General Relativity Lecture 1

[@DonaldEFlood]

It's fantastic that one of the leading universities in the World, Stanford, would, at their own time & expense, provide to the general public, for free, the very best lectures that are available on topics such as this. Thank you Professor Susskind and thank you Stanford University!

[@sourabhsaha5773]

Ikr.. this is just brilliant and shows how much more they care about education than money

[@lucasm4299]

Dawn Flood Go Stanford! 🇺🇸🇺🇸🇺🇸🏆🏆❤️❤️❤️

[@tNtNitro]

haha i get it GENERAL PUBLIC

[@ElixirOfEuphoria]

@@tNtNitro That's a stretch

[@nfergistink110]

Monetization x

[@lucasbuvinic240]

0:00 Intro 2:06 Original intuition : Gravitational forces = accelerated reference frame (-> tidal forces) 18:09 Curvilinear gravity (intro to coordinate transformations): Connection between gravity and curvilinear transformations of the coordinates of spacetime 24:02 Example of the elevator: equivalence principle applied to light 29:54 Intuitive notions on gravitational fields: you can't apply a coordinate transformation such that the tidal forces are eliminated (since gravity =/= accelerated frame of reference) 34:11 Fake gravitational field (created due to a certain nonlinear coordinate transformation) or a real gravitational field (tidal forces=real gravitational field) 43:58 The task: to find a coordinate transformation such that the tidal forces are eliminated 49:00 The mathematics that are involved in GR: Studying the geometry of spacetime (notion given to us by special relativity). 53:12 Riemannian Geometry 55:34 Curvilienar coordinates (and generalized distance) 1:06:22 The question of Riemannian geometry: Flat or not flat? 1:08:07 What does it mean for space to be flat? 1:08:47 Relation to the original problem of eliminating tidal forces 1:17:09 Coodinate transformations (intro to tensor analysis) 1:20:50 The notion of a contravariant vector (introduced from the perspective of the classic differential) 1:23:24 Definition a contravariant vector and how it's components transform under a coordinate transformation. 1:27:36 Einstein notation 1:28:57 The notion of a covariant vector (introduced from the perspective of the gradient of a function) (note the connection between a basis (direction) and the partial derivative along an axis) 1:35:17 Definition a covariant vector and how it's components transform under a coordinate transformation. Note: this whole introduction to coordinate transforms is nicely explained here but it's recommendable (and considering that most of us had to deal with linear algebra before getting to tensor analysis) that you'd watch eigenchris' Tensors for Beginners series 1:35:20 Central notion to tensor analysis: Tensors are defined by the way that they transform. 1:39:26 Generalization of this covariant and contravariant transformations (for rank 2 tensor with 2 covariant components or 2 contravariant components) 1:47:48 Transformation of the metric (unfinished) -> the metric is a tensor

[@chiragraju821]

thanks bro

[@the_sophile]

thanks

[@gunsandkithes6900]

****Spoilers!!!!! LoL it is actually of Great Help for re watching

[@pulga0907]

MVP

[@ishworshrestha3559]

Wow

[@tibees]

"I haven't been in a rocket ship but I have been in an elevator" I like how he uses the example that we can all imagine and understand. A great teacher 👏

[@keeratpanwar1499]

I am ur fan

[@pratyushranjanbohidar9983]

I came from your video 😂👍

[@dinaml7448]

hi😂

[@jaykay6249]

From the moment I watched your video, I have gotten so many suggestions for Genral Relativity lectures.

[@randomdude9135]

Yo

[@warpedwhimsical]

How could 1.2k people dislike this. You are being presented some of the highest knowledge of our world by an accomplished expert for free within the comfort of your home. People 100 years ago would have been grateful as hell for resources like this

[@mikeymike202]

Gotta agree 100%. Stanford physics lecture FREE. Even if you're not the least bit interested in the topic at least acknowledge the professor and thank Stanford for making it available TO THE WHOLE WORLD!

[@xJay600x]

Petty egotistical miserable people in this world. The world will never be free of them

[@Jamie0789]

I’ve no doubt the 1.2k dislikers are flat-earthers. They are gravity deniers, space deniers and pretty much everything else that science has taught us.

[@Jamie0789]

I’ve no doubt that the 1.2k dislikers are flat-earthers. They are gravity deniers, space deniers and everything else that science has taught us.

[@njvikings1]

Because it is a lecture on a theory, and how the theory replicates reality. While it is “accepted” by the public, by many, at its core it actually come close but does NOT describe all of the consequences we find. By close we see it leads to the rampant fission factors, but requires addendum algorithms to elevate other paths. It’s not 100%, more of 98%. Having said that the space of an atom is 98% empty, so describing reality and being right on Newtonian reality is essentially less then 1.99% right. In the induction of space and time it’s conjecture of “C” as being an absolute IS actually Newtonian since that limit doesn’t have the “limiting” factors listed as quantum/aether/zero point based. In our reality this may seem as inconsequential, but in the algorithms used, it is similar to the childlike answer “BECAUSE”. So while it given as a PHYSICS, lecture, the base science are the reasons for the physics leading to this point. Contemplate , 1910-1940, this time period contains the main algorithms for which Einstein developed, and “borrowed” choice algorithms from other physicists. As a definitive, look at the relevance of the Hopf fibration algorithm and then ask why Einstein did not use it…..

[@nethminnn]

In Einstein's time, academics used to travel halfway across the world in trains and ships to listen to a lecture like this. Learning is literally at our fingertips.

[@RalphDratman]

What a great teacher. He seems like an ordinary guy, and he often gets mixed up on details, but when he gets to the heart of the matter, he is just wonderful. Thank you so much, Prof. Susskind. This is so helpful.

[@amandajaynesparrow3591]

+Ralph Dratman He is truly amazing Ralph

[@jimkeller3868]

Disagree. He is obviously hyper intelligent, but not necessarily a great teacher. He begins by translating coordinate frames with little or no explanation as to why he is doing what he is doing, and what his goal is. In fact I disdain the type of teaching that simply, at least from my point of view, seems like "we are driving somewhere, but we have no fucking idea where we are going and why." HE obviously knows where he is heading, but suspect that he hasn't made it clear to his audience. The first few minutes of this lecture are confusing as hell to me.

[@RalphDratman]

I think you have a good point. A few months after I wrote the comment to which you are replying, I also began to feel dissatisfied with Susskind's teaching style.

[@rmsvideos1335]

There really is no business to be had learning GR anything deeper than the surface level if you're not very well versed in things like coordinate transformations and things of that nature.

[@bunklypeppz]

"I disdain the type of teaching that simply, at least from my point of view, seems like "we are driving somewhere, but we have no fucking idea where we are going and why."" But that describes basically any course on mathematics. That's why there's a difference between math and applied mathematics. You need to have a background understanding in the formalism before it makes sense to start learning the applications when it comes to studying any exact science. Any field of advanced physics has prerequisites in various types of mathematics and physics so it makes sense to start with sort of a crash course on those things. If you already are familiar with them, then it shouldn't be confusing because it's not even new; if you're unfamiliar with them, then you would need to know it before learning the rest to any substantial degree of detail.

[@AsMyTiGeR]

I wonder how Proffessor Susskind manages to balance his time between lecturing and being a hitman for Walter White.

[@thepakistallion9445]

+Arthur Morris lmfao

[@kaliheera2136]

aahhahhaha maybe he took advantage of the grandfather paradox and is HIDING it from us :P

[@davidlee2221]

i almost died after reading this.

[@victorfergn]

noooo!! soooooooooooo great joke! congratz

[@nidhishsharma9471]

hahaha lmao

[@JohnnyYenn]

It is such a privilege to be able to have access to these :0

[@elifece7847]

indeed

[@dev_time]

ikr

[@sye--turkiyetiktoklive8093]

Exactly this Gem... Online Free treasure lectures 😍😍😍😍

[@HyperSlash778]

:O

[@andreamannoni3199]

I've done Physics and then moved to business, it's just wonderful to have available these lectures that bring me back to my twenties. Great initiative by one of the leading universities in the world

[@qbtc]

I found that the best way to learn from these lectures is to watch them twice. This is because it is always easier to review something vs learning it for the first time. Also, you always miss something the first time around if you are processing what Susskind is saying. You should review or learn Calculus 1, 2, 3 and some basic linear algebra and differential equations. Watch all of his Classical Mechanics and Special Relativity lectures before this as well. I reviewed Calculus 3 from KZbin's Professor Leonard and that turned out to be a great review of all of Calculus 1, 2, 3 since he teaches and reviews at the same. He is the best professor I have seen.

[@Forever._.curious..]

Thankyou ❤️

[@mrhphysics7848]

This is great. Serves multiple uses. For people who want to learn and for people who can't sleep but are conditioned to sleep through lectures. I fit both categories so it makes for a nice sleep aid and hopefully I will learn coordinate transformations in my dreams

[@BartAlder]

Hahahh, loved this comment.

[@HACKINGMADEFUN]

@@BartAlder same

[@SirLucidThoughts]

I'm expecting results. Started listening to these lectures at night. But then I sleep so well I forget everything. Here's hoping that one random day I will suddenly be able to explain to some poor unsuspecting person.. or cat.. how various quantum physics theories and principles of their foundations work. It's in my head, but, I don't know how to teach or explain like these Masters of physics.

[@spb1179]

You found my secret

[@rickrocha255]

Here I am at 43 years of age trying to understand the basics of what I always wanted to know but couldn't figure it out what I wanted in life. So frustrating. I could blame my parents but its all my fault. At least now, thanks to this, I can do this without drooling on top of my school desk like the old times. Thank you.

[@davethinkingsystems]

This shows that someone who truly understands his topic can express it in a way others can understand.

[@Shelzastark]

We are highly fortunate to exist in a timeline where we can experience legendary people like prof Feynman and prof Leonard ssuskind..these are the people who have left hope to humanity and the world of teaching.. thanks to these people.

[@marcoguariglia7734]

I don't understand a single mathematical passage but I watch these videos to measure the distance between me and these geniuses. great professor susskind

[@reddevil211287]

lol you're funny

[@amymenjivar8960]

Honestly this is supposed to be an introduction to this topic and I feel like it's not the best way to teach this subject to someone completely new to physics. If anything, what sets this from a "great" lecture is that he's assuming his students know the context of everything. That's just me though lol

[@rbrtdff]

@@amymenjivar8960 I think it's an 'introduction' to people who are studying physics fulltime, with a decent level of undergraduate mathematics and probably after doing a good amount of work on all the fundamental Newtonian physics.

[@rbrtdff]

@@amymenjivar8960 I'm just watching the first one called: "Lecture 1 | Modern Physics: Quantum Mechanics (Stanford)".... it's a lot more of an overview/introduction

[@dustyrose9729]

Me too

[@realhbk316]

Thank you Stanford University for making such advanced knowledge easily available to the masses.

[@AnonYmous-sk7kp]

These are "continuing education" courses and we are very lucky to have them. You can tell by the questions from the audience that nearly all of them are in completely over their heads. He is doing a great service by presenting these topics at this level, considering the level at which he actually understands them.

[@sundarrajn1003]

susskind is doing a great favor to humanity by posting these lectures...thanks a lot..

[@theindianchannelmotivation]

he is just amazing he is the one who played an important role in developing string theory. He won the black hole war against hawking . he is awesome

[@alpineplace7451]

Enter the Braggn' wondering what the future of phychitric illnesses quentifacation is?

[@tthistlethwaite]

what war. there wasn't one.

[@theultimatereductionist7592]

Well said, Tom Thistlewaite.

[@sasmas1545]

Enter the Braggn' your comment is nonsense.

[@ozzyperez3190]

Thats a vague description

[@PhoenixMaster123]

i highly appreciate these free lectures. As a person who studies engineering but also really loves physics, it's very useful to have these to learn the content of a physics degree without actually paying money to do the degree

[@pepechill8118]

Who would have believed that I would have the right to hear lectures at such a level for free from the other part of the world

[@aSeaofTroubles]

Einstein was so brilliant! I mean who can IMAGINE this? Amazing lecture from Dr. Leonard Susskind.

[@BayesianBeing]

Couldnt agree more!

[@tclaughridge]

@@gullit97 fantastic counter-argument.

[@remo5097]

@Guglielmo Ferranti, your counter argument just made me orgasm

[@99bits46]

Newton for sure

[@mattbatcher802]

@@ericbitzer5247 Tesla posed for a photograph holding a book: Theory of Natural Philosophy, Roger Joseph Boscovich.

[@sudarshan750]

There is a unique elegance in your teaching style.

[@raffaelehuang8360]

The secret is that coffee. Coffee is the key to understand General Relativity.

[@jglazemoney]

Agreed!! That's actually what i'm doing now! Drinking coffee and studying general relativity.

[@PoloBoyMal]

your life sounds amazing! :)

[@erickschulz4637]

Truth was spoken. I think Susskind doesn't discuss this part of the theory because it is part of the independent homework one should go through. You start with nothing and learn how to make coffee.

[@stupidpdj]

And cookies.

[@alpineplace7451]

Erick Schulz pill of eternal alteration

[@Netanya-q4b]

He reminds me of my middle school math teacher, simple instructions on how to understand complicated ideas related with care and humor. Fantastic

[@saadhassan8813]

"Care and humour" the most apt description of his style.

[@dencameron3450]

I love this bloke. He taught me so much. A phenomenal physicist and a wonderful human being

[@Hello.Bye.123]

I really enjoy his style of teaching. Starting with simple things makes it easy to grasp the theory.

[@StarlightForce]

lmfaooooo

[@NPCvsNPC]

If I am ever able to do something with my life, a lot of credit has to go to these free Stanford classes

[@EscapeCondition]

Keep studying, learning always makes life better

[@sravanthkumarchintalacheru1359]

best wishes

[@justinhamilton8647]

Mike Blair this mindset really chilled me out, I was always so anxious about everything until I realized it won’t matter in the end, so just enjoy the moment and do whatever the hell you want

[@Jwhansink]

lol lol llolllllll lololl mo lllo lol l lol loooolll lol lol loll lol lol lol lllllllllll lol llllllllllll lol lolll lol loo ll loool llllllllllllllll lol l loll lol lollllllllllll lol llllllllll loool lol lollll I’l lol lllllll lol l lol loo

[@reading7324]

You're gonna be massively successful and live a wonderful life. I have total faith in ya.

[@atanumaulik7093]

I really envy today's students. They have access to stuff like these.

[@lawliet2263]

These videos should not be made available for the third world countries.

[@dean107]

@@lawliet2263 wtf

[@mangos2888]

Right? My day, circa 00's, we didn't get videos!

[@pfarinella]

Thanks Stanford for making this available. The fact that we can freely access this type of content, from one of the top scientists alive is remarkable!

[@martinhsl68hw]

Nice typo

[@jpatrick1967]

The only word I understand in this video is elevator.

[@programthis3805]

jpatrick1967 LOL

[@Oshoim]

The Third Wheeler ,all others are between dumb and einstein,which is C

[@johnnykwon3999]

i understood lil g. he ma homie.

[@wayneyadams]

I give you credit for trying to understand, you are a cut above most KZbin viewers.

[@muhendiseksper7026]

How a stanford professor could not teach his lecture without copy notes in hand.

[@bigfuss4135]

I can't believe I found this on KZbin. A whole set of lectures by Prof. Susskind himself!

[@jennydanza3974]

Almost anyone can learn it but not everyone is so good at teaching it, nice lecture.

[@crowdozer]

"now I know you know this, I know you know all this I just wanted to formalize it" me, clueless: 👁️🕳️👁️

[@giselediniz]

🤣🤣🤣🤣🤣🤣🤣🤣

[@jerrynews5803]

Thank you for these videos! No amount of reading Ta-Pei Cheng will give me such an understanding of Einstein's General Relativity !

[@tretolien1195]

I remember watching this 8 years ago being overwhelmed by all the amazing mathematics and rich insights. Now as a graduate physics student procrastinating on my particle physics homework just coming back from watching the Yang Mills construction on 2x speed this feels almost painfully slow. Love the guy though, great explanations and my as well as many others inspiration for getting into physics

[@BlueMushroomSmurfCat]

You have my respect. I want to be a physicist someday day too

[@wayneyadams]

It has been decades since I was in graduate school and worked with these advanced concepts, so this series is a great refresher. There is not a lot of demand for advanced topics like these teaching high school Physics, even in the AP courses. I remember a few years ago when these lectures were only available on iTunes and they were difficult to find, now thanks to KZbin they are readily available to everyone. It is still depressing to see that the greatest number of comments are inane sophomoric humor rather than scholarly discussions. It makes me wonder how many viewers came to this site expecting another watered down video filled with cute animations and bombastic commentary about falling into Black Holes. Surprise!!! It's a college lecture! LOL Having said that (correct usage), I just can't resist the temptation to make one inane comment myself. I love the way he says, curvilinear, as though it were "curvy linear." I apologize for giving in to temptation.

[@justmeeagainn]

Are you always this big of a dick, Wayne, or do you save it for KZbin comments?

[@Urdatorn]

“Being squashed to death is an invariant fact - it’s not something you can make go away by doing a coordinate transformation!”

[@colalightyear7859]

such a coordinate transformation some would consider unnatural

[@sartrevincent9322]

Thanks for this marvelous lecture. General relativity becomes accessible. I tried many times to learn it, it is the first I clearly understand the basic of RG. Few basic mathematics, a couple of sketches...Answers also to questions regarding the equivalence principe which is generally proposed in a trivial way: there's a way to distinguish acceleration from a gravity field, it is the essence of RG which linked to curved geometry.

[@tclaughridge]

My mind was blown at 28:50. The dots connected in my head and I understood the nature of the relationship between gravity, time, and acceleration. Truly amazing.

[@StarlightForce]

no u didn’t 😂😂😂

[@tomdeneckere]

Great course! At 1:26:48 Professor Susskind says he doesn’t know why this type of transformation is called ‘contravariant’ as opposed to another name. I always thought it has to do with this: imagine a vector in the plane and its components in a certain coordinate system (a basis). Now imagine another basis, say one that is rotated counterclockwise with respect to the first. Then the components of the vector in this second basis will correspond to the components in the original basis of a vector that has rotated by the same amount as the basis but clockwise. So for an observer in the second frame, the vector seems to be rotated clockwise (in the opposite sense as the basis itself) as compared to the vector in the first basis. In other words, the components of the vector transform in a way as to counteract the movement of the basis itself. Hence contravariant. Agreed?

[@jimpierce6811]

You like the word "vector"

[@ena131]

He has forgotten more knowledge than we will ever know ourselves

[@Snake_In_The_Box]

including how to draw parallel parabola

[@qwerpasdf]

@@Snake_In_The_Box he's just not using the correct TOOL

[@michaelvivirito]

Maybe more than you’ll ever know lol

[@vivalibertasergovivitelibe4111]

@@qwerpasdf nice

[@ena131]

Michael Vivirito y’all this was five years ago and it was about him having more intelligence and knowledge than common people

[@matteovissani1071]

Beautiful lecture. For the first time I really understood tensors.

[@rosskious7084]

To me the greatest achievement of Einstein was not General and Special Relativity, but his ability to give the world the concepts on a level that they could understand.

[@bonob0123]

what an age to be alive for stuff like this is free on the internet.

[@reading7324]

Im depressed I just had to say that to somebody

[@bonob0123]

​@@reading7324 Me too at times. Get outside, go for a walk or run, take a shower, clean your place. Make a plan. Better yourself in some way: work out, plan to finish a book, or even just watch a meaningful youtube playlist that which you will be proud of: intro to linear algebra, a physics class series, machine learning, whatever you are interested in but haven't gotten around to teaching yourself. Set a goal to better yourself in some way; if the activity involves helping others it will be even better and you will feel great. Corny as it sounds, volunteer or do something generous which helps someone else. I promise you will feel better. Forgive yourself. You had set goals before but you didn't feel like doing them and sat in the dark at home all day. So what? You needed a break and recharged. Now we start fresh today and there is no reason to trash yourself for yesterday. Being with other people you like helps but not all of us have people we can turn to. In that case think of yourself in a monastic process of bettering yourself and bettering the world. You are fucking bruce wayne in the mountains training with the monks to come out a badass for good on the other side. Be better. But first... get outside and take a walk. Good luck.

[@reading7324]

@@bonob0123 **tears** I can't believe you actually replied...and cared so much. Thankyou. I needed this. Probably gonna keep reading it for motivation. 💙🙏 That was PROFOUND

[@bonob0123]

@@reading7324 You made your way of your own accord to watch Lenny Susskind talk about relativity. Clearly you're already doing something right about your interests and interactions with the world. For the world to get to a better place it needs more educated, curious, good-hearted people interested in more than consumption and distractions. Good luck on your journey.

[@7mus7y]

Damn he drank that coffee for the full two hours

[@hm4939]

the secret is that its not coffee in the cup.

[@Peter_1986]

It's all about practice.

[@kilogods]

7mus7y it's not coffee, it's codeine syrup.

[@TopCroFutsal]

Here in Balkan (Croatia, Serbia, Bosnia) it is normal that we drink coffee a couple of hours

[@programthis3805]

he mathematically rationed each sip to last the full length of the lecture

[@imCurveee]

"Now I know you guys know this, I'm just doing this for the KZbin viewers at home who have no idea what I'm talking about."

[@dvl973]

He's 80 years old and still kickin'... I hope he lives at least another 20 :) what a legend

[@cyx4304]

More 80 t least

[@justinshin2279]

I’d trade 15 years of my life for 2 of his because he will have a way bigger impact on the future of humanity than I

[@tenn46]

Hate to say this but this is my go-to video for sleep. It literally works every time.

[@dgriffon]

Just finished this course and I highly recommend it! Professor Susskind might be a bit messy on the whiteboard, but he provides intuitive insights that really help you understand this complex topic.

[@MehrdadGivehchi]

What a gifted teacher... thanks for sharing

[@camilicristina2839]

It would be nice if there was subtitles, at least English, but even more interesting if it had several languages. a good tip, because I am Brazilian and I understand English very well, but sometimes I have difficulty and I know others who would like to watch but do not understand English. In fact, the class was very good.

[@ahmadyogi1340]

English subtitle would help me a lot to understand

[@meleseberehannu2861]

It has subtitles you do not know how to activate in your computer

[@ClaringtonMusic]

I wonder how many people can really understand how really special this lecture series is! - This sentence is sadly true and full of Baoley

[@ManyHeavens42]

I really can't I need your help hahaha

[@nazganaie]

Grateful to Susskind and Stanford for making This treasure available for free

[@MozzieSpector22]

as a young person, 14, this breaks it down immensely. very grateful 🙏🙏🙏

[@blackmambagyn]

The best thing about youtube classes is that you can simply skip the questions some students have, but yourself don't. The worst thing about youtube classes is that you can't clarify the doubts you had, but no one else did.

[@ManyHeavens42]

Bad answer : The answers are not in the , Answer ,It's in The Right Questions ?

[@omgsolikevalleygirl]

I want to have things explained to me by Leonard Susskind all day for the rest of my life :D

[@yousteve221]

I have done post grad. math... Chaos/Non-Linear Dynamics, Quantum Mech. along with Neural Networks.. Knowing the math, these lectures are a beautiful explanation of this theory I had never seen before!!! I discovered these lectures several years ago and cherish their existence. I have had to rejoin the 'Stanford' channel three times to keep these lectures in my review. WHY!!!

[@yousteve221]

Leonardo

[@zidaneabderahim7131]

Now i understand why the equivalence principle was Einstein's happiest thought.

[@WaterproofSoap]

Videos like this are among the truly redeeming qualities of the internet. .....they are also amongst the rarest.

[@3monsterbeast]

Man, great professor's always break the rules. In his case, eating while teaching!

[@tatsumakisempyukaku]

Maybe he’s diabetic?

[@robtheprocrastinator1197]

Don’t even know why I’m here when I’ve failed pre-algebra.....

[@Godakuri]

Rob the procrastinator how do you fail pre algebra. Your teacher must have been awful, or maybe you just didn’t pay attention. Pre alg is just adding, subtracting, multiplying, and dividing

[@chaoticstorm8145]

Study whatever you like. Let your curiosity lead you. If you see an idea that you haven't learned or dont understand then leave the video watch another video describing it and come back later. The internet has all the information in the world at your finger tips, you just have to use it

[@madyjules]

It’s awesome that you’re here & PLEASE don’t leave... there are many who are not ready for information when we’re exposed to it Pre-algebra is usually taught during middle school (most often during 7 or 8 grade-> when we’re approx. 12 or 13 years old ) More human beings are in the same boat as you then those who are exposed to math & science in our childhoods You’re here now!!!! 😎 If you want to be inspired even more I recommend you check out Walter Lewin’s Physics lectures (available on you tube)

[@aftermath4096]

rekt

[@spikeoac4248]

@the l33t hamm3rbro Hey asshat, not everybody is good at math

[@ShakeSpear1949]

Check out Spring 2010: Particle Physics part 3. Some lectures by Prof Susskind on Supersymmetry.

[@wayneyadams]

1:22:30 Those little backwards 6 symbols (stylized lower case d) are called partial differentials (or derivatives), they tell you the rate of change of the coordinate in the numerator as the coordinate in the denominator changes. Let's look at a real world example. You are standing on an uneven stretch of ground with a hill in front of you. Let's call the east-west direction X, and the north-south direction, Y. You want to calculate the change in elevation (height) when you walk from one point to another on the hill. Let's say the point is some distance in the X direction and some distance in the Y direction away from you. We'll use Z for the elevation. So, we are asking for the change in elevation, dZ. Here's the plan. You will walk in the X direction first and calculate the change in elevation, then turn and walk in the Y direction finding that change in elevation. Adding them together gives you the total change in elevation, dZ. To keep this simple. let's assume the changes are smooth continuous upward changes, in other words, you are always walking uphill. Let's say the hill has a slope so that the elevation changes at a rate of 20 cm per meter as you walk in the X direction. That is what the partial derivative gives you. It is the change in elevation in the X direction ignoring changes in the Y direction. Let's say you walk 10 meters. Your change will be the rate of change, the partial differential, times the distance you walked, dX. 20 cm/meter x 10 meters = 200 cm. Now you turn and walk in the Y direction. Let's say the elevation changes at the rate of 5 cm per meter in the Y direction. Let's say you have to walk 20 meters in the Y direction to reach your final destination. Just like before, you multiply the rate of change of the elevation, the partial derivative, times the distance you walked, dY. 5 cm/meter x 20 meters = 100 cm. Remember that you are already 200 cm higher because of the first part of the walk. Your total change in elevation for the walk is the 200 cm change from the walk in the X direction plus the 100 cm change from the walk in the Y direction. dZ = 200 cm + 100 cm = 300 cm. That is all partial differentials do, they break down paths into small independent pieces that are then added together to get the total. Now to keep everything honest. in real world applications all those changes would be very small, and dZ would be the rate of change of your elevation as you walk from from one point to the next. I used large numbers to help clarify the process with understandable quantities that we can all relate to. When we break a vector (a path in some direction) into pieces like this, the pieces are called components. Of course this can be extended to any number of coordinates. Wayne Y. Adams B.S. Chemistry (ACS Certified) M.S. Physics R&D Chemist (9 yrs.) Physics Instructor (33 yrs., retired)

[@lawliet2263]

Very nice explanation.

[@wayneyadams]

@@lawliet2263 Thanks, you are the only person to have ever commented on an explanation (lesson) I have written (there are dozens), and I really appreciate it. Wayne

[@DaveGrean]

In Europe we use an uppercase Greek letter delta Δ for that. If x = distance then Δx = displacement, if t = time then Δt = duration, etc... I would define Δ as 'interval' but I guess 'differential' does make more sense

[@cheeheifoo9282]

Leonard Susskind is such a patient teacher listening to all the difficulties

[@swaybryan524]

I just hit 2 blunts then watched this.....you don’t want to know how mind blown I am

[@scu8a]

I'm having a visit with Jack Herer this morning. It's nice to know that I'm not the only one who watches/reads scientific material after getting ripped. CBD of course ;)

[@diamondisgood4u]

​@@scu8a Herer has always been my fav, me and all my coworkers definitely use sativas while we learn stuff like reading papers about cannabis or me who watches stuff like this in my free time.

[@scu8a]

@@diamondisgood4u Yeah, it's between Herer and Girl Scout Cookie for me.

[@wayneyadams]

57:00 There is a convention called the "Einstein Summation Convention" that says that indices that are repeated are automatically summed. In this equation, the m and n are subscripts on the g, and superscripts on x, so the summation sign could be left out. It is a way to remove some of the clutter from long complex equations. It really does make them much easier to read.

[@ManyHeavens42]

Holy S, I barely understood that ?

[@gergelyfazekas7285]

I took up General Relativity at university, so I think I'm going to binge watch these lectures 😂

[@ManyHeavens42]

You are special ➿

[@marionascimento450]

Wow, I've always loved his lectures and just now I realized he was 73 (now 82). This guy is amazing.

[@hollaadieewaldfeee]

"Aquivalence principle" is unscientific, because the observation is restricted intentionally and arbitrarily. The following fraud is based on this comparison of restricted observations. Make a hole in the box, look through it, and the fraud is revealed.

[@rjhanna13]

Lenny is eating that forbidden knowledge cake throughout. But as an aside, I have a MS in physics and am immensely grateful for these, we only touched upon special relativity.

[@MuadDib2005]

That's a shame. I'm working on my BS as we speak and some of my keenest interest in life is on the subject of General Relativity. I've been doing my own work, research, and diligence, because I am getting the idea that physical modeling is going to be the brunt of my studies at university. Looks like I'll just have to keep working on my own 🤷🏼‍♂️

[@billyjean8066]

I love this guy... he makes me feel like im being taught physics by christopher walken

[@SniffyPoo]

I like that he gets confused at one point, even geniuses are human

[@MotivationStation275]

Even einstine had problem with his own theory.... and yess he is human

[@animationspace8550]

You've forgotten Hal 9000, GLaDOS, and Elon Musk. But yes, everyone else is human.

[@vivalibertasergovivitelibe4111]

We used a lot of tensor calculus in special relativity and it is kinda cool to see another approach vor introducing them. If you however are not really satisfied with this explanation and want a deeper mathematical understanding than "tensors are objects that behave like tensors" I would recommend the two video series the channel Eigenchris made on them called "Tensors for beginners" and "Tensor calculus". He explains perfectly and ectremely patiently what tensors are in regard, to space, dual space and the tensor product and why they transform as they do, what the metric tensor does and why etc.

[@M-uy1zc]

WRT @qbtc, I found that the best way to learn from these lectures is to watch them 6 times. I would REALLY appreciate closed captions, especially for audience questions and statements. i can hear and *understand* Dr. Susskind but sometime the audience id VERY difficult to understand (hear). Great Teacher.

[@redfruit1993z]

This is so awesome to have university level classes available for free to millions of people. Internet will revolutionize education.

[@p1nesap]

Bravo Prof. Susskind! I enjoy the ego / intelligence involved in students' questions & Prof's curt responses (one does not seem to exist without the other). Prof keeps the brakes on by not indulging students' questions that are ahead of the lecture at hand.

[@STEFJANY]

Einstein intelligence sends chills on my spine...how a human mind can come up with this counter intuitive ideas of curved space-time fabric...waw.

[@BartAlder]

Yeah it's mindblowing.

[@fanimeproductionst.v.3735]

Yeah, it's mindbending

[@ohohohitzmagic4536]

Sean Carroll says if anything Einstein is underrated.

[@teejayevans]

Einstein did not develop GR alone, he had help from mathematicians...which is probably where we get the myth that he flunked a math course. They get no credit. Look up Marcel Grossmann and Michele Besso. There was also an error in the math in the original version that got corrected in a revise paper.

​@@teejayevans Error in the math? Really, that's what you're holding on to? Isaac Newton's original Principia (which is a masterpiece) is RIDDLED with both conceptual and mathematical errors. LOTS of them. Even basic math errors you wouldn't expect from a great thinker like Newton. You will not find any great theory without mistakes. Maxwell's original papers on electromagnetism also have errors which were corrected (and then reformulated into a different mathematical formalism). Paul Dirac made mathematical errors pertaining to renormalization which were later corrected. They all make errors. Einstein was a one-of-a-kind-intellect. His mathematician buddies knew it too, read the letters. He taught them physics, they introduced him to new math (and he had to teach himself differential geometry and Tuli-Civita's tensor calculus). Emmy Noether did work for Hilbert. Max Born did much of the math for Heisenbergs matrix mechanics. Does Heisenberg - a distant, distant relative of mine on my dad's side - get less credit because he got math help? You're completely missing the intellectual context that General Relativity arose from. Einstein was engaging in what everyone believed was a fruitless journey: Newton's theory of gravitation was fine. Other than it's failure to predict the anomalous perihelion of Mercury, there was no urgent NEED to replace it. ONLY Einstein saw the fissures in the crack (and to my knowledge, he was only one who discovered the equivalence principle). Max Planck said to Einstein, "why trouble yourself with an impossible task? If you try, you will fail; and if you succeed, nobody will believe you." (Cited by Prof. Levinson at MIT, the date of the letter being 1909). Einstein was dealing with a field of mathematics that MOST physicists were not familiar with and that was relatively new - tensor calculus. It was such a new field that he got to correspond directly with one of the inventors of absolute differential calculus - Tullio Levi-Civita. It was such a new field that Einstein, the physicist, even occasionally corrected the pure mathematician who invented the field, Levi-CIvita during their correspondence. Marcel Grossman helped introduce him to the Riemann's math and Michele Besso was a great sounding board for complex math as well, but make no mistake it was Einstein who did all the heavy lifting. It was Grossman's misunderstanding of some of the physics that led them down the failed Entwurf Theory (great mathematicians sometimes make subpar physicists). By 1913, he was done working with Grossman and by 1914 he was teaching Hilbert, one of the finest mathematical minds of all time, HIS theory - which he derived from first principles and built WITHOUT an existing field theory. He had to BUILD his own field theory and develop rules for this theory out of thin air. I don't think you properly appreciate the degree of difficulty of what Einstein did. If General Relativity was being formulated today, it would've been done by many different physicists, much like quantum mechanics, who put different parts of it together. Einstein was putting this thing together by himself with the aid of his mathematics buddies who themselves didn't quite grasp the mathematical consequences of the physics. Einstein had also arrived, more or less, at the correct field equations by 1911. Again, we're talking about something that didn't exist until Einstein brought it into reality. From 1911 to 1914 Einstein grappled with something that's known as the "Hole Problem" and general covariance (which David Hilbert ALSO struggled with). By the time Einstein published his final paper in 1915 it was generally covariant (Hilbert hadn't figured out general covariance yet). The degree of difficulty was high man, I don't think these amateur physicists understand how hard it is to solve the Einstein Field Equations. In his lectures on gravitation, Feynman first derives general relativity using field theory methods and then says this about Einstein’s discovery of general relativity: "Einstein himself, of course, arrived at the same Lagrangian but without the help of a developed field theory, and I must admit that I have no idea how he guessed the final result. We have had troubles enough arriving at the theory - but I feel as though he had done it while swimming underwater, blindfolded, and with his hands tied behind his back!" Here is another quote from the same lectures. Feynman, on Einstein’s recognition of the principle of equivalence as the key to gravitation: "How much like Einstein this sounds, how reminiscent of his postulate of special relativity! We know the principle of equivalence works for springs, (as we knew special relativity worked for electrodynamics), and we extend it by fiat to all experiments whatsoever. We are used to such procedures by now, but how originally brilliant it was in 1911-what a brilliant, marvelous man Einstein was! " Here is another Feynman quote, in a different context [1]: "Einstein was a giant: his head was in the clouds, but his feet were on the ground. Those of us who are not so tall have to choose!" Without the mathematical work of Descartes and Fermat on analytical geometry, Newton never develops the Principia. This probably explains why a man with no formal training in math, Leibniz, beat him, a math genius, to publishing calculus first. Leibniz's formulation of calculus was also superior (especially because of its notation, dy/dx, which we still use today). Newton's original Principia was riddled with mistakes and errors - if you've read it, you would know. And Newton was a mathematics genius dealing with, relatively speaking, easy mathematics, calculus, that child prodigies can teach themselves these days. Einstein taught himself differential and integral calculus by the age of 14. The math Einstein was grappling with and the math Newton was grappling with are light years apart in terns of difficulty. Newton got his inverse square law from Hyuggens and Hooke. He got 2 of his laws of motion from Galileo - who had already shown the law of inertia. He and Leibniz both arrived at the infinitesimal calculus from reading the works of Descartes and Fermat (the latter being the one who most continental mathematicians believed was the true founder of calculus). Geniuses need help. They ALL do. Hilbert had Noether and Klein to correct his papers and check his proofs. Ramanajun had GH Hardy. Einstein was dealing with math far more advanced than what Newton was dealing with. And by the time he was done, he had mastered it well enough to contribute original ideas to pure mathematics - the Einstein summation convention being an easy example. There's a reason he's regarded as the greatest physicist ever. Link: www.huffpost.com/entry/einstein-fantasy-physics_b_4948045

[@milkonion]

How am I enjoying a relativity lecture at 2:39 in the morning... and I can’t even stay awake during the actual lecture😂

[@gullit97]

Man i get you bro...

[@utpalborah2896]

A valuable lecture also very interesting which I have found as a man of PHYSICS ! Hope to receive more.....

[@mikikaboom9084]

I watched the whole series now, 10 lectures. I want to say thank you for making this free.

[@Elrond_Hubbard_1]

General Relativity Lecture 1 -- 2.9 million views Lecture 2 -- 540k views Lecture 8 -- 70k views Quite a drop off rate for the Ytube class.

[@ajaysinghrathore1940]

People start but never completes.

[@mangos2888]

Have you read the comments? Half those 2.9m views are because people fell asleep and woke up here... Still a crazy drop between 2 and 8. 🤣

[@zemm9003]

​@@ajaysinghrathore1940it's not just that. The first lessons are way more interesting. I am myself a Physicist and I find later lectures very boring because they address topics I don't care about.

[@RabbitInAHumanWoild]

Yes, there's nothing wrong with the lectures. If you get lost it's because you don't have the background.

@Jože Ws Ive listened to a ton of GR lectures on KZbin. This is easily the best.

[@tensorwolf]

Jože Ws you don’t expect a 72 year old to just stand there for 2 straight hours? I’m sorry that you don’t have enough background to understand the material.

[@sajateacher]

If you get lost it's because you don't have those cookies.

[@kthwkr]

It would be better if there were no questions asked until the end. He is making a point and then they ask questions and the point gets buried.

[@cgme7076]

Oh, yes, of course! The elevator is an elevator. I'm with you up until that point.

[@dhruvshukla5591]

Professor Leonard Susskind is truly brilliant 👏👏 such a nice explanation

[@BrianOxleyTexan]

This is the best explanation of covariant vs contravariant I've seen. Say you have a chart of local temperatures in your area. Covariant is you move 1 km and I want to know that change by miles. Contravariant is that I ask you to move 1 mile, and you convert to km.

[@MoerreNoseshine]

They finally discovered HD recording at Stanford, hurray!

[@Jessrobbie]

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[@souza-t]

@Melissa REID

[@Ayasha_khan]

@Jones David oh my gosh I saw that recommendation last week but I didn't bother to chatting her up 🤦🤦

[@elizabeth5623]

@Clara Gregory I'm also happy for taking the bold step in and investing $20k with Mrs Galia Benartzi after a week I received $74k to my bank.

[@morkris3753]

The patience of a saint.

[@timmybear4449]

Excellent. Talked with a German astrophysicist today, very interesting conversation. I'm technically food science, but this is very interesting.

[@mangos2888]

Heyyy fellow food scientist 👋

[@adrianf.5847]

6:30 two reference frames that are accelerated in the exact same way are even related by zero velocity. 12:40 Earth's gravitation points downward 15:00 Actually, the equivalence principle as I understand it is that on a planet, say, there is a body force acting on a solid (here a human being), that induces a downward contact force against the planet, whereas in the rocket ship, the contact force is induced by Newton's third law. 17:10 The motion of a planet about a star is highly dependent on a mass, because both actually orbit a common center of mass, and the planet mass determines how much the star moves. This effect is especially visible in a heliocentric coordinate system. 19:40 You forgot the primes. 26:30 And now we know why textbooks talk about rocket ships instead of elevators. 30:40 Mathematically, the only obstruction should be the "hole" in the center. For a simply connected region in the exterior of the planet, there should be a curvilinear transformation that makes the acceleration look horizontal. (The 2,000 mile man will still be squashed to death, because calculating in arbitrary different coordinates won't change the laws of physics.) (Galilean transformations can't be found.) 35:40 The apparent gravity is generated by motion, not the coordinate transformations. 52:30 I suspect most of this theory to be due to Gauß. 53:00 For constant time, the ds^2 metric reduces to "Riemannian" geometry. 56:20 There are geodesics. 1:00:00 It's the cosine squared. sin(0) = 0.

[@Jrcoaca]

These Stanford students have some killer questions.

[@adrianwright8685]

They're not Stanford students - Susskind gives these evening lectures to the general public. “A number of years ago I became aware of the large number of physics enthusiasts .... so I started a series of courses on modern physics ….. specifically aimed at people who know, or once knew, a bit of algebra and calculus, but are more or less beginners.”

[@akshayrathore2882]

2 hours continues lecture old man got some stamina

[@bjornsahlin]

+akshay rathore Guilty of not paying attention m8! There's an intermission at 1:17:21 :D:DD

[@akshayrathore2882]

psynfel doesnt seem like an intermission. he maintained same flow

[@amandajaynesparrow3591]

+akshay rathore Show some respect akshay rathmore he is a genius He is a Professor of theatrical physics the same field as myself

[@michaelbauers8800]

+Amanda Jayne Bristow theatrical physics eh? You would expect more drama than is present here :)

[@amandajaynesparrow3591]

Professor Susskind is doing a Lecture on General Relativity one of Einstein's well known theories which I find fascinating This is how he explains his theories and he has always used this method Mr Bauers

[@shimesami]

One minute I was watching cleaning rug videos and now General relativity at 1:25 AM in the morning. And I have no business with neither of them. I need help

[@xinzeng-iq7zv]

studying physics takes persistence, dedication, and passion for the subject matter

[@nickvansickle6734]

Wow. I have adhd sooooo bad, I am so thankful for this knowledge free of charge with unlimited replays. 😫 This is going to take me ages to get through. Thank you, thank you, thank you, thank you 🙏

[@algebra5766]

Brilliant! I love these lectures!

[@hfof]

4:43 I was completely focused untill that moment when he said( "elephant").😂

[@foton3986]

Never done math in my life because the teachers were shite but this guy is the best

[@georgikostov6982]

The BEST "thing" you can watch ! Like it very much!

[@daltanionwaves]

GR is my favorite concept out of all the concepts of life. Because of how simple and intuitive it is as a tool, while having such far reaching & sometimes less intuitive consequences & implications

[@ManyHeavens42]

Everything's a program and everything is quantum mechanics, welcome to The matrix

[@zemm9003]

​@@ManyHeavens42that literally means nothing.

[@azra.ertas9]

Pls English caption 🙏🏻🙏🏻