Einstein Field Equations - for beginners!

[@francescomorchio4740]

I am a 67 years old man living now in Genova, Italy. I graduated in electronics but physics has always been something I have been loving since when I was young.... But working all my life on computers has left me not too much time to study this wonderful universe. Now as a retired man i can do that. I began with your wonderful lessons and I thank you for what I could get from them. Really a great jump-start for me!

[@emil6421]

I feel silly now for thinking that it’s too late to get into new hobbies and fields of study at the age of 24, thank you for inspiring me to keep learning, inquisitive old man. I hope you are well 3 years later :)

[@naveenn3014]

sir great

[@kurtmandelbrot8485]

Grande Francesco! Anch'io sono Ingeniero Elettronico studiando Física

[@bertincastillo156]

Im 26 and you inspire me as well . I majored in Finance but I have a calling for physics.

[@bertincastillo156]

@Carl Yelland yea I’m a Mortgage Loan Officer , I make great money . But more just to learn physics.

[@kevn420]

The amount of information we can find on KZbin is outstanding

[@UziPeak]

True that true that

[@wikingandersson2561]

As long as it is not a conservative worldwiev. YT is demonitazing many, many rightwing folks. I don't agree but I believe they should be able to use this platform as well. Now it's getting to become an echochamber.

[@vidhanp482]

@@wikingandersson2561 Bruh youtube will never agree to this. They behave according to the advertisers and the advertisers have liberal views because it sells better to the younger majority. They will do whatever sells better KZbin I dont think has a political agenda but they are greedy as fuck for sure

[@BiscuitZombies]

@@wikingandersson2561 Pre-goddamned-fucking-cisely.

[@chriswebster839]

@@wikingandersson2561 dude, this is a physics video. Piss off with the political bs, nobody cares.

[@BoundlessVision-d2]

I retired as a chief engineer, and physics always caught my attention. However, because I have spent my whole career in engineering, I have had little opportunity to investigate this amazing idea. I admire your excellent presentation. Einstein's Field Equations, including his indices, and their applications are now clear to me. Thank you kindly.

[@giannottister]

This is an outstanding masterpiece of clarity (in only two hours!).

[@LeoMRogers]

Contents: Introduction: 0:00 - Principle of equivalence 8:45 - What is spacetime, and why is it curved? 14:47 - The metric tensor 27:33 - Length contraction and time dilation 53:13 - Christoffel symbols 1:12:30 - Curvature 1:38:50 - Stress energy momentum tensor 2:04:23 - Cosmological Constant Let me know if i missed any sub-chapters or made any mistakes.

[@Crazy_Diamond_75]

I was hoping someone would have posted chapter links. Thanks a bunch! :)

[@bananian]

+LeoMRogers needs more likes!

[@tjejojyj]

Thanks. DrPhysicsA should just copy that into the description.

[@larryhernandez5062]

LeoMRogers , it's always been difficult to visualize the Physics ,and to teach myself what the meaning of The General relativistic equations . Your videos do A great teaching on the visuals , and explaining the mathematics : the tensor calculus . Sincerely Larry Hernandez . THANKS DrPhysicsA

[@bradleypleasant4574]

its the age of space

[@tidharcrimow6534]

0:00 - Principle of equivalence 8:45 - What is spacetime, and why is it curved? 14:47 - The metric tensor 27:33 - Length contraction and time dilation 53:13 - Christoffel symbols 1:12:30 - Curvature 1:38:50 - Stress energy momentum tensor 2:04:23 - Cosmological Constant

[@FactTalkOfficial]

Thank you, dude!

[@efeykay]

I cant anything and i have no money, E=mc² LöffelBeg. See you soon Milli Amen Super Super Love Babsi Boy Michi From Matrix with the Spoon, I hope eh ya... will be rescued... really... i am the last final ever Birth the last last last....4milliarden mal Last Fatal Birth :(( Wiktor Witas Kuhn ❤️ ❤️ ❤️? This are Satan Pactes...

[@bl4z3_kanazaki]

thank you

[@cameronmacmahon92]

THIS IS TRULY AMAZING! I HAVE NOT SEEN SUCH A CLEAR DESCRIPTION IN AGES!

[@alwaysdisputin9930]

Yes. UK's Prime Minister advised the Queen to give him a medal (the CBE - 'Commander of the British Empire')

[@paulcoy5201]

Description of what, don't understand a damn bit of it

[@ieatbananaswiththepeel]

@@paulcoy5201 description of the field equation. If you don’t understand then you either don’t understand calculus, don’t understand the other components in this video, or maybe these types of simplified ways to describe complex subjects might be your cup of tea. I’m the latter, so this video is a slight bit hard to understand, but that’s mostly because of how simplicity reduces information.

[@neonblack211]

@@paulcoy5201 What is your previous experience in theortical physics? If you have none then starting with Einsteins field equations ofcourse your not going to understand any of it.. they use super computers to solve these equations so don't worry..... you're in good company

[@ccdavis94303]

A seriously brilliant job of laying this out. One of the best pieces of pedagogy I can recall. The what and the why and the how.

[@danielhaslam5179]

I'm starting my first year in a physics masters in September so I thought I'd watch through this video amongst others for prior research and general interest. It's a complex topic and it'll take me a while to understand it all but your explanations are probably the best on KZbin, 8 years after production. Excellent quality content, thank you!

[@Me-kt3gh]

I almost went into physics because it’s almost magical how some of it works. Unlike other things that seem magical until you learn how they work, physics only seems more magical the more you learn about it. I also love that I was born in the 90s where I get to not only witness new discoveries being made on a regular basis due to the technological boom, but I get free access to the information behind it through KZbin (despite a lot of it being at least somewhat inaccurate)

[@KennyInVegas]

After a good dinner, watching this with a nice glass of wine is soooo cool! This is the bomb!!!! Why couldn't they have this 25 years ago? Thanks so much for posting!!!

[@cannong1728]

Yeah...it would have made my life easier at university. Oh well....

[@A_Man_In_His_Van]

They did. Just not for the public.

[@vibhabhale4522]

@@cannong1728 yilpug

[@ishworshrestha3559]

Ok

[@robbyandrews6318]

Hey, you forgot the football game. Wow! Did you see that field goldddd that he MADE. Man, I had to take another sip on that1

[@kzeich]

I work in the gig econ. Let's just say I'm not a furnace of ambition and I have issues... but in another life I did get a B.S. in Fin. Econ and math I love it. This content is priceless to me. That People dont have to go back to school to continue learning or to remember something special they've forgotten is a generous gift to humanity- and at risk of sounding hacky- a noble pursuit. Thank you so much. Truly a gift.

[@abillyparviz]

I aspired to be a physicist as a child, Isaac Newton was my childhood hero. but my interests switched completely to other fields (politics, etc.). When I was 16, I watched this lesson and learnt basics of general relativity from it. Then I became interested in physics/mathematics again. Throughout the years, I've read hundreds of papers, books, and learnt hundreds of theories, but this video started it all. Thank you for starting the most wonderful journey of my life.

[@brainxd]

Thank you so much for this. I am 17 years and always wanted to understand these equations. I was limited with my mathematical skills and interest by school as you only learn what school intends you to learn. Your interests get left behind. You are a great person, whoever did this, and I can't thank you enough for explaining the mathematical aspects of the general theory of relativity in such an easy and understandable way :)

[@suhanipahariya5929]

Same goes with me .

[@Mster_J]

"Your interests get left behind" Did you not have Electives?

[@brainxd]

@@Mster_J No. Lol.

[@dr.tartaryempireesquired.o932]

Einstein the shill lord

[@babytime1]

@@dr.tartaryempireesquired.o932 not a biologist or nothin but its gettin Tensor in this bitch.

[@patriciaanders2925]

took The Calculus and Physics in college over 20 years ago. watched this video to see if it still made sense to me. at 74 is nice to know 1) the brain still functions and 2) can still understand and do the partial derivatives. thank you, Doctor for the video.

[@amigodaverdade4448]

You were in College when you were 54 YEARS OLD!!??? You're sort of a persistent fella! 😝

[@amigodaverdade4448]

You were in College when you were 54 YEARS OLD!!??? You're sort of a persistent fella! 😝

[@VaiskHD]

@@amigodaverdade4448 yeah that's quite odd lmao it seems like bs

[@huonghuongnuquy7272]

Hello, I would like to say thank you for this video. It's crystal clear and very helpfull. Really I found that you are genius because you can explain the Einstein field equation with the detail for the beginner in only 2 hours. It's really incredible, you are really talented. Finally, I learned so much from you and thank you very much. From Vietnam.

[@sarangtamirisa5090]

I wanted to be a theoretical physicist and a mathematician when I was in high school. But when I dived into it a bit, it was very complicated and didn't seem fun anymore. Now I am an engineer, coming back to these concepts with better understanding of math and physics. Thanks a lot for making these videos

[@Me-kt3gh]

Same here. I spent countless hours (I’d estimate at least a few hundred) watching lectures and Ted Talks by professors and people like Sean Carroll. Not necessarily going over the math behind it, but rather the concepts and it was like it was all magic but in real life. Then I took a higher level physics class (with a shit professor, and then it got interrupted by COVID which put us online with a professor who could hardly use a phone let alone set up a camera, mic, and go through slides effectively) and it scared me away from the field.

[@ytbasketball101]

You are literally the exact same person as me!

[@anshiman]

This is THE best educational channel for theoretical science on KZbin, hands down. It's great to see doctors and researchers talk about these concepts in interview-style videos on Numberphile, Sixty symbols and such, but nothing is like seeing the mathematics and conceptual rigour that is omnipresent in these videos. Keep it up, DrPhysicsA, I'm glad I've been following your channel!

[@alwaysdisputin9930]

Well said. It takes quality to recognise quality.

[@waynebollman]

Such a good instructor. I'm surprised at how well I am understanding this 37 years after my college calculus and differential equations classes. Thank you for making me feel smart again.

[@kimchi_taco]

Great overview of Einstein Field Equations. "Mass tells spacetime how to curve; Curved spacetime tells mass how to move"

[@gsanewphysics8902]

Fact: Einstein didn't understand on the basic astronomy.Hypothesis and Einstein proposed test of general relativity are closely related to astronomy, especially celestial navigation. For understanding that hypothesis and the test are not valid, physics training is needed; but more importantly is celestial navigation training. Unfortunately, physicists and astrophysicists are not trained to become experts in the field of celestial navigation. The navigators around the world will be easily to know the fatal mistakes of these hypotheses and test. Actually, general relativity cannot be proven or tested by any means. No doubt, the entire tests that says ‘general relativity is correct’ really are the case of ‘knowing the result they wanted to get’.

[@Erik20766]

GSA New Physics that made no sense whatsoever, general relativity has made some of the most accurate predictions in the history of science. The orbital period of Mercury, which cannot be predicted with classical physics, gravitational lensing and gravitational waves are some of the many examples.

[@omarshindala]

Totally agree with GSA

[@qbtc]

Watch this video and get enlightened then read the comment by@@gsanewphysics8902 and get dumbed down again. That's the conundrum of having to interact with the bottom half of the bell curve.

[@SharperthanA]

You could mention the period of mercury, GPS, gravitational lensing, and redshifts, and people like this guy will refute your facts forever with nonsense from some random conspiracy dude on youtube. That or they will put it out of their ass. Either way, they haven't actually put in the time to learn anything.

[@IqbalHamid]

Bob (Dr Physics), you sir are a model teacher. You set a fine example which I hope other teachers will follow: You are clear. You are well spoken. You are so easily understood. Your presentations are well thought out and perfectly structured. You are aware of potential points of confusion and take great care to pre-empt them by explaining unfamilar or potentially confusing concepts. You deserve praise. I am so glad to have found your channel and am happy to declare I have subscirbed and favourited many of your videos. You seem to have tackled so much of O'level and A'level physics. Perhaps you might consider venturing into similar territory, Mathematics perhaps? Or how about degree level topics on physics?

[@randymartin5500]

Fantastic I wish I had seen this before spending 20 hours watching Lenny Susskind's 12 part series of lectures. You have explained and derived the exact same content with university level mathematics in 2 hrs.

[@willmiller7712]

Incredible. Truly incredible. I am in calculus AB as a junior in high school and have been looking for so long how to take my math to the next level without school (because the school system is so messed up). This video showed me something new, something beautiful, and in a way I could understand it. Thank you so much!!

[@danielsolomonaraya118]

Dear professor, I would love to express my appreciation to your precise and very clear instructions. I thank you very much for sharing this wisdom in a very beautiful manner of presentation.👍👍👍

[@DanCalloway]

Extremely well done. Thank you. This is the best explanation for the derivation of Einstein's field equations that I've ever encountered. I have a degree in Mathematics and so have a full understanding of the Calculus and Analytical Geometry, but limited understanding of tensors which falls into a post graduate level of Mathematics which I do not have. You make the derivation of Einstein's Field Equations understandable and look easy.

[@-scieng-6592]

Finally finished making notes on everything that has been covered throughout this entire 2 hour video! took me weeks because I had to take breaks, but now I can just read the notes. Great video!

[@Bastro3000]

"You might fancy a break, now". That lovely expression is like music to my ears, especially with that accent :D

[@alwaysdisputin9930]

*A LIST OF THE EQUATIONS IN THIS VIDEO* ------------------------------------------------------------------------------ 2:05:44 EINSTEIN's FIELD EQUATIONS: Rᵤᵥ - ½gᵤᵥ R + Λ gᵤᵥ = 8πG Tᵤᵥ \___ ⏟ ____/ ̅ ̅c ̅⁴ ̅ ̅ Gᵤᵥ Rᵤᵥ = Ricci curvature tensor 12:28 gᵤᵥ = metric tensor R but with no indices = curvature scalar Λ = the cosmological constant Tᵤᵥ = stress energy momentum tensor 1:54:54 Gᵤᵥ = Einstein's tensor 13:13 _"Now, the whole point about this equation is that it balances 2 things: everything on the left hand side refers to curvature of spacetime; everything on the RHS is to do with mass & energy."_ [Sorry: subscript μ b c d don't seem to exist so i used: ᵤ ⱃᆮㆳ ] 26:50 EQUATION 1 |¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯| | dØ = Σ ̲∂̲Ø̲ dxⁿ | | ⁿ ∂xⁿ | |__________________| 31:30 EQUATION 2 |¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯| | ̲∂̲Ø̲ = Σ ̲∂̲Ø̲ ̲∂̲x ̲ᵐ ̲ | | ∂yⁿ ᵐ ∂xᵐ ∂yⁿ | |_________________________| 33:50 EQUATION 3 |¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯| | Vᵧⁿ = Σ ̲∂̲y ̲ⁿ Vₓᵐ | | ᵐ ∂xᵐ | |_________________________ | 42:00 EQUATION 4 Contravariant |¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯| | Tᵧᵐⁿ = Σ ̲∂̲y ̲ᵐ ̲∂̲y ̲ⁿ Aₓʳ Bₓˢ | | ʳ ˢ ∂xʳ ∂xˢ ⎯⎯⌵⎯⎯⠀⠀| | Tₓʳˢ | |________________________________| 43:38 EQUATION 5 Covariant |¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯| | Tₘₙ(y) = Σ ̲∂̲x ̲ʳ ̲ ̲∂̲x ̲ˢ ̲ Tᵣₛ (x) | | ʳˢ ∂yᵐ ∂yⁿ | |__________________________________| 49:30 Metric Tensor = equation 6? |¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯| ds² = | 𝛿ₘₙ Σ ̲∂̲x ̲ᵐ ̲∂̲x ̲ⁿ ̲ | dyʳ dyˢ | ∂yʳ ∂yˢ | |____________________| 1:37:30 _"& what are metric tensors? They can be thought of as the device that you need to correct for Pythagoras on a curved surface."_ 1:07:12 _"It corrects Pythagoras for curved space."_ 1:03:34 EQUATION 7 __________________________________________ | ᵣ | | Tₘₙ(y) = ∇ₙ vₘ = ̲ ̲∂ ̲v ̲ₘ ̲ + Γ vᵣ (x)⠀| | ∂yⁿ⠀⠀ ⁿᵐ⠀⠀ | |_______________________________________| 1:05:46 EQUATION 8 The transformation of a tensor from 1 frame of reference to another. |¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯| | ∇ₚ Tₘₙ = ̲∂̲T ̲ₘ ̲ₙ ̲ ̲ + Γ ᣘ Tᵣₙ + Γ ᣘ Tₘᵣ | | ∂yᵖ ᵖᵐ ᵖⁿ | |________________________________________| 1:10:57 EQUATION 9 The Christoffel symbol in terms of the metric tensor. ___________________________________________________________ | ₐ | | Γ (x) = ½ gᵃᵈ { ∂gㆳᆮ + ∂gₐⱃ - ∂gⱃᆮ } | | ᵇᶜ ̅ ̅∂̅xᵇ̅ ̅ ̅ ̅∂̅xᶜ̅ ̅ ̅∂̅xᵈ̅ ̅ | |_______________________________________________________| 1:44:13 _"where we're talking about low gravity, low speed...general relativity must reduce to Newtonian gravity. When that happens: g becomes: 1 & the derivative terms are very, very small with 1 exception & that is the time term."_ Γ = ½ ∂g₀₀ ≡ a force term, F ̅ ̅∂̅x ̅ 1:35:57 Ricci tensor 0 - [ dᵤ , Γᵥ ] + [ dᵥ , Γᵤ ] + [ Γᵥ , Γᵤ ] | | | | ̲ ∂̲Γᵥ̲ ∂̲Γᵤ̲ ∂xᵤ ∂xᵥ 1:55:26 Momentum in special relativity: P = m ⎧ ̲ ̲x₀ ̲ , ̲x₁ ̲ , ̲x₂ ̲ , ̲x₃ ̲ ⎫ ⎩ τ τ τ τ ⎭ | | | | ↓ ↓ ↓ ↓ mc² mvₓ mvᵧ mv mc² has equivalence with T₀₀ ᙆ 1:57:06 Tᵤᵥ ___________________________ | |⠀⠀ |⠀⠀ |⠀ ⠀ | T₀₀ = the time component of Tᵤᵥ = the energy part of Tᵤᵥ | T₀₀ | T₀₁ | T₀₂ | T₀₃ | |______|______|_____|______| T₀₁ T₀₂ &⠀T₀₃ = the energy flow parts | |⠀⠀ |⠀⠀ |⠀ ⠀ | T₁₀ T₂₀ &⠀T₃₀ = the momentum density | T₀₀ | T₁₁ |⠀T₀₂ |⠀ T₀₃ | |______|______|_____|______| | |⠀⠀ |⠀⠀ |⠀ ⠀ | | T₂₀ | T₂₁ |⠀T₂₂ | T₂₃⠀| |______|______|_____|______| | |⠀⠀ |⠀⠀ |⠀ ⠀ | | T₃₀ | T₃₁ |⠀T₃₂⠀|⠀T₃₃ | |______|______|______|_____| _"& the 9 components which are left are essentially the momentum, flux, stress, pressure parts of the tensor. In other words, we are embodying every part of energy that we can think of whether it be pure energy, rest mass energy, momentum, stress, all of it somehow finds a place in this stress energy momentum tensor. It is if you like a measure of energy per unit volume."_ Please upvote so that this comment might help other people & so that I get compliments.

[@nubestouo]

Pro

[@luisgomez24]

Holy cow, this is epic. Well done.

[@alwaysdisputin9930]

@@luisgomez24 Thanks guys for your kind words.

[@bianchiviolin]

This is a wonderfull presentation for an aging old mathematician. However, amongst the 1.4 million viewers there may well be a genius of two that will study this video, be inspired, and take the thinking on perhaps even explaining dark energy, dark matter and perhaps even throwing light on the mystery of gravity. KZbin is force for good and will no doubt accelerate the progress of knowledge.

[@awakenconsciousness1320]

what’s crazy is actually that’s the reason i’m seeking information about einstein, because i’ve been getting signs (my awareness is very high) about dark matter & energy and it’s just like an thought that been surfacing my head, i’m going to look into it im only 17 but hopefully one day i can finish off where einstein left off and find lots of more mysteries of our world (one thing i’ve noticed before i even knew of einstein quote was that no one is stupid, if you can think then you are intelligent and if you use that to your advantage you can actually get a lot of information from nature because thinking is where everything starts.)

[@LolanBadeauxMakes]

After 4 years watching most all videos i could find, it is always yours that brings me to the eureka of understanding and visualizing how the math and Universe come together. Thankyou again

[@mutedroar]

I fell asleep listening to Ask a Mortician, and woke up here... I have never studied physics. I don't know how I got here. Having rewound this though, this is super cool

[@EmmanuelEdim-pp7kf]

Cool

[@rktiwa]

You vanished like you had never existed but not before you changed me. Wherever you are I pray for you safety Prof.

[@DidivsIvlianvs]

13 minutes in and I'm already getting tenser and tenser.

[@thattwodimensionalant4626]

You mean tensor and tensor?

[@MuhammadHamza-tl2sd]

Good

[@subramaniana3740]

Me too

[@mathematicaldisasters7627]

For Mathematics on LIGHT-BOARD visit #mathematicaldisasters

[@arunshrivatava9531]

Thanks for beautiful explanation

[@berzerk1450]

Greetings from Bavaria/Germany. I am 45 years old and by watching this video i am not only refreshing my physics and math knowledge, but also my English language, cause this is clearly understandable also for a not native english speaking audience.

[@johnnythreefour2902]

Goddam, you're a great teacher. I'm fascinated with this stuff, but maths has never been my strong suit. However as dumb as I am, I can now understand the core concepts of Einstein. I've watched a ton of physics videos on youtube, but never had so many "ah-ha" moments as I have on this channel. The way you explain things.. everything just fits intuitively with everything else. I can pull back and SEE how the concepts work as a mechanical whole, instead of little glimmers of understanding isolated from each other as I do with so many other videos. I'm going to make short work of your other videos and beg you to post more. Thank you so much.

[@legomaster3189]

most of this stuff in the video is incorrect, i prove it time and time again

[@higheststrpk]

+Edison_tinkerer Edison_tinkerer oh really? go ahead and prove Einstein wrong

[@legomaster3189]

bastard im not even halfway on that endeavor 😐😧

[@jomen112]

+Edison_tinkerer Edison_tinkerer Then don't make a fool out of yourself by saying it is wrong.

[@legomaster3189]

jomen112 My bad...i was in a bad mood...just wanted to get a technical reaction ...i know it is what he says it is...im still going try prove the mr. albert wrong one day

[@thejmcexperience8755]

You've made the Einstein Field Equations FUN! This is awesome, and what's even more awesome is that I understand what is being taught here. I admit that I will need to watch this video a few more times, but something this complex (and fun) is worth watching again, and again, and again! Thank you so much! I love watching Leonard Susskind's lectures. Maybe soon, I will understand what he's talking about, as well. I greatly appreciate your work. Thanks also to the person who asked about the viewing order of all of your videos! Keep up the good work.

[@TwDjLsT]

Einstein made Einsteins Field Equations FUN . :P

[@shannonmcdonald7584]

This is the most accessible version I have found. I am actually gaining confidence and skill learning from this video. Granted I'm only thru the first 3 parts but I just learned A1 last winter, A2 this past summer, and a minimal amount of calc 1 last month. So much fun!

[@paulg444]

He is an international treasure to all of humanity !!

[@stewarthayne8304]

Incredibly well explained. The breaks were appreciated! Amazing to follow down so very many chains of reasoning. For the first time I can say have a fleeting understanding of the final form. I may have to watch this again in a few weeks!!

[@dexivoje]

There is hope in humanity. First, the sheer existence of people who are willing to provide such clear explanation of a difficult topic. Second, 2.5+ million views on a topic like this is more than encouraging. One of think that a topic like this would attract 3000 die hards....Personally beyond thrilled to learn this. In school, there was zilch.

[@koroglurustem1722]

The gravity of your passion coming off of your voice is so strong that it is almost impossible to escape its attraction to learn the general relativity

[@tweedyburd007]

This is the only place where you can see a full derivation without going to university

[@nge1301]

That's far trom the truth. You can find many free text-books, lecture notes, and even recorded lectures on the internet.

[@blackholedividedbyzero]

@@nge1301 fact

[@alwaysdisputin9930]

@@nge1301 They all require a PhD to understand & start with the Ricci tensor, like trying to climb up a long hard cliff instead of a reasonable walk up the mountain via a gentle path x. This is why this video's hit 3 megaviews I plan to memorise Eigenchris after this but it's due to a lack of better options

[@PeTr01]

I only got through half of the video 3 years ago and couldnt come back due to my studies. Now that I’ve graduated, I’m so glad to have found this video again as I remembered it explaining everything so well and clearly!

[@TimJSwan]

00:00 Intorduction 14:45 Metric Tensor 53:13 Christoffel Symbols 72:33 Ricci Curvature Tensor and Curvature Scaler 98:53 Stress Energy Momentum Tensor 2:06:20 End

[@not_potaytoes_hobbit]

Thank you! Very useful!

[@morkris3753]

I wish I’d had KZbin 30 years ago! Thank You

[@meowwwww6350]

he is a excellet teacher and a singer too ,check for bob eagle in youtube he sings in a pleasing way

[@Altekameraden79]

At 02:00 I though of the signal resolution we get from Cs-133 which can show a difference in freefall time of objects with different height within the same gravitational protentional. The fact he immediately quantified that we can actually tell a difference soon after 02:00 in the gravitational body case is impressive, respectable, and highly desirable for future people to also take care to do. I went through undergrad the year of and after these videos were made, so cool that they persist to inspire or teach.

[@nikshetty1243]

"I'm gonna consider one of the most basic fields of all..." Me: Ah, yes, the gravitational field! "A field of grass, where the cows graze..." Me: Enlighten me.

[@KuldeepYadav-rl8fc]

Consider a "relevant" formula, the one which you can remember and start with it. And then consider any result from Einstein's equations. Finally equate the results. 👍

[@forgedwithsteel]

@Coronavirus was a Zionist job stop you nutjob

[@robbyandrews6318]

Well that would depend on light. Or being spread upon with bio chemistry.

[@captainprice2346]

@MoonLandingAgain zionist are Israeli people, basically who invaded Palestine.

[@VadimBolshakov]

X,Y and Z cowordinates :D

[@davidzhu1993]

the way how Dr Bob explain it is more impressive than the Equation itself.

[@mugwumpgao]

I have read many books on general theory of relativity and often stopped at first few pages. This lecture is so clear that I can understand and follow it through. Thank you!

[@hlvtxstd5148]

thank you for this video! your pronouncation is so good i can hear every word clearly.... its a blessing for someone like me who's not very good at listening in english

[@danijelcecelja5000]

Wow. I thought I was out of youtube material! Gonna be spending a lot of time on your channel in the next couple of weeks/months. Thanks for doing this!

[@landerverstappen4439]

Check dan ook zeker numberphile

[@danijelcecelja5000]

graaf

[@hannaha4305]

I have no calculus background, haven't done algebra in eons and physics was in Uni, this gentleman scholar has done such an exquisite job of breaking down these formulas so even I can have a basic understanding of what he's explaining. Well done!!

[@jacobharris5894]

I remember seeing this video years ago when I was a kid and thinking it was way beyond me at the time. Now I'm on the verge of graduating with a bachelors in physics and astrophysics with a minor in math. I am excited because I feel like I'm almost ready to learn General Relativity, something I've wanted to learn formally since I was 10 years old. I just need to go learn some tensor calculus and differential geometry and I should be set.

[@abhishekmithran2269]

I got a bit motivated after watching Christopher Nolan's "Interstellar", So I set out with a pen and a huge paper to learn more about space, time and gravity. Happy to find this video on my recommendations . I hope I find a breakthrough in Quantum Physics. In reality I am just a 11 year old trying to complete school but sudden surges like this one that I am experiencing right now is amazing. I dont even know a thing about physics but setting out to find something huge with an equation as small as V= D/t might sound funny to you guys but for me its an unearthly feeling.

[@miloophoven1863]

Keep going! I was just like you now I’m halfway through my undergrad in physics u got this!

[@Kedar752]

I don't know whether you still read comments or not. Just wanted to say that i have been going over references for a week now, but your 2 hour explanation explained me a lot more a lot more clearly and with visual understanding, that the books somewhere fail to do. You have my appreciation, and best wishes!

[@GcoRevs]

Me at 3 AM with no math or physics knowledge: Interesting…

[@frfryes]

m

[@hughwheaton8201]

I don't know how you do it DrPhysicsA, but you make General relativity look like a piece of cake!!!

[@markjust86]

I wish I thought of watching KZbin videos when I was failing my physics degree (7 years ago). It might just be because I have learned all this before but I am finding it so much easier to grasp now than I did back then!

[@wknight8111]

This has been extremely helpful in understanding some of the math involved in these equations, and it has also helped expose some areas of weakness where I require further study. Thanks for this!

[@onesevenfiveone]

I'm at 53:14 right now, just about to get onto the Christoffel symbol. I ought to be revising for an exam but this is really awesome. There are a few things I'm a little confused about with the metric tensor but going over that part a few more times should probably help. Great video so far, DrPhysicsA.

[@msumungo]

Ah, "tensor". Tensor, and what it actually means as "a factor", it just might be that it Could be in your case essentially perceived as a Physics construct (Just A Proposition, ..). Like with how it was taken by Grisha (Grigori Perelman). I was truly disturbed myself, however I have personally learned that the "First Understanding" may sometimes take mysterious paths. And a smile may occur or not, certainly. :)

[@a690ac52ed7]

msumungo What in the hell are you talking about?

[@msumungo]

Robert Harrington Are You really asking for real? Here?

[@onesevenfiveone]

msumungo He's not wrong for asking, since what you wrote basically makes no sense whatsoever.

[@msumungo]

ThymineC Certainly, that's perfectly okay.

[@kummer45]

By definition this is an outstanding teacher. Tensor analysis and vector analysis should be explained like this.

[@yakoboss]

Men i was sleeping and guess this video played automatically and i was dreaming and hearing it at the same time and i was like thats it i understand everything i am genius at the same time my dream was kind of hard core crasy.. then i woke up kind of sad so weird but i guess you talked directly to my saol and we had a good connection and you explain things well. Anyway thank you take care

[@anandb6673]

Fantastic video. This 2 hour video is equivalent of a fortnight of General Relativity lectures. GR is considered one of the most aesthetically pleasing theory with a mathematical beauty that has few parallel. As a result, many conisder it a pleasure to explain it in their own style. Like the plays of Shakesphere or Jane Austen which do not loose their value even after centuries and the modern adaptations of these are as enjoyable as they ever were, GR lectures still interest us even after being in academia for more than two decades. This presentation takes you through the essense of GR without any compromise on the claraity. Salutes to the author. I am subscribing to your channel! 🌹🌹

[@raydelaforce8149]

Dr. Physics, you are the better teacher that Dr. Suskind. You know how to get into the mind of the student. Dare I say it; you are more modest.

[@BongboBongbong]

Awesome video! I have already passed a special and general relativity undergrad course a while back but still I learned something from this video. Thank you DrPhysicsA!

[@kangthumper2185]

This channel is free? I enjoy watching this videos so much. Well put together... Thanks so much

[@Strav9]

KANG THUMPER it's not free You have to pay your fees

[@rohitdhawan5636]

After watching the whole lecture at a stretch , I am almost aghasted and enervated too. No words to explain the wonders of science.👍👍👍

[@MrTheBigNoze]

You are a fantastic teacher and explain these complex concepts very well. Build confidence from previous knowledge and apply it in new ways. I think I learned more in 2 hours than in 2 years of physics classes in college 😂

[@rv706]

1:01:26 - There's a sign mistake in equation 7: the sign just before the expression you call the Christoffel symbol should be a minus not a plus. What you should get, following from the previous computations, is dV(y)/dy=T(y)+CV(x), that is T(y)=dV(y)/dy-CV(x) not T(y)=dV(y)/dy+CV(x). Also, I have no idea if your expression actually corresponds to the usual Christoffel symbol. I don't think so.

[@maschinelab8598]

I was about to write the same thing. That is a MINUS because you are transposing it to the other side of the equal sign. Good catch!!!

[@christophelollivier4383]

2 things are so impressive 1 - When Einstein saw a roofer and imagined what he would feel when falling : Nothing. How to translate this into a phenomenal equation ? 2 - How this teacher can make it so easy to explain. My own maths lessons, when I was student, long time ago, are enough to catch the principle. Congratulation.

[@swampwiz]

This is a great introduction. It should serve me well as I delve into this topic deeper. It would be great to view a video of the math that the author had glanced over.

[@TheInstantKiller]

This is some hard stuff but you do it step by step and that really help to keep up the pace. I never understood that chain rule in derivatives and thanks to this, I went down on it again and, by Odin's grace, grasp it right away jajaja xP. Keep up the good work :D

[@alwaysdisputin9930]

Praise Odin!

[@gijbuis]

At 25.00 min you show the change in height as dφ (d phi) instead of dφs (d phi subscript s). That is a tiny bit confusing, but despite this, your explanation of the mathematics involved in Einstein's field equations is what I have been looking for during pretty much the whole of my adult life. THANKS SO MUCH for the time and effort you put into this...

[@javiercabrero5573]

A lot of things unsolved in the universe... and one of them is your endless scroll of paper 🤣🤣 great video tho! Only half way through it but ive been able to understand all of it and stay interested, very nice style of teaching.

[@dreamtheater_92]

Totally off topic, but how big is that piece of paper?

[@adamfattal9602]

He uses the "fabric" of space and time, and writes with a "cosmic pen"

[@gouravsingh9146]

Adam Fattal 😂😂😂😂😂

[@scubasteveandunderwaterroc3547]

I think it would be something like the doctors use when they roll that peice of paper into the bed if you know what im talking about

[@rogerwood8285]

Mark Richman it's a toilet roll

[@lowersaxon]

+ infinity. When infinity is reached he flips it around and goes to - infinity. He says that the paper will be sufficient for far more vids to come. If the end (- infinity) is there he has to buy a new one. But “ wonder paper” is made in China and not that expensive.

[@gustavobarrera564]

When I was young, I thought I was dumb since I couldn't understand math at all.... Little did I knew that in reality, I had bad teachers! You make it easy to understand and it just makes so much sense.

[@mathbbn2676]

The teaching of the teacher was so good I could understand what he was teaching

[@محمدالزريقات-ز1ه]

Really thank you, I watched many videos about this equation, but this is the simplest video explains the equation in details.

[@shauryaseth8859]

I was 3 months into a general relativity course with with fairly loose understanding of everything and I won't even being to describe what this man has done in 2 hours.

[@nangjangexplains5059]

*Short* *Revision* -> 1:37:03

[@legobuildingsrewiew7538]

im at 850 and almost cried 2 times already this is beautiful i finally understand it

[@kidzbop38isstraightfire92]

You shut your f*cking mouth

[@isaachester8475]

I don’t understand all the math in here, but I’m using this as a study guide to go learn/brush up on certain topics as they appear in the video. Then I can come back to this video and get a greater clarity. The fact that it’s neatly presented like this makes it so much easier to do that! Thank you!!

[@AkamiChannel]

“You’ll be pleased to know that some of these you already know.” Me: “Oh, splendid” “You know what 1/2 is. You know what 8 is.” Me: Not pleased.

[@lcchen3095]

Lol don’t be lame....

[@joshuakyanaalampour]

hahhaa

[@edunitianmanab2836]

Well you know what G is

[@xedxeam]

then realises 8 is for the 4 dimensions doubled because of half spin

[@dixshants1227]

lmao lolol

[@sushanmodak]

Things were going SO well but went south towards the end starting at 1:38:53. It feels rushed and somehow finished. A lot of derivations are skipped, a lot of hand waving is done.

[@frankdimeglio8216]

THE NEW SUPER LAWS OF PHYSICS/PHYSICAL EXPERIENCE: GRAVITATIONAL force/energy is proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. This is proven by F=ma AND E=mc2. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (This is proven by F=ma AND E=mc2.) "Mass"/energy IS gravity. ELECTROMAGNETISM/ENERGY IS GRAVITY. "Mass"/energy involves BALANCED inertia/INERTIAL RESISTANCE consistent WITH/AS what is BALANCED ELECTROMAGNETIC/GRAVITATIONAL FORCE/ENERGY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS GRAVITY IS ELECTROMAGNETISM/ENERGY. ACCORDINGLY, a given planet sweeps out equal areas in equal times; AND this is THEN consistent WITH F=ma, E=mc2, AND what is perpetual motion; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. VERY IMPORTANTLY, outer "space" involves full inertia; AND it is fully invisible AND black. By Frank DiMeglio

[@acobflp]

This is a proper example of good information. We have such a plethora of information that it start becoming negative like tick tock and other socials. Keep educating yourself. You won’t be disappointed

[@chanch0618]

Excellent video, it is very pedagogical. However, in equation 7 1:03:13 when entering the covariant derivative of a covariant vector a minus sign should go before the Christoffel symbol. Not consider this, leads to an error in 1:09:10, because the covariant derivative of the metric tensor must include negative signs since this way the expression for the Christoffel symbols can be correctly determined.

[@Periastron540]

Hello. This is the first time I was introduced to covariant derivates and covariant vectors, so I don't know how this is noticeable to you. May I ask you to enlighten me on how a minus sign goes before the Christoffel symbol (in this video)? I was following his explanation, and I cannot find any means for it to be negative from his equation in 59:18. From reading an online forum, I know how the minus appears before the Christoffel symbol. But in this video, it is a plus. Does this mean there was a wrong step before 59:18?

[@irun_mon]

Am I the only one here who are not a physics/hard science student? I am very interested in physics, but I just don't know where to start :(

[@DrPhysicsA]

+Irun Mon I wouldn't recommend that you start with this one! It is far and away the most difficult video I produced. If you want a good grounding in physics I suggest you start with my GCSE playlist and then my A Level playlist. The videos are in a sensible order in each playlist for viewing.

[@irun_mon]

DrPhysicsA Thank you, keep making video like this. your explanation is very easy to understand, unlike my teacher in my school.

[@astronomyguy976]

Start with equations for mass. Force/newton's, akselerasjon, distanse, velocity, KE, PE

[@MorganFreemanIsLife]

+Irun Mon Everyone starts out with GCSE physics. Also make sure you know some calculus.

[@irun_mon]

Brandon Espinoza I just started with pre algebra, I know it's stupid. But I want to learn from the bottom again, forget many things about math since I never use them in many years. Can you imagine my reaction when I open calculus for physics book? my jaw dropped to the ground, so I gave up on book, so now I am looking for lectures on youtube, like this one, very helpful :)

[@JTerry-zl5un]

This Gentlemen is a Great Teacher, I thank you for the knowledge I have received in the Lesson. Peace and Harmony family

[@mathematicsfanatic832]

I noted down all these on curved spacetime with a cosmic pen

[@chocolatepiano7366]

Me too.

[@sudiptoits]

Me too, I noted down everything important in here, including how you derive Einstein's field equations. It covered 10 and 1/2 pages, even though my writing is about triple the size of an ant. Very good explanation...

[@6996-y1l]

@@sudiptoits read his comment carefully

[@sudiptoits]

@69 96, I didn't write my whole comment. The pages were inside a black hole while I had my laptop and didn't get sphagettified due to the gravitational field of a black hole as I was in a relatively big black hole, while also writing them with a cosmic pen when I got out to another galaxy as some theories suggest

[@6996-y1l]

@@sudiptoits understandable,have a good day

[@pipertripp]

Pretty damn cool that this video has 750K+ views.

[@KennethMeyerson]

815,505 views now. This subject is explained so clearly. Highly recommended!

[@fsh3702]

I have already contributed dozens of times of views now.

[@pipertripp]

Rock on!

[@lespowicz906]

人活着钱没了 Stop with the chicken scratching pornography already. It belongs on the sides of passing railroad cars with other graffiti. however if you must, than only Egyptian hieroglyphics is acceptable hear or is that here or maby its beer. I forgets. LOL

[@EstiagoGaming]

NOW it has a million

[@riadhalrabeh3783]

I am a great admirer of this series of lectures for being simple yet quite accurate. All of them are great. But I have a small observation that everyone seem to wrongly think that because light has no mass it can't bend in the Newton theory. In fact F=G mM/r^2 can simply be written F/m=a=GM/r^2. Thus the acceleration is independent of the mass of the projectile and it is there even for light. That says that the curved space time and gravity force are equivalent points of views.

[@lassenlautta]

Here I'm just drunk in my home learning about tensors and shit. Thx for the video.

[@lPlanetarizado]

LOL

[@rtensor]

"What did you do last night?" "Got wasted and learned how to derive Einstein's field equations."

[@donfarlan214]

Einstein was the greatest thinker there ever been his equations were so advanced

[@emiliorodriguez8104]

No, newton was the greatest scientist in history. He developed the laws of motion, optics, universal gravitation and he INVENTED differential and integral calculus even before he turned 26

[@bobbwc7011]

@@emiliorodriguez8104 Bunch of bullshit. General Relativity is considered the greatest performance of pure thinking by a human being. Einstein also made groundbreaking contributions to literally every field of physics. Also, Newton DID NOT invent differentiual and integral calculus. Newton used something he called "fluxions". 1. Fluxions are not 1:1 identical to differential and integral calculus, and Newton lacked mathematic rigour and accuracy, and Newton did not develop a deeper understanding of what he was doing there. 2. The German superpolymath Leibniz invented differential and calculus, published it before Newton AND in contrast to Newton: Leibniz developed a profound understanding of the mathematical structure he had found; Leibniz read Cavalieri and, as a first milestone, found integral calculus first, yet he intuitively understood that this was the "inverse tangent problem", so, as a second milestone, he found derivatives and differential calculus via limits and the "tangent problem". 3. It was Leibniz who introduced the famous notation: d/dx as the "differential operator" and the stylish elongated S for "integrals" (lat. "Summa"). 4. Newton used fluxions like a tool to conduct physics without paying attention to mathematical implications. His "fluxions" were quickly forgotten as Leibniz' new groundbreaking "calculus" gained tremendous popularity. The only thing in physics today which is left from Newton's fluxions formalism is "x dot" for the time derivative of x ...or as Leibniz would write: dx/dt. And unlike Leibniz, a far better scientist and a far higher educated person than Newton, and Einstein, Newton was a disgusting personality. He could not bear the thought that someone was better than him and that this Leibniz person from Germany did not only find the same new "tool", but Leibniz clearly understood more of it, plus his formalism was really slick ...unlike Newton's clumsy fluxions. Newton's reaction was scandalous and unworthy of the Royal Society: Newton leashed out and accused Leibniz of plagiarism -- which later could be proven to be absolutely wrong. Leibniz found differential and integral calculus earlier and independent of Newton. But Newton went all in with his disgusting attempt; he used all of his reputation, pulled all the favors he could, mobilised all of his contacts to discredit and destroy Leibniz. An absolute scandal of a very poor human being. In the end, he was wrong, Leibniz was right.

[@henryd4331]

I appreciate the effort put into explaining these equations and concepts. I still don't understand any though. It used to frustrate me, but as years went on, I have developed a sense of amazement instead. Seeing math equations is like seeing Chinese ideograms or a music partition to me. Neither make sense, but they're equally beautiful and great.

[@sarthakjain3648]

Brilliant explanation beautiful blend of calculus and vectors

[@Roedygr]

at 10:19 "the longer you go, the further you go" should read "the longer you go, the faster you go".

[@MP-wy8ir]

This is a tremendously amazing masterclass. I learn in this video dozens of things others never barely did

[@NothingMaster]

Universities are in desperate need of talented individuals like Susskind and the gentleman who's giving the lecture here, instead of a bunch of incompetent, egotistical, paper pusher, wannabe physicist lecturers who think they are the hottest thing since the invention of bread.

[@hawkeye2958]

Well someone here got a B ... ^

[@NothingMaster]

You're absolutely right Billy Willy.

[@Moronvideos1940]

I agree !

[@stevimichael5553]

NothingMaster ...susskind is bright but not the most dynamic lecturer..

[@oceaneer7623]

you all sound like bitter dropouts

[@orwellhuxley6301]

Terrific lecture... Better than anything I've ever seen on KZbin!

[@jvals12]

Thanks a lot. I finally got lt. Your explanation is enough simple but mathematical to understand these equations. My admiration and gratitude for sharing your talent.

[@not1but2and37]

I don't understand any of this, but the beautiful symbols look so impressive.