of a solution for the energy momentum tensor for stars and planets. i would have liked to see other examples, such as a particle in an accelerator
or a photon, or a gamma ray, or a gyroscope
what does the energy momentum tensor of a millisecond pulsar look like
Sean is one of the most brilliant science communicators...We are so lucky to have him in our time period.
I explained this with a simple prop without any complicated gobbledygook or idiom just revelation
And relativation ... water.....hermetic ... enertia ie. gravity or GRAVITY flux.... ground effect ie .. boundary effect .. shear plain ...friction frictionless principle of least action ...
water has atributes and modes !!!!!.... hence its suface tension makes water bead up .....
no mater what height that you drop water from it will return to as long as you do not introduce impedance.....ie .. flow stream... stream line .....😎 slick as a bic
A dynamo dose not have an active resistance it is passive as in I must introduce energy by converting the mass of a standing colom of water next too an arc/parabola of the same height ... and have a pendulum for least time.. and as above so below
pendulum dual aparatus as water is like a yo yo .
..ctrinity .BIG G little g .... tesseract
. Torus .... figure 8 but1 ...top down and sideways .
Maximum mode minimum not maximum minimum mode
A freaking 5 year old could do Relativity... you all been hoodwinked ... hornswoggled ....bewitched...bamboozled gypped..... corn-fed ... ignorance is bliss 😊 who thought... you thunk ....about think...bet you can't hear tone deff .... sweet devotion Chandra ....soma mantra ...
@@manicmadpanickedman2249 it’s a pity your a 4 year old then.
@@Isclachau exactly in which way or is it because I don't care about the jargon just the idea ... to put ords too it does not do it any fairness
I'm addicted to pigger nussy 😻
Sean is such an eminent and humane and eloquent teacher. He makes me feel fairly bright for an hour. It is an honour to bask in his knowledge.
This is the kind of lecture people have been expected from a professor who knows how to communicate the difficult concepts in physics. I have to praise Prof. Sean Carroll for NOT backing down to the publisher crooks who want to get rid of all equations (I am sure they would prefer to print money instead of books if they are allowed to do so). If you talk about science without equations, it is like talking about investment without money or literature without words. Mathematics is what nail down the concept so that at the end of the day you know what you have learned. For those who really understand the subject, it is a joy to be able to explain difficult equations using language that laymen could understand. Keep it up, Prof. Sean Carroll. If the audience could understand your video, they would have no problem in buying your book too. People are expecting more of the same kind to come in the future.
This is crazy. I’ve been trying to understand the math behind this for over 40 years. This is the closest I’ve ever gotten. I’ll need to listen again, and again, and take notes. Dr. Carroll, I can’t thank you enough. Oh, and I ordered the hard cover.
I sympathize with you
Try e=ymc² where y is the Lorentz effect.
I love listening to Sean Carroll speak and do every chance I can
I'm the same with Brian Greene
I agree, As long as Sean sticks to Physics and the Philosophies related to this field and science in general
Sean has his own channel on RUclips where he has uploaded many podcasts, lessons, QnAs and he interacts with his subscribers regularly!
@@CorezMon never even thought to look for my favorite scientists having RUclips pages! thanks for opening up my universe in terms of content!
I always listen to his mindscape podcast, especially the monthly AMA
It's beautiful how Sean explains things in a simple fashion. This is art. Ever since I read his books, he has inspired me to learn more, know more, understand more in ways in which I never knew I can. He is one of the best science communicator out there, surpassed only by the great Carl Sagan. Sean I loved your explanation and will continue watching your videos, gaining insights, and continue to be inspired from your work. Thank you for such a brilliant session. Hoping to see more from you.
Simple, not simplistic. Simplistic is derogatory.
@@REDPUMPERNICKEL Sorry about that. Made the edit. Thanks !!
@@shantanulokhande3730 You're welcome,
no apology necessary,
we all use words whose meanings we have extracted incorrectly from their contexts.
A similar thing happens in regard to pronunciation.
I remember reading 'Persephone' and
in my head hearing it as per-seh-phone and
being amused to hear it pronounced per-seh-phony, i.e. correctly. lol.
James Beacham is my favourite
@@REDPUMPERNICKEL Like when I was a kid one of my favorite cartoon characters was Yosemite Sam; to me, YOSS-might Sam.
Sean Carroll is the best presenter Physics has!!! And all the great scientists would thank him for that-- make it simpler for the masses to understand!!
I don't think anyone explains physics like Sean Carroll. I might not be an 'Everettian' but he sure makes sense to me when talking about these things
Sean Carrol is by far the best communicator I have heard in high- level physics. The formulas in this are over most people's heads but do not hesitate to look at Carroll's other lectures, he always brings some good information for every level of viewer.
sabine hossenfelder and janna levin are pretty good, and amusing too....
@@HarryNicNicholas Sean Carrol is a firm believer in the Multiverse, Sabeine is not. Would like to see then in a panel discussion.
@@Tore_Lund Do you mean the many worlds interpretation of quantum mechanics? That is quite a different thing from the multiverse - either one of these or even both could potentially be real at the same time. I get the impression that he is agnostic on the multiverse - it might be true or it might not, but there's nothing suggesting that it must be, but on the other hand there are very good reasons to believe in the many worlds interpretation of quantum mechanics. Schrodinger's equation of quantum mechanics is the most successful equation there is for how the universe works and it already contains the so called "many worlds" (aka superpositions - e.g. Schrodinger's cat being both alive and dead). The many worlds interpretation is the simplest one - to just believe what the equation says; it's all the other interpretations that try to somehow make those superpositions/worlds disappear when a measurement is made, for example by adding an additional rule saying that the wavefunction somehow collapses, because many people are uncomfortable with the idea that all those possibilities could be real.
@@Neme112 Yes, many worlds as the solution to indeterminism.
I lost vision for about 3 weeks. I survived just listening to these lectures. Thank you Sean. You are a great communicator like feynman
Did you get it back?
@@Seekthetruth3000 Yes. "For about 3 weeks" implies that he lost his vision at some point, and regained it about 3 weeks later.
One of the biggest things that kept me out of physics as a career was the math I thought I could never ever get down.
Sean absolutely makes the math digestible and makes its application seem so easy to follow.
Wish he was my high school math teacher; I might just have become a physicist!
This was absolutely riveting for me! I mean, a good portion of it went a bit over my head, but I _got_ enough of it for this to really be enjoyable! Thanks!
Fantastic presentation Sean! Thank you for bringing cosmology so close to the rest of us so that we may appreciate it too.
Absolutely brilliant talk. Touched my heart . Thank you sir.
Three cheers for Dr. Carroll. In this lecture, he displays
all the finest qualities of an excellent teacher. He presents some of the knottiest issues in physics in an understandable, non-threatening way. He shows great respect for his listeners by liberally tossing around some very complex equations, carefully explaining each one. I'm just a bohunk Georgia boy, but I never miss Dr. Carroll's lectures, and indeed, often find myself viewing them a second and third time.
Perfectly digitally rendered on the Kindle version if you can't get your hands on the hard copy. He is a genius in explaining a difficult subject, a deeper understanding of space and time that can only be had by going through the concise formulation.
Extremely brilliant as always. Sean explains so much better. I understood way better and will be looking forward to more lectures from Sean. The univers is just beyond incridible
Absolutely brilliant talk. Thank you very much.
Most lucid explanations of recondite concepts and relations by Sean Carroll. Thank you.
He is so good at explaining things!
Wow this was phenomenal. I've been casually following modern pbysics since college and have never seen an approachable explanation of GR before that actually follows the math. Sean Carroll is a national treasure.
It's mind-blowing that black holes were already in the equation without anyone even Einstein knowing anything about them.
I got it all, perfect understanding, and then came the instantaneous applause and I lost it. How and where did the applause come from?
after listening to Sean I think now 50 times, all different lectures. The picture in my head becomes more and more complete. I am not a mathematician (like Einstein lol) I do kind of get it now, I remember that a long time ago I set myself a goal that if I get the change I would try to understand Einstein's theories. And I feel that I am getting there, so thx Sean and You Tube. And now I think I will order your book.
Still stunned by how good this lecture is. The way Sean intersperses history and his use of graphics to communicate
an idea works really well. Whatever it is you’re doing Sean, please don’t stop.
Request, if I may be so bold,
I’ve been trying for a couple of years to understand how Planck solved the, at the time, 40 year old Blackbody problem problem but to no avail.
An explanation of how he solved it without using any of the nomenclature, words, ideas, or concepts that came into being post 1900.
Danke! With those YT videos Ri contributes to global, individual knowledge by providing very interesting subjects which are very well prepared and thus easy to follow.
We're very glad you like them!
I feel like I've heard a lot of this before, but the way you say it is excellent. Thank you.
This was by far the best leture on this Subject I've listened to.Thanks Sean!
The guy who switch me from engineer to work as a high school physics teacher.❤
It's all very interesting. I will need to watch this again after some consideration.
Really well explained!! Never seen this topic like this. I want more of him!! It seems so.... understandable 😅
This is about as well explained as is possible. Impressive.
What a great communicator.
Your best on the subject so far. I am super into all your podcasts etc. keep up your work. It’s very important.
Amazing! One of the best presentations of GR I’ve seen! Thank you sir!🤓🥳🤩
"Your channel is something very very special. Top 3 on RUclips for this type of programming in my opinion. It boggles my mind almost as much as the information you provide in the shows, how you only have half a million subscriber’s. I feel like I’m getting in early on a community with the potential to reach 10 million subscribers or more. Just fantastic ground breaking work you’re doing here my friend. I’m honored to be a part of it. I will be making donations to the channel going forward. Thank you for what you’re doing from Canada.
🙏💫🇨🇦🍻"
Great lecture, Sean 😊😊 looking forward to getting the new book! 🎉
What a nice surprise! In the middle of an introductory GR class right now :). I Definitely need to get this book! Riemann a student of Gauss. Oh that wouldn't be intimidating at all! :)
So, in a nutshell, the equation presented in Slide 2 predicts Black Holes, gravity waves, and much more. Brilliant! Thank-you. We'll be wrestling with some of this for a long time.
Aww man, love this guy, sucks that he can't be there in person.
The best science speaker by far.
Sean podcast its currently at his 218 episode, i highly recommend people to check it out, its full of gems
Very, very good. You helped me see something with a brand new perspective. Thank you.
Since you're including the math I'll check out the book. I don't always understand the math, but I do like to see it in hopes one day I will finally get it.
Thank you to Sean. He has put these ideas clearly and freely into the public domain
I understand why it is so complicated and has been difficult for people to make use of it
I appreciate that some people devote a lot of time and study to make use of it
Maybe this is artificial intelligence and not the first. Something we create that s smarter than we are
Brilliant
No nice to listen to Prof Carroll. He is an excellent teacher and researcher.
I really love listening to the learning and speed up on reading.
Thank you to Sean for using a good microphone! I love The Royal Institute's videos, but most of these remote ones have painfully terrible audio, so I quickly lose my motivation to watch them, this one, not so much!
I saw this guy live at Glasgow Uni. Very engaging fella. Thanks, as ever.
I love that presentation! Sean Carroll wisdom gets better by the years.
Great to see him back in the RI. I wish other scientists would dare to show the real math behind these concepts. If you keep hiding them, things will never change. Bold move to explain the Riemann tensor in less then 53 minutes 😃
Sean Carroll makes me feel that Mathematical Physics, Tensor Calculus and GTR are not that difficult at all. I wish my professor in physics class made me feel that way, years ago! 🙂
I knew most of the parts of this talk, but this is the best joining up of the dots that I've seen. Excellent!
(My only quibble is the use of the can of worms that is the twin paradox, but it's tricky!)
1. I'm a traditionalist... I prefer seeing c or c squared explicitly in relativity equations, rather than ”oversimplifying” by setting c=1 as Sean did in this video.
2. The minus sign in the Minkowski ”pythagorean” equation can be eliminated by subtracting the negative term(s) from both sides of the equation. (That moves the negative term from the right side of the equal sign to a positive term on the left side, so that all the terms are positive.) This leads to a truly pythagorean equation. (With the minus sign, it's actually a hyperbolic equation, not pythagorean.) With a bit of algebraic manipulation, you can arrive at a pythagorean equation where the hypotenuse of the right triangle is the speed of light c, and the other two sides of the right triangle are an object's velocity through 3-dimensional space and the object's rate of aging. The interpretation of the equation is that everything -- including light, and including you & me -- is traveling through 4-dimensional Minkowski spacetime at the same speed c that light travels through 3-dimensional space. That ”speed of everything” has the aroma of a fundamental equation... one that I wish I'd been taught when I was young.
It'd be a good idea to learn to take c=1 to fully understand relativity. You can certainly swap the proper and world-time to make the equation exactly pythagorean if form (a "mixed" coordinate form or my-space-their-time metric) but this doesn't change anything. Note: It is true that the tangent vector to any world-line norms to the speed of light, but extending this to the light itself is, well a little bizarre, as there is no proper time affine parameterization of a null curve.
@@kylelochlann5053: 1. How does setting c=1 help one ”fully understand” relativity? Isn't it just a convenient choice of unit that makes the equation look simpler, but obscures an important piece of physics information?
2. I don't see why you're quibbling about “extending“ it to include light. The implication of the equation is that light doesn't age... all of its travel in 4D spacetime is confined to 3D space. Objects age more slowly as their speed through 3D space increases, and the limit is zero aging as an object's speed through 3D space approaches the speed of light.
@@brothermine2292 No, it's the exact opposite. Relativity understood through the causal structure of the gravitational field is deeply illuminating as to what is going on.
Setting c=1 is measuring time in terms of length. If you take a graduate level (or advanced undergrad) textbook you'll see that distance, time, mass, energy, and electric charge are all measured in meters (or the length units of your choice).
For example understanding time dilation and the clock effect and properties of black holes is an entirely different experience when understand in the context of spacetime foliation and distances along world-lines, and experience that is more clear and in alignment with common sense.
@@kylelochlann5053 : I guess we disagree on what it means to ”fully understand.” Choosing a convenient scale factor can make some relationships easier to see due to limitations of human cognition, but that simplification has a cost. I would conjecture that an AI (or augmented human mind) would be able to see those relationships as clearly without the crutch of setting c=1, and I would call this a fuller understanding. It's the advanced math tools (differential geometry, etc) that offer a deeper understanding, not setting c=1.
@@brothermine2292 Setting c=1 has nothing to do with scale factors and is emphatically not a scale factor. It is a fundamental shift in the meaning of the equations. Instead of explaining this, which you're clearly not understanding, explain to me how it is that given two clocks, one of which remains and rest and another taken on a journey around campus come back reading different elapsed times? What is happening to the clocks?
Awesome talk, was hoping you would explain the Cosmological Constant too!
A very well put together lecture for everybody to understand. My biggest aim is to give people the chance to compete in events who never did good at school or sport. This is a very good general knowledge lecture and so are a lot of the other lectures from The Royal Institution.
That was really helpful actually, I'm thinking of studying geometries now
1:17- enlightening revelation that is why you are the best sci educator
Love the explanation on the curvature here. I did not know this until now although I knew about metric tensor. That is so cool!
Great presentation! :)
This guy is really, really, REALLY good at explanations
I can describe all this in 5 words; It's all Greek to me! For some reason I just love reading about things like this even if I understand none or very little about it...
Six words, not five
Thanks Sean
Sean does a good job as a teacher
Sean, thanks for mentioning Leibniz! Nobody ever does when explaining gravity and physics.
Thank you for the excellent explanation. Now I know the problem with our current physics. We have built on a foundation that doesn't quite match observations of nature. Newtons postulates. The solution is going back and refining Newton's postulates to be more accurate descriptions of nature. Fyi, Walter Russell has already done this.
I'm glad there are people much smarter than me around.
Sean Carroll on RI……must be my Birthday or Santa 🎅 has come early 😁.
I love the bit around 39:10, "Skipping some steps...guess what?"
Excellent. I'm much the wiser on tensors now.
Thank you! You provided the most comprehensive, most intuitive explanations for one of the most iconic and complex equations: Einstein Field Equations! 🙂
Well done prof. Carroll! I like your simplification way through GR.
I think that the geometrical meaning of Ricci's tensor and scalar should be better explained (in general). Possibly as the first "Taylor terms" (constant and first linear term) of the expansion of the "curvature state". Probably Geometric Algebra could help. I think that the full Riemann's tensor is unnecessary and cumbersome.
Have a beautiful day!!
Thank you
Great presentation!
Prof. Sean Carroll knows what he talks about. 🙏
37:25 You're not quite a member of the last generation who had to calculate these tensors by hand. A few years ago I learned tensor algebra at a German university from a stern Russian professor who still made us calculate these entries by hand during exams.
It was in the context of continuum mechanics instead of General Relativity, but it's still the same kind of mathematics with Einstein's summation convention and stuff.
Believe it or not, some of what I learned in that course is still useful to me, as I keep impressing some of my colleagues at work with it every now and then by finding neat solutions with it. :)
That was an amazing presentation.
Thanks for that well explained connections we should plant into our brains now. It is very inspiring and leads to dive into the math more manually than just accepting the theory.
Excellent presentation… :-) So good I feel like I actually understood it… M
It's really amazing lecture. And it's very important how to correctly to interpret Einstein's equations in GR. We can see also:
Rethinking the Formal Methodology (II): Cognitive Content of Relativity (On the Centenary of General Relativity)
Totally fascinating
Really great presentation, thank you for doing this.
Great Sean!!! ⭐️⭐️⭐️ the best in talking about psysics in an easy way 👍🏼
Impressive presentation
Thanks!
Thank you for making this so understandable. Even though I may not be able to do the math or even want to do the math. Understanding how it all works and what the math is trying to say. I can now appreciate the strugle that is going on in the world of physics. Maybe my theory of ST1 dimention and the TS1 dimention entertwined together beeing respocible for the quantum foam that we expolor today and will show up one day described by the math. Then prove I was right all along. This is a fun ride. Thank you.
Hello Sean, I like how you try to explain quantum theory, I have an opinion that it's on the right track, however it is somewhat different from how I understand creation to be. First of all though I must explain that I've never attended university and have no formal qualifications. Although I have attended a 3 year training programme in Maori arts & culture graduating in 1982, and for the past 40 years I've been studying The Urantia Book, which aligns with our Maori culture, history and teachings.
The universe of universes (current creation) is not an infinite plane, a boundless cube, nor a limitless circle, it certainly has dimensions. The laws of physical organisation prove the whole vast aggrregation of force-energy and matter-power functions ultimately as a space unit; as an organized and co-ordinated whole. The observable behaviour of material creation constitutes evidence of a physical universe of definite limits and order.
The successive space levels of creation (the evolving master universe) constitute the major divisions of pervaded space, total creation, organized and partially inhabited or yet to be. If the master universe were not a series of elliptical space levels of lessened resistance to motion, alternating with zones of reletive quiescence, it would conceive that the cosmic energies would be observed shooting off on an infinite range of straight line paths into trackless space, and creation would not form, but would instead continually fly apart, and that is not observed as happening, ever the universe of universes whirl, always swinging onwards through the great circuits of space... (The Urantia Book, Paper 12 The Universe of Universes, pg 128)
Superb explanation of a challenging topic
Symmetry does help simplify a bit, taking sixteen equations down to ten.
Well done!!!
Bedankt
Thx. Very good video.
Pure genius explanation
Who is listeners of mindscape?
Very nice! Kudos for the book!
WAIT A MINUTE: at 7'07" you show 'ma', but in the previous equation I only saw "m" (small m).
Now, I spent dozens if not hundreds of hours learning about both quantum mechanics and astrophysics, but I am totally ignorant about math and shivers in fear when I see an equation.
But, now I feel I am ready to take a dive (well, actually I am ready to dip my toe in the water, but, whatever.)
So, I was interested to discover this lecture and I thought: this is exactly what I need, a Virgil who takes me by my hand and patiently teaches me to understand.
But then, bang, you pulled the rug under my feet.
Where is "m" and where did "ma" comes from?
Are they the same thing?
What happens when g00 becomes negative?
Great video!!
Excellent!! Thank you.
Great video.