1. Introduction and the geometric viewpoint on physics.

MIT 8.962 General Relativity, Spring 2020
Instructor: Scott Hughes
View the complete course: ocw.mit.edu/8-...
KZbin Playlist: • MIT 8.962 General Rela...
Introduction; the geometric viewpoint on physics. Review of Lorentz transformations and Lorentz-invariant intervals. The 4-vector; basis vectors and vector components. Introduction to component notation. The inner product between two 4-vectors, and the metric tensor.
License: Creative Commons BY-NC-SA
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We encourage constructive comments and discussion on OCW’s KZbin and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at ocw.mit.edu/co....

[@mitocw]

View the complete course at: ocw.mit.edu/8-962S20. Best wishes on your studies!

[@meowwwww6350]

Thanks

[@abduljabar9676]

SO THANKS ! 🇺🇸©️®️📐💵🔬🔭💳💳💳💳💳💳📐💵📐🇺🇸©️®️📈☎️📉📐🗳🇺🇸©️®️

[@mitocw]

@Bob Mama You are right! Typo in the playlist link. Now we need to fix it on the 22 other lectures. 😝

[@meowwwww6350]

@@honeymavi628 that's why MIT is world no 1 because they value the student's learning and research,than their marks . But in India they only value getting a job and scoring marks not in interest Students won't fear of exams if you value their learning than their marks - Richard Feynman. And MIT does value their students learning and curiosity than marks

[@honeymavi628]

@@meowwwww6350 we are not demanding to cancel but we are demanding to postpone it for more few days in america 97 thousand students got positive after the reopening of the school America being the super power is not able to overcome from this problem How we indians will??? Having more than 1.30 crore population We jee and neet aspirants are about 3 millions, 3*4 =12 millions families ,our government do not think of the students they think of their own There is not even a single tweet from indian PM i dont know what will happen with us all Students on twitter are protesting from many days but the corrupted government is blind

[@physicsmaster]

If KZbin was a library MIT open courseware channel must be it's most important books shelf.

[@physicsmaster]

@@monstersp8331 I think universities all over the world should write to the indian government about delaying exams.

[@monstersp8331]

@@physicsmaster thank you for you support but MIT's support is biggest support.

[@elonmusk352]

@@monstersp8331 I guess you should send

[@bipinaryal1494]

@Yolo 2.0 Haha It's just insane !

[@ankitneelkanth5480]

​@@physicsmaster Brother you please first go and see the Swayam portal and NPTEL portal which is organised by the MINISTRY OF EDUCATION, GOVT OF INDIA

[@gurunandhaelamezhagan3669]

9:03 start - str, 11:07 spacetime manifold 14:16 Event 14:47 Coordinates 16:54 Metric 19:47 Special Relativity 21:07 Inertial Reference Frame 27:08 Einstein 's Synchronization procedure 30:06 Synchronization procedure 35:05 Units of length and time. 38:59 Some geometric objects - start 40:33 Displacement vector? 1:01:58 Spacetime vector

[@sayandey1478]

Goat

[@mattlitton1255]

I really appreciate these lectures, as well as other OCW series. Ive always wanted to learn GR but never had the chance during ugrad. I’ve been working through carrol’s space time and geometry but found some sections difficult to tackle on my own. It’s incredibly useful to have a recorded lecture to watch as I work through the material! Thanks OCW!

[@getaphd]

MIT you made my day! Just yesterday I was thinking how good it would have been if MIT had a course on the subject. Thanks!

[@princeyt3837]

🎓💋660 P👄7û8 80's o😂pooooo999iooo😂o😂o😀😄💋🤣🤣😝😝😎

[@owen7185]

Agreed 💯💯💯

[@kunalverma6940]

totally agree!

[@ihorstepanov7961]

me too 😅

[@mattagamer98]

It is quit mind blowing that we can acces all this information from such a high ranked university, thank you

[@prashantpanta2508]

MIT is really great to post this. I have been searching the materials for GR from quite a while that this course comes as a recommendation in my KZbin. But I wasn't able to find one. Now, I get this one. Thank you a lot!!!

[@aishwarytiwari2534]

Beautiful lecture. understood nearly everything. Now gonna test my understanding by doing PSets. Thanks MIT OCW. Thanks Prof.

[@shivamjalotra7919]

2006 Psets are what are available : ocw.mit.edu/courses/physics/8-962-general-relativity-spring-2020/assignments/index.htm

[@danielstanlan1794]

@@shivamjalotra7919 late reply but do you know where I can find answers to these Psets?

[@shivamjalotra7919]

no idea bro@@danielstanlan1794

[@randeepsinghmatharu9071]

I think we need to stop and pause sometimes to realise how lucky we are that this is free and available at a click!!

[@rifatzehra6546]

All flowed over my head but I am glad that I watched this anyway . Thanks MIT 😇

[@youtubeaccountno4447]

Lecture starts at 8:50

[@thinac]

Hero

[@sameepsingh4095]

Super thanks

[@renrenhamster1535]

Thanks MIT! I finished 7 MIT physics courses (8.01-8.06 and 8.286) and this is my 8th! Been enjoying it!

[@mitocw]

Fantastic!

[@meowwwww6350]

That's awesome

[@TheNevarranSeeker]

Thank you, MIT! I've been taking GR this semester and wasn't getting enough out of the lectures and the textbook to fully understand the material. Having this course available has been an immense help. I'm so grateful for your whole physics OCW library!

[@igorschmidlapp6987]

Any good relativity textbook is massive enough to have its own gravitational field.... ;-P

[@latt.qcd9221]

Any textbook is going to have its own gravitational field. Lol

[@amritkumarpatel5717]

Lollol

[@amritkumarpatel5717]

A piece of feather will also curve space time . Lol

[@judedavis92]

It’s not mass, it’s density

[@fahimjunayed5894]

that's exactly why we don't understand anything from it as it doesn't allow any information to escape from it.

[@personanongrata987]

It has been over forty years since I studied General Relativity (MTW and Dirac's thin book). This lecture is a great review for me. --

[@henridelagardere264]

9:20 Start of: *Special relativity in a form that emphasizes its geometric nature*

[@notintheobservableuniverse2594]

Sir, you're a true hero.

[@ourdictatorship]

For mathematicians, Wald is indeed fine; another suggestion would be Callahan, Geometry of Spacetime. Needham's Visual Differential Geometry with Forms will soon change the way the subject is taught (as his Complex Analysis book did) once enough time passes and enough generations are raised in its greatness - it may be the best textbook in mathematics written in the 21st century so far (and I've read a few), but its focus primarily on diff geo and secondarily on GR may sink it as a singular course text for a grad physics class.

[@swaree]

I miss the Commons License lady

[@l.berents5753]

Commons License Lady here. 👋🏻 I’m still working behind the scenes to help share MIT knowledge with the world. Use dental floss, wear sunscreen, and share your creativity with a Creative Commons license!

[@meowwwww6350]

@@l.berents5753 oh it's you!!! That's amazing!!!! 😲😃😃

[@eddie1136]

@@l.berents5753 That's amazing! LOL

[@veeradityabishnoi4010]

@sware jinx, you owe me a gum

[@peterjesus9087]

Thanks for giving us an opportunity for the preview of your lectures for those of us who can't afford to get admission at your campus, txs

[@conscarcdr]

Nobody: MIT: it's General Relativity time!

[@sumneetkaurbamrah1982]

Thank you for sharing the content! Have a nice week ahead. 🙂

[@vortexsci]

MIT OCW inspired me to create content for my own channel, especially on General Relativity. And what a surprise, around the same time I started, OCW created this beautiful series on relativity. Love it.

[@martinnyberg6553]

37:16 If you use the old Swedish foot (29.69 cm) you get even closer to a light nanosecond. 😊 (0.965 % error as opposed to 1.017 %)

[@wagsman9999]

I remember FORTRAN. And punch cards. And standing in line to submit batch jobs I am old. Lol.

[@hetaeramancer]

thank you for this MIT, My dream school...

[@KipIngram]

I somewhat object to discarding terminology like "covariant" and "contravariant." I agree with your assessment of the value of those terms for understanding the subject matter, but part of your job is to teach these students how to communicate with other professionals in the field.

[@AkamiChannel]

I'm sure they'll pick it up. It just can be confusing in the beginning and he wants them to focus on the ideas that are important rather than which is which.

[@meowwwww6350]

Hi mit ocw iam learning physics through your videos very thanks

[@gurumann9158]

There is a huge difference in MIT UNIVERSITY Education and MIT OPEN COURSE but MIT OPEN COURSE is better than other College and UNIVERSITY so think that what is inside in MIT i am coming MIT in 2024 It Is my 10th class now but i have seen all lecture from MIT open course Thank you MIT Love from INDIA 😊

[@tanushka7779]

Thank you, MIT and the educators!

[@zakoyaki]

What a great lecturer! Super clear

[@nicolasmaillo2165]

Hi, and thanks for the great content! I was wondering if it has been scheduled/planned to upload video lectures on 8.044 Thermodynamics and Statistical mechanics or any other thermodynamics courses since I consider the graduate level course as too hard with no prior knowledge. Also, is there any place where we can see what video lectures are being recorded and coming soon? Again, thanks for all the resources!

[@mitocw]

Here's what we have for thermodynamics: ocw.mit.edu/courses/find-by-topic/#cat=science&subcat=physics&spec=thermodynamics. Best wishes on your studies!

[@frankdimeglio8216]

​@@mitocw THE ULTIMATE AND CLEAR MATHEMATICAL PROOF OF THE FACT THAT E=MC2 IS F=MA: Ultimately and truly, TIME is NECESSARILY possible/potential AND actual IN BALANCE; AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. SO, time DILATION ULTIMATELY proves ON BALANCE that E=mc2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. The stars AND PLANETS are POINTS in the night sky. A PHOTON may be placed at the center of THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the SPEED OF LIGHT; AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=mc2 IS F=ma. Great !!! "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. E=MC2 IS F=MA. Consider the man who IS standing on what is the EARTH/ground. Touch AND feeling BLEND, as ELECTROMAGNETISM/energy is gravity; as E=mc2 IS F=ma. GREAT !!! E=mc2 IS F=ma. The linked AND BALANCED opposite of what is THE SUN is A POINT in the night sky. The stars AND PLANETS are POINTS in the night sky. A PHOTON may be placed at the center of THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the SPEED OF LIGHT; AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=mc2 IS F=ma. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. Therefore, the linked AND BALANCED opposite of what is THE EARTH is ALSO A POINT in the night sky. Great. Gravity IS ELECTROMAGNETISM/energy. ELECTROMAGNETISM/ENERGY IS GRAVITY. E=mc2 IS F=ma. Gravity AND ELECTROMAGNETISM/ENERGY are linked AND BALANCED opposites, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Accordingly, the Earth AND the Sun are linked AND BALANCED opposites; AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy, AS E=mc2 IS F=ma. The stars AND PLANETS are POINTS in the night sky. It ALL CLEARLY makes perfect sense. Great !!!!!! Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE. E=MC2 IS F=MA. The EARTH and the SUN thus constitute and comprise what are the MIDDLE AND THE FULL DISTANCE in/of SPACE (IN BALANCE) in full and BALANCED compliance and conformity with the CLEAR and universal fact that E=mc2 IS F=ma, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Great !!!! It ALL CLEARLY does make perfect sense. (The stars AND PLANETS are POINTS in the night sky.) INDEED, BALANCE and completeness go hand in hand. Now, very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. Great. NOW, OVERLAY what is THE EYE in BALANCED RELATION to/WITH what is THE EARTH. Notice the black space of THE EYE. The stars AND PLANETS are POINTS in the night sky. THE DOME of a person's EYE is ALSO VISIBLE. Now, carefully consider what is the semi-spherical, translucent, QUANTUM GRAVITATIONAL, AND BLUE SKY. Great. E=mc2 IS F=ma. It is CLEAR. THE EARTH is ALSO BLUE (AS WATER). GREAT. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. INSTANTANEITY is thus FUNDAMENTAL to what is the FULL and proper UNDERSTANDING of physics/physical experience, as E=mc2 IS F=ma; as ELECTROMAGNETISM/energy is gravity. Gravity IS ELECTROMAGNETISM/energy. It ALL CLEARLY makes perfect sense. Inertia/INERTIAL RESISTANCE is proportional to (or BALANCED with/as) GRAVITATIONAL force/energy, as this unifies AND balances gravity AND ELECTROMAGNETISM/energy; as this balances gravity AND inertia. (This clearly explains BOTH F=ma AND E=mc2, AS ELECTROMAGNETISM/ENERGY IS GRAVITY !!!) ACCORDINGLY, gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. SO, the BALANCE of being AND EXPERIENCE is essential; AS E=mc2 IS F=ma. Our EXPERIENCE is NECESSARILY that of what is the FULL DISTANCE in/of SPACE, AS we are BALANCED between what are THE SUN AND c (A POINT); AS E=mc2 IS F=ma. The stars AND PLANETS are POINTS in the night sky. SO, a given PLANET (INCLUDING WHAT IS THE EARTH) sweeps out equal areas in equal times; AND this is THEN consistent WITH/as F=ma, E=mc2, AND what is perpetual motion; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. E=mc2 IS F=ma. BALANCE and completeness go hand in hand. It ALL CLEARLY does make perfect sense. THINK about what is QUANTUM GRAVITY. "Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Indeed, gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Therefore, the rotation of WHAT IS THE MOON matches it's revolution !!! Objects fall at the SAME RATE (neglecting air resistance, of course), AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. Gravitational force/ENERGY is proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE; AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Stellar clustering ALSO proves ON BALANCE that ELECTROMAGNETISM/energy is gravity, AS E=mc2 IS F=ma. Magnificent !!! E=mc2 IS F=ma. Is a two dimensional surface or SPACE visible or invisible ? The answer is that it is BOTH. So, the electron AND photon are structureless. A PLANET (INCLUDING WHAT IS THE EARTH) is a balanced MIDDLE DISTANCE form in relation to E=mc2 AS F=ma. A PLANET (INCLUDING WHAT IS THE EARTH) is a balanced MIDDLE DISTANCE form in relation to the Sun AND c (A POINT). The stars AND PLANETS are POINTS in the night sky. E=MC2 IS F=MA. ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. BALANCE AND completeness go hand in hand. Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. E=MC2 IS F=MA. It ALL CLEARLY makes perfect sense. The BALANCE of being AND EXPERIENCE is essential. The INTEGRATED EXTENSIVENESS of THOUGHT (AND description) is improved in the truly superior mind. INSTANTANEITY is thus FUNDAMENTAL to what is the FULL and proper UNDERSTANDING of physics/physical experience. (THOUGHTS ARE INVISIBLE.) It is a very great truth that THE SELF represents, FORMS, and experiences a COMPREHENSIVE approximation of experience in general by combining conscious and unconscious experience. MOREOVER, the ability of THOUGHT to DESCRIBE OR RECONFIGURE sensory experience is ULTIMATELY dependent upon the extent to which THOUGHT IS SIMILAR TO sensory experience. Beautiful. It ALL CLEARLY makes perfect sense. E=mc2 IS F=ma. By Frank Martin DiMeglio

[@jurgenblick5491]

Love the way he teaches

[@phenomenalphysics3548]

i expected better

[@michaelwesterland1853]

I mean no disrespect, but i'm going to stick to the books. IMHO this professor hasn't decided whether he's going to lecture or write on the blackboard. "Today we will ... tap tap tappity tap tap ... be discussing manifolds ... tap tap tap tappity tap ... and ... tap tappity tap tap ... events and ... tap tap tap tappity tap tap ... the metric ... tap tap tap." Not for me, sorry.

[@aishwarytiwari2534]

@52:00 i think X0 should be x and X1 should be t. Because X0 = t and X1 = X doesnot fit in the formalism there.

[@debasispal4619]

Very useful during the era of online classes.

[@iKenFax]

The manifold discussion was enjoyable to think about, as well as the rest of it.

[@jim1898]

Love these lectures - thank you MIT. My only nitpick is that these prof's really should have presentations prepared - as a student, I always resented the wasted time of sitting there watching a prof write stuff on a blackboard.

[@tattah96]

This lecture series is more similar to how F.Shutz teaches it in his book, reccomending Sean Carroll in my opinion is misleading because Sean Carrol's book relies heavily on Abstract mathematical formalisms which can be initmidating to a first time introduction to this topic. Lecture 2 of this series is right out of Shutz chapter on Lorentz transformations. To new students trying to learn this stuff, use Shutz as a main and sean carroll as a complimentary, trust me it will make your life easier. Don't get me wrong, I love sean carrol's book, it has alot especially in the last chapters, he even gets into string theory and anti de sitter space, but as an introduction it has confusing definitions and not enough examples.

[@meowwwww6350]

Hi Mit please upload the missing videos on exploring black holes

[@benwilms3942]

Picture a lattice of rods and clocks. That is the most ambiguous instruction I've ever heard. Worthless if not better explained.

[@musselchee9560]

Hmm. Formal foundation. I like it. I'm an old school drop out. I have taken the time out to finally learn a thing or two. Over my life time I have spent 420 hours in therapy for, as one therapist asked "... are you still restlessly searching?" Up to the age of 14 I endured violent abuse (manifold) as remembered by my current IRF. The degradatious event(s) occurred over years, again as seen from my current IRF. The metric has gradually, with the benefit of distance through my desperate attempts at wanting to know Why!? enabled me to reach my current inertia and to now breathe a long sigh of relief, if you can dig it. THANK YOU for crossing the tees and dotting the i's for me (with your noisy chalk🙂). Great lecture.

[@sterlist]

I know this is a graduate course and the answer might be obvious, but do I need to have prior knowledge about special relativity? Or is it included in this course?

[@mitocw]

The prerequisites for the course are: 18.03 Differential Equations, 18.06 Linear Algebra, and 8.07 Electromagnetism II. See the course materials on MIT OpenCourseWare for more info at: ocw.mit.edu/8-962S20. Best wishes on your studies!

[@TylerMatthewHarris]

My favorite unit of measurement is the furlong per fortnight

[@Felipe-zm6xs]

i can't believe this much information for free, i didn't know

[@jackbradley4737]

lecture starts at 8:50

[@smartscience5305]

Hello sir. I am 12 years old and I am learning these great videos, because my dream is to be ASTROPHYSICIST, so I am learning quantum gravity,string theory,thermodynamics, electromagnetism spectrum and relativity. Thank you for your important and great videos🌸🌹

[@aayush_dutt]

I'm a computer science graduate coming from The Big Bang Theory watching this entire lecture series in COVID-19 lockdown :P

[@christophedlauer1443]

last I checked, the speed of light was roughly 300.000.000 m/s not 300k m/s. Very enjoyable lecture otherwise, thanks alot for making these publicly available.

[@NoActuallyGo-KCUF-Yourself]

300,000 km/s

[@jessewolf6806]

Same thing

[@jacobvandijk6525]

@ 19:16 Unfortunately, General Relativity isn't compatible with Quantum Physics (or v.v.). So our current understanding of reality is based on two theories not being able to communicate with each other. But when you're dealing with black holes, etc. you don't seem to care that much 20:03. "A pretty good job". This really is a personal opinion. Don't believe me? Try this: kzbin.info/www/bejne/iZ-TiJKjrKZqh5I (Don't remove this. It will come back again and again ...)

[@jjuns1420]

감사합니다 이런 수업 ㅠㅠ

[@LarryRiedel]

Crystal Clear so far...

[@RayJin-dq1td]

Time to make sure that I REALLY learned general relativity.

[@lokeshappanlokeshappaghpsh7894]

Like from India

[@p_square]

MIT OpenCourseWare can you please tell which book you are referring to? Thanks

[@mitocw]

The required textbook is: Carroll, Sean M. Spacetime and Geometry: An Introduction to General Relativity. Cambridge University Press, 2019. ISBN: 9781108488396. See the course on MIT OpenCourseWare for more info and materials at: ocw.mit.edu/8-962S20. Best wishes on your studies!

[@p_square]

@@mitocw Thank you

[@sunnyz2074]

Great lecture, very clear and easy to follow 👍

[@pkgoswami2351]

Thanks for this🤩

[@kosalaherath1350]

Thank you MIT

[@DeepakKumar-yk8cb]

One day, definitely gonna find a way to get admission there 😾

[@Siddharthpandeyji]

Great😀

[@YashKnowsBest]

Supreme ideology you’re a comedian if you think IIT is even close to MIT

[@Johncornwell103]

@Yolo 2.0 You are a fucking idiot

[@sankalp2231]

Finally we've GR from MIT!

[@TranscendentPhoenix]

Chatrapati shivaji sp STOP POSTING THIS COMMENT EVERYWHERE DAWG

[@Mrosen7542]

Thank you.

[@seanmacfoy5326]

58:02 - I didn't know Michael Penn was teaching GR at MIT now

[@mathematicalmonk1427]

I also caught it 😂

[@ujjwalb1729]

lmao

[@Physics_]

is time stamp wrong i didnt see him?

[@seanmacfoy5326]

@@Physics_ ahahaha it was a bad joke - listen to what the lecturer says again xD

[@Physics_]

@@seanmacfoy5326 got it mate-"i think it is a good place to stop"😂...... Nice observation

[@yuanyi827]

Thanks a lot!I have seen that 8.07 Electromagnetism II is one of the prerequisites of this course.I am wondering would 8.07 be uploaded soon?

[@dragoneagle11]

Assuming you have done an EM 1 course then you can easily self teach yourself EM 2 using Griffiths EM. It's a very well written textbook for undergrad EM. For EM 2 read chapters 3,4,6, 7.3.4-6, 8 and 9.2. That will essentially give you everything you need. Of course, if you have not taken EM 1 also do chapters 1,2, 5, 7.1, 7.2, 7.3.1, 7.3.2, and 7.3.3. They cover a good intro to vector calculus as well as electrostatics and magnetostatics

[@chrisallen9509]

@@dragoneagle11 Isn’t that missing the section on special relativity? For someone self teaching E&M for GR, I would argue that is one of the most important parts since E&M is a classical field theory, and seeing a coordinate independent way of expressing equations in it will be incredibly useful for GR.

[@dragoneagle11]

@@chrisallen9509 That's true, I saw that in EM III so I think it slipped my mind when I was putting the chapter list together for EM II

[@adrianwright8685]

Is there an advantage to using chalk and blackboard rather than projecting already composed computer notes which obviously have the advantage of legibility and speed?

[@NewYork1231000]

beautiful lecture! thank you so much! keep it up with the good work xoxo

[@justpranker3165]

Nice

[@samuelvieira1395]

For anyone using the captions, a manifold is a topological concept, not tautological.

[@alex1114_]

Really well structured lecture

[@arturocordovap]

Thanks, Thanks... Professor Scott and M.I.T.

[@abhayphanse9509]

48:50 what a save

[@seanpaul2562]

please update the course for Quantum theory I 8.321 as well we have only lecture notes for that no video lectures

[@strandedmusicians]

At 53:54 he says "You can read out the components of the lambda matrix from what I've got over there". He was so careful up to this point that I was a bit surprised that he didn't define capital lambda and was confused that he calls it a matrix. As far as I can tell, Lambda_nu is not a matrix but a 4x1 vector which is multiplied by the scalar delta x^nu (resulting in another 4x1 vector). Doing this for nu = 0,1,2,3 and adding together, we still get a single 4x1 vector, that will incorporate the Lorentz transforms if Lambda has the correct coefficients of the delta x's in the Lorentz transform equations. This uses the fact that they are linear in the delta x's. So in the example which he refers to as "what I've got over there", the Lambda_0 vector would be [gamma, -gamma*v, 0, 0] as these are the coefficients of delta x^0. Am I thinking of this correctly?

[@adrianwright8685]

Lambda is a 4 by 4 matrix, he defines it as having two indices.

[@Iconic_Alex27]

Very neat lecture. Thanks 😊

[@vivekanandmohapatra8255]

And the lecture begins from 9:02

[@puneettripathi740]

Thank you for this.

[@thehystericalleprechaun3356]

I always measure speed as Furlongs per Fortnight

[@omarbriones2453]

Writing on a chalk board during a lecture is an antiquated practice. This is MIT, where people are supposed to be using cutting edge technology.

[@gourabray6533]

Have you ever been in university math class?

[@omarbriones2453]

@@gourabray6533 Have you ever posted a comment on KZbin?

[@gourabray6533]

@@omarbriones2453 Yes, what's your point?

[@omarbriones2453]

@@gourabray6533 Obviously, my point is I have taken university math, and obviously you don't understand that mathematicians and physicists should use technology better to facilitate their lectures. The students don't need to watch the lecturer write on the chalkboard because that's a waste of time. Instead, the lecturer should have all that written out beforehand and present the written information in the lecture. This would allow for more time to answer questions in the lecture. In addition, the written information should be given to students before the lecture so that students can study it and come up with questions to ask in the lecture to clarify their understanding of the information.

[@gourabray6533]

@@omarbriones2453I disagree. I don't think giving the material beforehand facilitates majority of the students in university, as majority of them don't study before going to class (that's just an unfortunate reality). Writing in chalkboard live slows down the learning process, and helps students digest the material and ask questions live on the go. The student can ask questions later in office hours or via one on one meetings if possible.

[@forheuristiclifeksh7836]

17:16 events in

[@SomeshRajvlogs]

Always Wanted to Study it.

[@e_m_met]

Thank you for uploading. I have just finished watching this lecture. It was fascinating but I fear if this was the boring easy stuff I am going to start struggling in 3-4 lectures time. I have a question. Time was spend defining manifolds, event, metrics, how measurements or length and time are made, etc but no definition of length or time were given. Could these two concepts be defined, please?

[@TheMajorpickle01]

Can I ask, have you had any undergraduate education? Moving straight into this kind of mathematics will be very hard as it's usually a 3rd year or master qualification level being taught in GE

[@e_m_met]

@@TheMajorpickle01 I've a PhD in computer Science from University of Kent but that was a long time ago and my Maths has gone very rusty since then!

[@TheMajorpickle01]

@@e_m_met Oh then you should be very quick up the pickup! I'm a lowely theophys graduate haha. If you are willing to spend a little (or do some googling) there are two fantastic books to do some prereading for this module, "Engineering Mathematics" by KA Stroud, and "Essential Mathematical Methods" by Riley and Hobson. If you are mainly doing this for a dabble i'd suggest the latter! Doing Comp Sci i'd imagine you didn't interact with a ton of tensor, although i'd think you are probably somewhat familiar with vector mechancis. The only essential reading is essentially an understanding of tensor mathematics (which is basically vector notation)

[@rickprice7919]

It is possible that the lattice clocks are entangled.

[@dynamixthunder724]

love from indian village student❤️

[@ourdictatorship]

It is not easier to just say that a given structure is a manifold if there is an isomorphism between the structure and (real) space of some dimension?

[@hemungkapoor1368]

Thank you so much!

[@igorschmidlapp6987]

But, does he use Hagoromo chalk? ;-)

[@igorschmidlapp6987]

The tapping of the chalk is quite soothing, actually... ;-)

[@dhyangandhi4344]

How do I watch 8.07- which is the course on Electromagnetism. I really want to get started with relativity here but i read that knowing Electromagnetism is an important prerequisite for this course.

[@dhyangandhi4344]

I am unable to find it on KZbin

[@mitocw]

@@dhyangandhi4344 8.07 has not been recorded on video. There are course materials available at: ocw.mit.edu/courses/physics/8-07-electromagnetism-ii-fall-2012/. Best wishes on your studies!

[@paulmccartney7433]

In several lectures, the Professor says that he is going to upload certain material to the course website. Does anyone know how to access this material?

[@mitocw]

Any materials we have are posted on MIT OpenCourseWare at: ocw.mit.edu/8-962S20. Best wishes on your studies!

[@breakingmath1]

Nice guy, excellent lecture!

[@maneeshawijesingha1885]

thanks

[@hugovangalen]

So how do the two clocks actually synchronise? If the light is reflected by clock 2 -- how does clock 2 sync with clock 1? Or is the pulse not actually reflected, but emitted when the incoming pulse is detected?

[@hywelgriffiths5747]

clock 2 sets its 0 time to when it sees the light, and clock 1 sets its 0 time to halfway between when it sends the flash and when it receives it back

[@juancarlosdominguezsolis.4665]

Mit please we need the qft 3 course and the manh body problems ,confesante mattter and highly corrrelate systems please please ,maybe quantum theory and that It

[@meowwwww6350]

Hi mit please can you say me what textbooks do you use for black holes and cosmology course

[@mitocw]

The required textbook for this course is: Carroll, Sean M. Spacetime and Geometry: An Introduction to General Relativity. Cambridge University Press, 2019. ISBN: 9781108488396. See the course on MIT OpenCourseWare for more info at: ocw.mit.edu/8-962S20.

[@meowwwww6350]

@@mitocw thanks mit

[@meowwwww6350]

@@mitocw for all the cosmology courses?

[@57arungarg69]

Does this series completes the whole general relativity from basic to advanced?

[@mitocw]

From the course description, "8.962 is MIT's graduate course in general relativity, which covers the basic principles of Einstein's general theory of relativity, differential geometry, experimental tests of general relativity, black holes, and cosmology." Visit ocw.mit.edu/8-962S20 for more information and materials. Best wishes on your studies!

[@mioumitsou]

at 33:49 I dont understand the word 'synchronise''. Could somebody explain to me what is meant by synchronising the clocks?

[@lorenzogiorgi262]

hi everyone...thenks for this course...can i ask which are maths and physics prerequisites for it?

[@mitocw]

From the syllabus, "18.03 Differential Equations, 18.06 Linear Algebra, and 8.07 Electromagnetism II Students should also be familiar with Lagrangians and action principles, Green’s functions, and numerical analysis (some homework assignments will require the numerical solution of systems of differential equations)." See ocw.mit.edu/8-962S20 for more info and materials. Best wishes on your studies!

[@PrinceBlake]

Pop quiz: There is a 7-minute 20 second gap between two events in this video. Convert this gap to units of seconds. Now watch the video and then come back here and tell me the what you think - was this gap accidental or a sign of a hidden Controller? kzbin.info/www/bejne/iKWWdnSGedNgi8k Bonus question - what two events in the MIT lecture mark the endpoints for the gap?

[@SaemPhysics]

Pursuing my dream BSc without certificate

[@RabindraNathBose-w5l]

A good lecture.

[@paulhowrang]

Finally..GR...Big relief :D

[@davidwilkie9551]

From observation, a raw and undeveloped analysis of the e-Pi-i sync-duration connectivity elements in WYSIWYG Physics, a "philosophically intuitive" version of preparation for Mathematical POVs is to make a combined assessment of accumulated intuitions collected by real-time/ realization, physical analysis techniques. So a line-of-sight analog amplitude numberness density-intensity analysis, by "numerically condensed" analog sync-duration frequency alignments, ..logarithmicly positioned by pure-math relative motion probability in Singularity point Perspective, an example of AdS/CFT type image projection-drawing, ie of how to construct a Polar-Cartesian AM-FM precision functional coordination-identification picture of "geometrical" dimensionality, Entanglement and loop-resonances at "atomic" positioning, is required. (Precision tools do not guarantee accurate results) Here-now-forever @.dt zero-infinity e-Pi-i sync-duration Eternity-now is holographic Modulation Mechanism Mathematics, Physics, Chemistry and Geometry.., and then the more accurate academic analysis approach "makes sense" of intuitive observation. (Ie String Theoretical Calculus => potential logarithmic "ideal" possibilities in the phase-locked projection-drawing of e-Pi-i omnidirectional-dimensional, logarithmic condensation, ..primary probability sequences, of Super spin-spiral Super position-pointed Super duration of Eternity-now specifications) Re-evolution and necessary adaptation to ever changing natural circumstances, requires "learning by doing" accumulation of skilled Intuition, and reduces hands-on experience to a wordless teaching-learning acceptance of the superimposed superficiality of observational math-measurement, and the pervasive complex messiness creates an artificial demarcation with Pure Dynamic Mathematics, as if we were in alternate universes, eachin our own skin. For example, the education of Engineering Students requires direct experience of phenomena to the extent that Conservation Laws loose their apparent magic of consistency and become quantisation tools. When a Power Station generates Electricity and distributes it everywhere, that is not using different properties of Actuality Conception than Mathematics teaching-learning, it's a similar distinction between Space-time and QM-TIMESPACE via Quantum-fields of Math-Phys-Chem and Geometry, ..and "it's always NOW", in the Universal Holographic Principle of Singularity. We are all together in one coherence-cohesion objective mind-body in cause-effect self-defining time duration timing superposition.., for better or worse.

[@Dhwaj1]

Hey there, I am here looking for specific proof that gives the result as u=sqrt(r/2MG-1) the velocity measured by an observer static in Schwarzschild metric as we get near to the horizon

[@eliezeralvesmartins]

best class!!