Einstein Field Equations - for beginners!
ฝัง
- เผยแพร่เมื่อ 21 มิ.ย. 2013
- Einstein's Field Equations for General Relativity - including the Metric Tensor, Christoffel symbols, Ricci Cuvature Tensor, Curvature Scalar, Stress Energy Momentum Tensor and Cosmological Constant.
- วิทยาศาสตร์และเทคโนโลยี
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The amount of information we can find on TH-cam is outstanding
True that true that
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.
@@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 TH-cam I dont think has a political agenda but they are greedy as fuck for sure
@@wikingandersson2561 Pre-goddamned-fucking-cisely.
@@wikingandersson2561 dude, this is a physics video. Piss off with the political bs, nobody cares.
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!
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 :)
sir great
Grande Francesco! Anch'io sono Ingeniero Elettronico studiando Física
Im 26 and you inspire me as well . I majored in Finance but I have a calling for physics.
@Carl Yelland yea I’m a Mortgage Loan Officer , I make great money . But more just to learn physics.
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.
This is an outstanding masterpiece of clarity (in only two hours!).
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.
I was hoping someone would have posted chapter links. Thanks a bunch! :)
+LeoMRogers
needs more likes!
Thanks. DrPhysicsA should just copy that into the description.
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
its the age of space
13 minutes in and I'm already getting tenser and tenser.
You mean tensor and tensor?
Good
Me too
For Mathematics on LIGHT-BOARD visit #mathematicaldisasters
Thanks for beautiful explanation
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
Thank you, dude!
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...
thank you
"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.
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. 👍
@Coronavirus was a Zionist job stop you nutjob
Well that would depend on light. Or being spread upon with bio chemistry.
@@forgedwithsteel no chinese
@@moonlandingagain3228 zionist are Israeli people, basically who invaded Palestine.
This is the only place where you can see a full derivation without going to university
That's far trom the truth. You can find many free text-books, lecture notes, and even recorded lectures on the internet.
@@nge1301 fact
@@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
Great overview of Einstein Field Equations. "Mass tells spacetime how to curve; Curved spacetime tells mass how to move"
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’.
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.
Totally agree with GSA
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.
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.
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 TH-cam, 8 years after production. Excellent quality content, thank you!
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 TH-cam (despite a lot of it being at least somewhat inaccurate)
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
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 :)
Same goes with me .
"Your interests get left behind"
Did you not have Electives?
@@twstdreality No. Lol.
Einstein the shill lord
@@dr.tartaryempireesquired.o932 not a biologist or nothin but its gettin Tensor in this bitch.
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!!!
Yeah...it would have made my life easier at university. Oh well....
They did. Just not for the public.
@@cannong1728 yilpug
Ok
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
Me at 3 AM with no math or physics knowledge: Interesting…
m
You vanished like you had never existed but not before you changed me. Wherever you are I pray for you safety Prof.
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.
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.
He is an international treasure to all of humanity !!
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.
THIS IS TRULY AMAZING! I HAVE NOT SEEN SUCH A CLEAR DESCRIPTION IN AGES!
Yes. UK's Prime Minister advised the Queen to give him a medal (the CBE - 'Commander of the British Empire')
Description of what, don't understand a damn bit of it
@@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.
@@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
*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.
Pro
Holy cow, this is epic. Well done.
@@luisgomez24 Thanks guys for your kind words.
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.
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.
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
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.
You are literally the exact same person as me!
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.
You were in College when you were 54 YEARS OLD!!??? You're sort of a persistent fella! 😝
You were in College when you were 54 YEARS OLD!!??? You're sort of a persistent fella! 😝
@@amigodaverdade4448 yeah that's quite odd lmao it seems like bs
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!!
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.
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!!
This is the BEST, clearest, and most thorough explanation I have ever seen. THANK YOU.
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.
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!!
This is THE best educational channel for theoretical science on TH-cam, 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!
Well said. It takes quality to recognise quality.
"You might fancy a break, now". That lovely expression is like music to my ears, especially with that accent :D
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!
*Short* *Revision* -> 1:37:03
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?
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!
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!
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.
I wish I’d had TH-cam 30 years ago! Thank You
he is a excellet teacher and a singer too ,check for bob eagle in youtube he sings in a pleasing way
“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.
Lol don’t be lame....
hahhaa
Well you know what G is
then realises 8 is for the 4 dimensions doubled because of half spin
lmao lolol
By definition this is an outstanding teacher. Tensor analysis and vector analysis should be explained like this.
I used to study math and hated it since the lecturers were dull and showed huge deficiencies in real understanding of the topic, I love this material, and I have started revision with this channel.
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.👍👍👍
the way how Dr Bob explain it is more impressive than the Equation itself.
The equation around 11:00 in was one of the first I learned when I started studying physics. It's probably the reason I love it so much.
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.
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
Thank you! Very useful!
Those are the best videos, I absolutely love how you can explain the world by showing it using math.
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!
After watching the whole lecture at a stretch , I am almost aghasted and enervated too. No words to explain the wonders of science.👍👍👍
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.
most of this stuff in the video is incorrect, i prove it time and time again
+Edison_tinkerer Edison_tinkerer oh really? go ahead and prove Einstein wrong
bastard im not even halfway on that endeavor 😐😧
+Edison_tinkerer Edison_tinkerer Then don't make a fool out of yourself by saying it is wrong.
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
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
I wish I thought of watching TH-cam 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!
Finally understand everything on a decent level. It took a few rewind moments particularly around 50 minutes.
I watched this like 7 years ago and thought I understood it, but with new math/physics background i really notice the depth :)
This helped me understand the general idea of GR theory. The math got a little too heavy to follow, but i did learn alot especially regarding the Christoffel symbol being used as a correction factor for curved space time.
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. TH-cam is force for good and will no doubt accelerate the progress of knowledge.
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.)
It fascinates me that people who are able to understand these concepts can sincerely relate with kindness to those who can't.
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
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 :(
+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.
DrPhysicsA
Thank you, keep making video like this. your explanation is very easy to understand, unlike my teacher in my school.
Start with equations for mass. Force/newton's, akselerasjon, distanse, velocity, KE, PE
+Irun Mon Everyone starts out with GCSE physics. Also make sure you know some calculus.
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 :)
I think he's explaining the best way that anyone could understand
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.
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.
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.
Einstein made Einsteins Field Equations FUN . :P
I noted down all these on curved spacetime with a cosmic pen
Me too.
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...
@@sudiptoits read his comment carefully
@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
@@sudiptoits understandable,have a good day
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.
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.
Pretty damn cool that this video has 750K+ views.
815,505 views now. This subject is explained so clearly. Highly recommended!
I have already contributed dozens of times of views now.
Rock on!
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
NOW it has a million
I don't know how you do it DrPhysicsA, but you make General relativity look like a piece of cake!!!
I’m a 71 year old retired engineer and for the first time, Einstein’s Field Equations are starting to make sense!
I like how I’m in 8th grade and we haven’t learned anything remotely about physics, chem nor biology yet but quarantine is messing with my brain and now I’m interested
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
Damn. I wish I were as wholesome amd smart as this dude.
The algorithm works in mysterious ways with its recommendations
As a physics professor, I learned years ago, that Einstein derived the Sphincter Equation to describe the ring of a Black Hole. This while he was sitting on a toilet at the Institute for Advanced Study at Princeton. Then along came Hawking and his glow...
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.
Beautiful Humbling Video. This is such a great motivational video because Einsteins derived equations were like a piece of art! I want to create something of the sort, will now study hard.
This is a tremendously amazing masterclass. I learn in this video dozens of things others never barely did
This Gentlemen is a Great Teacher, I thank you for the knowledge I have received in the
Lesson. Peace and Harmony family
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.
Well someone here got a B ... ^
You're absolutely right Billy Willy.
I agree !
NothingMaster ...susskind is bright but not the most dynamic lecturer..
you all sound like bitter dropouts
I pay homage to your outstanding ability of explaining complicated things in easy way. Thanks
Wow. I took mathematics in University, and it has been so long since I actually had to do much of it, working in an industry where only a subset of my mathematical knowledge was needed, so it really did start to rust, and so lately I have been more and more curious about physics, and quantum field equations, and relativity, etc. So having always wanted to understand some of these physics equations on a more practical level vs theoretical like most explanation videos you find on the web, i am happy to say that despite just doing this all on simple paper, compared to even the fancier breakdowns I have seen on youtube with lots of graphics, etc, i found your breakdown far more practical. It was very straight forward to see each part of the field equation, and how it was derived.
Even though much of the math is stuff I had encountered before, your explanations were just so easy to follow. I think doing as you did, taking the time to go back to basic understandings of what a tensor is, what partial derivatives are, etc, really made it far easier to follow. So just wanted to say thank you. I know i am a bit late on this, but this video was very helpful. thank-you for posting it!
The work of a real math genius, who can even divide zero by zero.
Wonderful video! Been wrapped around the axle lost in tensor summations/nomenclature/mathematics. Beautiful job relating this material to what most people watching know (vectors, gradients, etc.). Took me a few times to get comfortable, but can now move forward. Well done!
I admire all your work.
This might be the best compact look at the math of general relativity that I have come across. Quite a detailed discussion of the left side of the equation, less so for the right side. To follow the video you will need a reasonable background in calculus. Before watching this video, I recommend first watching The Maths of General Relativity and developing a general understanding of tensors generally, and the metric tensor in particular. TH-cam has relevant videos.
Jesus! What a great teacher! Even my grandmother can understand this!!! Wow! Thank you!
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.
Brilliant explanation beautiful blend of calculus and vectors
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.
So glad to see so much information in a single video Marvellous
Awesome lecture! I love the way you explain :D
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
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
Dear Sir, It was fun to learn from you. You are one of the best lecturers i have ever seen... I appreciate you...
Really thank you,
I watched many videos about this equation, but this is the simplest video explains the equation in details.
The teaching of the teacher was so good I could understand what he was teaching
Wow !! He makes it understandable !! He is a really good teacher.
I like how the simplified version for beginners is still 2 hours, Einstein truly was on another level