Sean is really one of the most entertaining lecturers on science for laypersons. He’s a great personality and excellent at simplifying complex ideas for us average enthusiasts. Thanks Sean!
It's been over 30 years since I got my M.S. in Physics, and during that time I have been teaching high school Physics, which can become mind numbingly mundane, even the A.P. classes. The upshot is that I have gotten rusty on advanced topics like Einstein's equation. His book, "The Biggest ideas in the Universe, Space, Time, and Motion" was a great review, and I can honestly say I learned some very useful Physics. In fact, it has inspired me to pull my intimidating 1,280-page book, "Gravitation" by Misner, Thorne, and Wheeler off the bookshelf and dive into it. However, even if you do not plan to go into the subject this deeply, you will benefit greatly from his approach. Having taught Physics for 33 years, let me give you some advice on how to approach this book to get the most benefit. 1) While the book is available as an Audible book from Amazon, you really need to buy the hardcover or Kindle versions. If you are an auditory learner, you can benefit from both, but do not rely solely on the audible version. I also recommend you have pencil and paper handy, and actually write down equations and study them until you feel you truly understand what they are saying (yes, I said "saying" because they tell a story). Doing this gives you two modes of learning, and if you also get the Audible version, you will have three modes of learning (auditory, visual, tactile). 2) Do not move on to the next concept until you are sure you understand the concept you are reading. This is not like reading a novel, missing something early on will affect your ability to learn and understand later concepts. 3) Take your time. It has been widely accepted that you will forget more than 50% of what you learn in the first hour after learning it. In fact, it is worse than that, you will forget 40% within the first twenty minutes. The way to combat this is to read and study a section on some concept, stop and come back to it an hour or two, a few hours, or even a day later and reread it. you will be surprised at how much you forgot. Don't believe this is true? Try answering this, how much do you remember from his talk? I mean truly remember to the point where you can explain it to another person, or even yourself. See what I mean? If you approach his book using these techniques, you will end up with a firm understanding that will stay with you for a lifetime. This is a great book so you should do your best to get as much out of it as he put into it. Wayne Y. Adams B.S. Chemistry M.S. Physics R&D Chemist (9 yrs.) Physics Teacher (33 yrs.)
I think I must have listened to every single Sean Carroll lecture,Interview, podcast he's ever appeared on. I'm just about to watch him at the Royal institute,, probably a similar lecture to this one. My memory is soooo bad ,,I need to keep at it . I promise myself one day I'll go back to school & learn all this for real.
Love the picture of the original Fiat 500 at 17:00. The "500" was the battle cry of a resurging Italy in the early '60s. It is admirable how the picture is showing the car in its most likely status through its lifetime, i.e. in need of some external energy input...
I have so many interests that viewing your channel today was like going back in time. Thanks to all involved and a special thanks to Sean for his tireless work in bringing Physic to the masses..
Sean's humor makes me laugh more than most comedians do. Like most humor, it is a connection between things that you had never imagined, but suddenly realize are completely obvious. In his case, though, the realizations are usefully educational, where he often reduces a complex idea down to a simple giggle. Then there are the statements about his "obvious" observations of life. _"You don't become a famous physicist by proving your predecessors right."_ Who discovered the Higgs boson? Who knows. But we know that Higgs was right. He's an amazing physicist, and a pretty good philosopher.
Very great lacture , I have watched many lactures on GR but today I had what I wanted. You are very knowledgeable professor, I look forward to watch your every lacture however if I find them.
26:44 Not in Newtonian mechanics (its equations do not presume a preferred system at rest) but in Maxwell's electrodynamics (Maxwell's equations are true only in a certain system "at rest" (unless one changes the concepts of space and time which is what Einstein did), this was a huge conceptual problem before 1905). What Newtonian mechanics does presume is the idea of absolute simultaneity, so I think Sean misspoke here. 1:04:16 Schwarzschild was even better than that: he solved Einstein's equation already in 1915! His letter to Einstein informing him of his solution is dated 22 December 1915 and contains in it the formula shown on the slide. 1:07:00 In all fairness, this is not what they said. What Schwarzschild and Einstein thought (and many others until the early 1920s) was that the locus r=2GM merely corresponded to _the location of the central point mass._ This was an easy mistake to make in those days because Schwarzschild actually used a different coordinate system in his solution than Sean is showing on his slide, so for Schwarzschild this locus corresponded to r=0, and it seemed perfectly sensible to have an infinity there, given the fact that a spherical coordinate system is not even well-defined at the origin, as everyone remembers from high school. But this was a mistake, a particularly nasty mental trap to fall into, due to the fact that tensor calculus was still in its infancy in 1915 and nobody at the time had yet figured out that line element singularities need _not_ correspond to the _actual_ singularities of the _geometry._ They can be simply artefacts of the coordinate choice. Which is what happened here, and sometime in the 1920s (IIRC) people have finally figured out that r=2GM was not the locus of any geometry singularity, it was just one of those fake artefacts. Today we recognise r=2GM (Schwarzschild's r=0) as the location of the event horizon. 1:27:00 I believe the question was whether light _itself_ can be a source of gravity. The answer is yes because light also has its own energy-momentum tensor T which couples to spacetime curvature per Einstein's equation. 1:27:32 Strictly speaking Einstein's theory does not say that matter curves spacetime, it only says that the two are always correlated in that certain way. But correlation does not imply causation. So it may be that both are a result of something _else,_ yet undiscovered, which is the actual cause of both. So for now the answer is: we don't know. 1:29:59 I think Sean misunderstood the (clumsily formed) question: what would happen to the theory if we let the speed of light parameter go to infinity. The questioner had the right idea: the Schwarzschild spacetime would become flat. Similarly, if in _special_ relativity one allowed c go to infinity, one would obtain Newtonian mechanics with the Galilean transformation instead of the Lorentz one. An _excellent_ lecture, BTW.
Why couldn’t my high school math teachers explain the fundamentals like Dr Carroll does? It would have put my brain in the right place conceptually and made trig a whole lot easier and calculus attemptable.
Just found the channel. I saw to all the videos from Sean on the Biggest Ideas in the Universe. This lecture is a great summary of those lectures. Always enjoy listening to Sean, he has a knack for taking complex ideas and making them understandable to most folks.
47:40 The dimensional notation of the components of the metric tensor need to be labeled in the order in which they were historically described in the scientific literature. This is because AI needs to parse together language from scientific research documents to draw the proper conclusions during the study of higher dimensional analysis. So you want x=x^1, y=x^2, and z=x^3; but you need to label t= x^4 because the next dimension is δt and that’s described as x^5 or the 5th dimension. You mustn’t use x^0 because that causes a bunch of local math errors in the MLP's transformer.
Loved it all. I am an enthusiastic novice, and this was pitched perfectly for me. Brilliant. I especially like the Q&A - he really knows his stuff, even if he does try to keep it simple for guys like me
E=MC2 Energy=Mass Converted two times. It has to do with Warp Drive technology. One part Hydrogen exhaust and two parts oxygen exhaust converts matter behind a spaceship from gases to water, that then converts a second time into ice and expands. To make matter expand behind a spaceship while warping space infront of the space ship is as easy as using hydrogen and oxygen.
When I wrote the Miguel Alcubierre papers (I never imagined someone would give a child the name before sending him to school to claim false credit for the papers) E=MC2 is the missing equation that has be prodominate in the scientific communtity for years and wasn't missing. The Alcubierre equations explain warping space infront of the ship and my Einstein equation eE=MC2 has to do with expanding matter behind the spaceship
My equation for gravity was Newton's equation, I wrote E=MC2 as well, that is why Einstein said talk to Nikola Tesla if you want to talk to the smartest man on the planet.
Matter going into a blackhole and the blackhole shinking is compression theory. Kinda like putting a pillow into a plastic bag and vacuum sucking the air out to cause compression.
When I did "science" in school, Newton was correct and Einstein wasn't mentioned. That was obviously "old school" science. Perhaps, in the future, Einstein will suffer the same fate as Newton.
x2 is the positive x axis and negative x axis same for y2 and z2, they do a much better job explaining that in school than this guy does.... Generally y has an upside counterpart for the negative axis. It is important to be aware of the x2 y2 z2 axis's when flying a plane or a spaceship, not so important for driving a car x0 y0 z0 would be the neuatral axis. G is gravitally pull. Round objects in space is spacetime curving into itelf. The Earth, moon sun and so on and so forth. If there is a sphere or ball in space, it has a gravity well in its center pulling mass around.
Einstein's equations assume continuous variables. Quantum mechanics assumes discontinuous variables. We know the latter is correct, therefore the former is incorrect !
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Sean is really one of the most entertaining lecturers on science for laypersons. He’s a great personality and excellent at simplifying complex ideas for us average enthusiasts. Thanks Sean!
Thank you sean, fabulous 👌
He’s a born teacher. And a great one.
Agreed!!
one of the best lectures that manages the balancing act between a popular scientific approach and mathematical derivation. On spot prof Carroll
That was BEAUTIFUL! No one has brought all the details together in a easy to understand way like Sean did.
It's been over 30 years since I got my M.S. in Physics, and during that time I have been teaching high school Physics, which can become mind numbingly mundane, even the A.P. classes. The upshot is that I have gotten rusty on advanced topics like Einstein's equation. His book, "The Biggest ideas in the Universe, Space, Time, and Motion" was a great review, and I can honestly say I learned some very useful Physics. In fact, it has inspired me to pull my intimidating 1,280-page book, "Gravitation" by Misner, Thorne, and Wheeler off the bookshelf and dive into it. However, even if you do not plan to go into the subject this deeply, you will benefit greatly from his approach.
Having taught Physics for 33 years, let me give you some advice on how to approach this book to get the most benefit.
1) While the book is available as an Audible book from Amazon, you really need to buy the hardcover or Kindle versions. If you are an auditory learner, you can benefit from both, but do not rely solely on the audible version. I also recommend you have pencil and paper handy, and actually write down equations and study them until you feel you truly understand what they are saying (yes, I said "saying" because they tell a story). Doing this gives you two modes of learning, and if you also get the Audible version, you will have three modes of learning (auditory, visual, tactile).
2) Do not move on to the next concept until you are sure you understand the concept you are reading. This is not like reading a novel, missing something early on will affect your ability to learn and understand later concepts.
3) Take your time. It has been widely accepted that you will forget more than 50% of what you learn in the first hour after learning it. In fact, it is worse than that, you will forget 40% within the first twenty minutes. The way to combat this is to read and study a section on some concept, stop and come back to it an hour or two, a few hours, or even a day later and reread it. you will be surprised at how much you forgot. Don't believe this is true? Try answering this, how much do you remember from his talk? I mean truly remember to the point where you can explain it to another person, or even yourself. See what I mean?
If you approach his book using these techniques, you will end up with a firm understanding that will stay with you for a lifetime. This is a great book so you should do your best to get as much out of it as he put into it.
Wayne Y. Adams
B.S. Chemistry
M.S. Physics
R&D Chemist (9 yrs.)
Physics Teacher (33 yrs.)
thank you for your advice especially on needing to revisit concepts at regular intervals
Sean, this one of your best lectures. Q & A session is awesome too! Well informed educated audience so the quality of the event is great!!!
Sean Carroll and Kevin Rudd are some of my favorite speakers for their fluid verbal continuity of a topic.
I think I must have listened to every single Sean Carroll lecture,Interview, podcast he's ever appeared on. I'm just about to watch him at the Royal institute,, probably a similar lecture to this one.
My memory is soooo bad ,,I need to keep at it . I promise myself one day I'll go back to school & learn all this for real.
Love the picture of the original Fiat 500 at 17:00. The "500" was the battle cry of a resurging Italy in the early '60s. It is admirable how the picture is showing the car in its most likely status through its lifetime, i.e. in need of some external energy input...
I have so many interests that viewing your channel today was like going back in time. Thanks to all involved and a special thanks to Sean for his tireless work in bringing Physic to the masses..
Sean Carroll for Prez!!
Best lecture ever!
Great talk and very good questions from the audience.
Great stuff, more people should watch this!
always a good feeling when you see not a single person looking at their phone
Outstanding presentation!
Jesus. Best, most comprehensive Q&A ever.
Sean's humor makes me laugh more than most comedians do. Like most humor, it is a connection between things that you had never imagined, but suddenly realize are completely obvious. In his case, though, the realizations are usefully educational, where he often reduces a complex idea down to a simple giggle.
Then there are the statements about his "obvious" observations of life. _"You don't become a famous physicist by proving your predecessors right."_ Who discovered the Higgs boson? Who knows. But we know that Higgs was right.
He's an amazing physicist, and a pretty good philosopher.
Very nice lecture... I'm glad the humanity can still produce such beautiful minds...
we need more of these kind of lectures
good stuff .. thanks
Very great lacture , I have watched many lactures on GR but today I had what I wanted. You are very knowledgeable professor, I look forward to watch your every lacture however if I find them.
I like the decorative painting/stenciling on the walls and the marbling of the columns.
26:44 Not in Newtonian mechanics (its equations do not presume a preferred system at rest) but in Maxwell's electrodynamics (Maxwell's equations are true only in a certain system "at rest" (unless one changes the concepts of space and time which is what Einstein did), this was a huge conceptual problem before 1905). What Newtonian mechanics does presume is the idea of absolute simultaneity, so I think Sean misspoke here.
1:04:16 Schwarzschild was even better than that: he solved Einstein's equation already in 1915! His letter to Einstein informing him of his solution is dated 22 December 1915 and contains in it the formula shown on the slide.
1:07:00 In all fairness, this is not what they said. What Schwarzschild and Einstein thought (and many others until the early 1920s) was that the locus r=2GM merely corresponded to _the location of the central point mass._ This was an easy mistake to make in those days because Schwarzschild actually used a different coordinate system in his solution than Sean is showing on his slide, so for Schwarzschild this locus corresponded to r=0, and it seemed perfectly sensible to have an infinity there, given the fact that a spherical coordinate system is not even well-defined at the origin, as everyone remembers from high school. But this was a mistake, a particularly nasty mental trap to fall into, due to the fact that tensor calculus was still in its infancy in 1915 and nobody at the time had yet figured out that line element singularities need _not_ correspond to the _actual_ singularities of the _geometry._ They can be simply artefacts of the coordinate choice. Which is what happened here, and sometime in the 1920s (IIRC) people have finally figured out that r=2GM was not the locus of any geometry singularity, it was just one of those fake artefacts. Today we recognise r=2GM (Schwarzschild's r=0) as the location of the event horizon.
1:27:00 I believe the question was whether light _itself_ can be a source of gravity. The answer is yes because light also has its own energy-momentum tensor T which couples to spacetime curvature per Einstein's equation.
1:27:32 Strictly speaking Einstein's theory does not say that matter curves spacetime, it only says that the two are always correlated in that certain way. But correlation does not imply causation. So it may be that both are a result of something _else,_ yet undiscovered, which is the actual cause of both.
So for now the answer is: we don't know.
1:29:59 I think Sean misunderstood the (clumsily formed) question: what would happen to the theory if we let the speed of light parameter go to infinity. The questioner had the right idea: the Schwarzschild spacetime would become flat. Similarly, if in _special_ relativity one allowed c go to infinity, one would obtain Newtonian mechanics with the Galilean transformation instead of the Lorentz one.
An _excellent_ lecture, BTW.
👍👍👍👍👍👍👍👍 . . . More thumbs up needed!
Thx for uploading and all the best for PSW from a german scientist!
Great q&a.
Why couldn’t my high school math teachers explain the fundamentals like Dr Carroll does? It would have put my brain in the right place conceptually and made trig a whole lot easier and calculus attemptable.
Great presentation. I am also very impressed with the editing. Probably the best edited lecture I have ever seen.
THANK YOU GENTLE PEOPLE!!!!
Just found the channel. I saw to all the videos from Sean on the Biggest Ideas in the Universe. This lecture is a great summary of those lectures. Always enjoy listening to Sean, he has a knack for taking complex ideas and making them understandable to most folks.
Love this one. Been listening to Einstein: His Life and Universe for the 2nd time with Audible. This is timely for me!
Great lecture. He introduced tensor very different then we learn from vector calculus and bases vector and linear transformation.
47:40 The dimensional notation of the components of the metric tensor need to be labeled in the order in which they were historically described in the scientific literature. This is because AI needs to parse together language from scientific research documents to draw the proper conclusions during the study of higher dimensional analysis.
So you want x=x^1, y=x^2, and z=x^3; but you need to label t= x^4 because the next dimension is δt and that’s described as x^5 or the 5th dimension. You mustn’t use x^0 because that causes a bunch of local math errors in the MLP's transformer.
This was truly a great physics lecture. Being led into insights about the math behind GR was amazing.
Great lecture
Amazing exposition
Loved it all. I am an enthusiastic novice, and this was pitched perfectly for me. Brilliant. I especially like the Q&A - he really knows his stuff, even if he does try to keep it simple for guys like me
thanks Sean ,,,,,,, really interesting and the first time I understood the maths =(at least a little bit!!) Alan, UK
Sean has an appreciable dry wit.
Well done.
Great lecture, thank you
thank you for your work - thank you for educating me. May you live long and well. Bye.
Awesome lecture! Everybody can learn science, when served by mind like prof Carroll.
My "Sunday mass".
That was a great job.
fantastic speaker!
E=MC2 Energy=Mass Converted two times. It has to do with Warp Drive technology. One part Hydrogen exhaust and two parts oxygen exhaust converts matter behind a spaceship from gases to water, that then converts a second time into ice and expands. To make matter expand behind a spaceship while warping space infront of the space ship is as easy as using hydrogen and oxygen.
what a great appearance !! and good questions !
An excellent lecture, and the implications are simply astonishing! Thanks!
Truly fantastic, brilliant and gorgeous!
When I wrote the Miguel Alcubierre papers (I never imagined someone would give a child the name before sending him to school to claim false credit for the papers) E=MC2 is the missing equation that has be prodominate in the scientific communtity for years and wasn't missing. The Alcubierre equations explain warping space infront of the ship and my Einstein equation eE=MC2 has to do with expanding matter behind the spaceship
I love that. Thank you very much
very good
Very interesting. I wish I had studied more physics.
My equation for gravity was Newton's equation, I wrote E=MC2 as well, that is why Einstein said talk to Nikola Tesla if you want to talk to the smartest man on the planet.
very interesting.
Great talk. Tensors are hard to wrap my head around unfortunately
I learned so many things today, I loved this.
phenomenal intellect!
My favorite
2GM is 2 Gravity Mass or twice the gravity of the mass
Matter going into a blackhole and the blackhole shinking is compression theory. Kinda like putting a pillow into a plastic bag and vacuum sucking the air out to cause compression.
Great
Maybe the man I gave the name Albert Einstein wasn't fond of spacetime, but I have been warping spacetime since the day I was born
good, very good !!!
0:10 I wish they had RUclips in 1871❤🎉 😉 🤓
Anyone who says that gravity is a weak force has never ridden a bicycle.
It's a claim that's relative to the other fundemental interactions and forces of QFT and electrodynamics.
I think he means at subatomic level it is the weakest of the fundamental forces🫤
lol. Nice joke. As for the other replies, your premise holds. Subatomic particles have likely never ridden a bicycle.
When I did "science" in school, Newton was correct and Einstein wasn't mentioned. That was obviously "old school" science.
Perhaps, in the future, Einstein will suffer the same fate as Newton.
x2 is the positive x axis and negative x axis same for y2 and z2, they do a much better job explaining that in school than this guy does.... Generally y has an upside counterpart for the negative axis. It is important to be aware of the x2 y2 z2 axis's when flying a plane or a spaceship, not so important for driving a car x0 y0 z0 would be the neuatral axis. G is gravitally pull. Round objects in space is spacetime curving into itelf. The Earth, moon sun and so on and so forth. If there is a sphere or ball in space, it has a gravity well in its center pulling mass around.
Einstein's equations assume continuous variables.
Quantum mechanics assumes discontinuous variables.
We know the latter is correct, therefore the former is incorrect !
Now that we know this, invite Nima Arkani-Hamed
I'm not late -- my personal spacetime is just slower than yours.