How Mass WARPS SpaceTime: Einstein's Field Equations in Gen. Relativity | Physics for Beginners
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- čas přidán 14. 06. 2024
- How does the fabric of spacetime bend around objects with mass and energy?
Hey everyone, I'm back with another video! This time, we're looking at the Einstein Field Equations. These are some of the most important equations found in the theory of General Relativity.
The first thing worth mentioning is that the common way to write the Field Equations is as one single tensor equation, where the subscripts added after different terms can take the values 0,1,2,3. The meaning of these subscripts is discussed in the video, but it's important to note that what looks like a single equation is actually a convenient way of writing multiple equations.
We have already mentioned tensors. The terms in the Einstein Field Equations refer to these tensors, which are rather interesting mathematical objects. They can be represented by matrices, which are just a particular way of displaying information.
The first tensor worth mentioning, labelled T_mu,nu is known as the Stress-Energy tensor. This contains information about the distribution of mass, energy, momentum, pressure, and so on, within the region of spacetime we happen to be considering. Often, this region happens to be the entire universe. Some of us may be familiar with the idea that the existence of mass and energy can cause the "spacetime fabric" around it to warp and bend. And this is exactly what the Einstein Field Equations are about.
The G_mu,nu tensor seen on the left hand side of the equation, is known as the Einstein Tensor. It contains information about the curvature of spacetime. This allows us to understand how the region of spacetime we happen to be considering is curved and warped.
In other words, the Einstein Field Equations can be simply thought of as relating a mass / energy distribution to the warping it causes to spacetime.
The final term on the left hand side of the equation is a product of lambda, the "Cosmological Constant" and g_mu,nu, the "Metric Tensor". The metric tensor simply contains information about the exact shape of the spacetime fabric. Whether it is flat, or curved, and exactly how it curves. It is a very important tensor in relativity.
The cosmological constant is simply Einstein's way to encode the fact that the universe is expanding, into these equations. In other words, the behaviour of the spacetime fabric is not only dependent on the mass / energy inside it, but also on the fact that it just seems to be inherently stretching. We have observed the accelerated expansion of the universe - galaxies very far away from us are moving away from us faster and faster, as compared with galaxies much nearer to us. The positive cosmological constant accounts for this expansion of the universe.
The cosmological constant has an interesting history. Initially, Einstein published his field equations without the constant. Then he realised it was necessary in order to combat the probable collapse of the universe due to gravity causing everything to eventually attract everything else. Then, he called it his biggest blunder. But now, we see that the universe is not just expanding, but it is expanding at an ever-accelerating rate. Therefore, the constant is indeed necessary in our mathematics.
Finding solutions to the Field Equations is hard - but we have found a few. For example, we know that flat spacetime is a solution of the field equations - we can have a region of spacetime in our universe where there is no mass or energy, and this is a flat spacetime. Also, we have the Schwarzschild and Kerr solutions that look at stationary and rotating black holes respectively - check out my Black Holes playlist here: • Black Holes EXPLAINED
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I am a retired medical physicist and my recall of Special/General relativity learned in undergraduate courses has become rather warped over time (pun intended). Moreover, my lifetime of physics experience causes me to now "dig deeper" and seek intuitive/graphical understanding of these fields (no pun intended). I deplore numerous relativity textbooks that "hide" behind equations and the algebraic gymnastics of finding their solutions, without intuitive interpretation of the main terms and their units. This is where your videos are unique by providing clear intuitive interpretations and illustrations. Thank you for helping so many viewers understand relativity conceptually. Richard Feynman would be proud of your teaching content and style! 🤓
Excellent. Best description yet on Einstein’s Field Equations. Now we need the video on tensors!
I agree. He raised the bar on understanding a difficult subject. Einstein himself would be happy in this attempt to simplify this topic.
A tensor is best thought of as a matrix with potentially more than two indices or "dimensions"
@@astrobullivant5908 Just curious if Tensor cores in SOCs somehow related to tensors he discussed?
@@imyasharya They are related because the Tensor cores perform matrix multiplication at a very fast level to make GPU's effective. If a bunch of tensor cores are each doing a form of matrix multiplication, collectively, one could say they can perform tensor multiplication because tensor multiplication is ultimately one form of multiplication of a specific set of matrices. However, I don't know if that's why NVIDIA calls them tensor cores or not.
Better Than Relativity
Here is Dark Energy cP!
Here is Cosmological Constant cDel.P
Here is Swirl cDelxP
F=[mGM/r^2 - cDel.P, cdP/dr + mGMR/r^3 + cDelxP]
3rd Law
0=[mGM/r^2 -cp/r, cdP/dr + mGMR/r^3]
0=mGM/r^2 - cmv/r=c - v !
Universe is Bounded
Parth G: A physics channel trying to look like an asmr channel that's trying to look like a physics channel.
Ya got me :D
@@ParthGChannel THE BALANCED, ULTIMATE, TOP DOWN, AND CLEAR MATHEMATICAL PROOF REGARDING THE FACT THAT E=MC2 IS F=MA:
Time dilation ultimately proves ON BALANCE that E=mc2 IS F=ma, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Time is NECESSARILY possible/potential AND actual IN BALANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity ON BALANCE. Gravity is ELECTROMAGNETISM/energy.
Great !!!! QUANTUM GRAVITY !!!! E=MC2 IS F=ma. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. What are the EARTH/ground AND the SUN are CLEARLY E=MC2 AND F=ma IN BALANCE. Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. The stars AND PLANETS are POINTS in the night sky. GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. BALANCE AND completeness go hand in hand. It does ALL CLEARLY make perfect sense. GOT IT !!!! THE SKY is BLUE, AND THE EARTH is ALSO BLUE. Great !!! Now, think about the man who IS standing on what is THE EARTH/ground. Perfect !!!!
Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/energy is gravity. E=MC2 IS F=ma ON BALANCE. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS E=MC2 IS F=ma ON BALANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (ACCORDINGLY, the rotation of WHAT IS THE MOON matches it's revolution !!!) Gravity IS ELECTROMAGNETISM/energy. TIME DILATION ultimately proves ON BALANCE that E=MC2 IS F=ma, AS ELECTROMAGNETISM/energy is gravity. News flash ! Gravity IS ELECTROMAGNETISM/energy, AS E=MC2 IS F=MA. The Earth (A PLANET) is a MIDDLE DISTANCE form that is in BALANCED relation to the Sun AND the speed of light (c), AS the stars AND PLANETS are POINTS in the night sky; AS E=mc2 IS F=ma. TIME is NECESSARILY possible/potential AND actual IN BALANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY !!!
By Frank DiMeglio
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What an amazing teacher. I have a basic mathematical understanding yet I can follow everything he says. What a talent.
Aint no way I understood this video having no prior knowledge about it, best explanation I’ve seen
This is fantastic! I've subscribed to a lot of physics channels, but you have achieved the following: 1) Seized the bull by the horns by the explaining the equations themselves; 2) Explained them in a way so intuitively, precisely and compactly that even an amateur like me feels he understands them (instead of just getting eyestrain, as used to be the case).
I like your pace and the fact that all of what you say is information, and closely related to what you intend to explain. Much, much appreciated!! Congratulations!
Thank you I was the one to suggest this I remember , and you replied you would like to do it .
@Divyesh Raj yeah don't remember that bit pal but have a nice day anyway.
@Divyesh Raj Yep
@Divyesh Raj usless guy that suggestion of including this topic in community was given by paul
@Divyesh Raj I think rockets and more had some sand in his vagina when he wrote that comment
Absolutely earned a subscription brother. Great work !!! Please keep up!! Really appreciate the intuitive simpler way of explanation of complex topics
I've been waiting for this one from a long time.... love your videos❤️❤️
These videos are so so so helpful! Kudos to your efforts man👍
Awesome! Thank you for this simple and clear explanation of the Einstein's Field Equations👍
Such a simple yet effective explanation! Please keep making these videos!
Simply THE BEST explanation for us "mortals" !!!
Congratulations !!!!
This is a genuinely fantastic explanation. Thank you for sharing!!
Gifted teacher. Using different colors in slides adds greatly to clarity
You explain this in a way that I can kind of understand. That's a feat in itself! Good man.
Superb Explanation.. Thanks Parth
most simplified description......thank you
Just wonderful explaination. Thank You !
Quite a good video. Different from most I've seen. Well done!
Excellent description. Crystal clear....
Thank you thank you. I’ve been watching a few of these concerning the field equations but yours is the absolutely best explained.
Great video. Just a quick note that it looks like you forgot to increment your Mu index in the matrix / tensor description at 6:30 and 6:50. They are all showing first index = 0, but as an example your pressure terms should be (1,1), (2.2), and (3,3).
Brilliant description !!!!
Nice work Parth, explained this most difficult concept in a quite simplicistic way, keep it up bro. 👍
Please, make more videos on this! I enjoyed it and would like to learn the actual details.
Thanks for the explanation. Physics is my passion, this equation is beautiful linking geometry to energy.
Thanks for the vid - very helpful explanation of some of the complex detail underpinning a more generally accessible conceptual framework.
thanks for the video. great explanation.
YOU ARE SUCH A GREAT TEACHER!!! EXCELLENT!!!💯
Very good Parth. Excellent explanation
Your video explaining it in much much simpler way than others
Great overview. Motivating me to dig deepr: thanks a lot :)
Congratulations... Very clear explanations...
You are a very very good teacher. Thank you!
Always ready for your video
Thanks, because I was looking for it.
This was a great but easy explanation of the Einstein equations! Thank you very much!
i am literally watching ur vids like 5hrs straight just because you tell something that is in another vid im instantly switching to it
great work dude
Outstanding....Easy explanation.... Looking for more....Suscribed just now...
Excellent explanation... I had tried a lot of videos before this and this one really made me understand the concept.. 👏👏
wow, you are so genius and well prepared i wish that this video should be in billions seriously i lov it
Thankyou so much for such amazing explaination ❤️
You are so good at what you are doing!
Awesome video man❤ really like how you Explane this
your style of teaching is very unique and educational. please keep making videos and don't give up. you deserve a million followers and it takes time to get there. but your styles guarantees it.
Awesome video, Thanks!
Thank you so so much! Your videos feed curiosity in an amazing and relaxing way! I love your calm energy - it definitely helps the nerdy learning :))))
Man this is excellence keep up the good work please continue uploading
Excellent explanation
It is so exciting to find your videos. I'm a fan after only watching a couple. I love physics especially Quantum mechanics and Relativity, but sadly I never formally studied it or maths because of various complexities in my personal history.
I have a question that I've been posing to a variety of great communicators of physics, especially on relativity. Your title suggested you would answer it but you didn't. So far no one else has been able to answer it. I loved the way you explained the equations of General Relativity and it was a great help and it confirmed that it doesn't answer my question even though in your explanation you use words that suggest you are answering my question. You say these equations tell us "how mass bends space-time." But they don't.
They tell us that mass causes space-time to curve or bend. Brilliant! They help us MEASURE the effect of Mass on space-time very accurately. Brilliant!
But not what CAUSES the curvature that would be the true HOW of the curving effect.
It is as if you were saying that measuring the current in amps tells us what electricity is and how it works. Our capacity for measuring current is very accurate, it tells us a lot that is useful and important, but it's not quantum mechanics which helps us understand electricity (and its related topics of electromagnetism and matter) in profound ways.
It seems to me if we truly practically understood the mechanism for how matter interacts with space-time, we'd get closer to the much sought so-called "theory of everything". In your video, on the basic postulates of quantum mechanics, you talked about the "kinetic theory of gases". You said that if you change the size of the enclosing space of gas then the standard theory falls over. We know that a gas under pressure requires a different explanation as it is liquified and the temperature changes. Is this analogous to what happens in a black hole? More importantly, is there a way of talking about how space-time works inside matter, whether talking about a planet or a lump of metal? How do state changes in matter affect space-time? Since there is a change in the space (at least) occupied by matter in different states. Further different types of matter can occupy the same size space but have different effects, such as weight, on gravity, therefore space-time.
Excellent Video Brother God Bless you....
Nice work Explain i hav been waiting for you to introduce me to these equation
Great experience waching it...
Very nice explanation
Thanks. Great video 👍
Thank you for the video.
Really you explained field equation so simply and so beautifully.thankyou very much sir.
excellent explanation whenever i see your video time goes faster i feel it just starting,thank you for sharing this type of knowledge
Thank you very much ! Remembering that tensors are here 4X4 matrices quiet helped to understand how these 3 little terms are supposed to describe the universe! Awesome videos as always!
Wow❣️😻
Best explaination i ever seen 🔥💯
Outstanding video
Good description.
You are a great teacher
A very great explanation for a layman like my self. Colloquially put!!
best tutor ever!!!!!!
I'm always impressed of how well you explain anything!
My duuude hope you're doing well man :)
Thank you young man, for this lucid description! Not that u've made me a GR expert 😁, but now I know how the structure of GR, though complex, leads to varied derivations - black hole, big bang, gravitational warp ...
It is all to do with different values of the tensors involved. Thanks again.
The description was perfect, I always wanted to know about the mathematics behind the field equations but can you explain tensors in detail, I really want to know about them. Also, subscribed first then watched the video😁😁.
Good description 👍
Great video!
Thank you for the explanation. It is a very helpful video to understand Einstein equation.
Verigood Explanation with mathematics. Exelent assult.
The best video from Parth 😍😍❤️❤️❤️
thanks for explain this
Amazing explanation
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Great Video.
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This video was the one I wanted, its just awweessoomme....
As described by your fans, I also think you should make a video on dirac eqn😅😅
Bravo Sir.
Nice explanation.........
Great teacher
Love your videos.
Paarrthhhhh this is amazing! I am trying to study for my GR module and could do with many more videos on it
Tensors, Christoffel Symbols, basically Tensor calculus
Hope you can make these!! Love your videos! 😁
Very nice explanation(s). ❤😊
You earned a new subscriber
Parth G condenses maximum information in minimal time. So d(inf)/dt is close to an extremum! Thank you, Parth.
Ingenious !
Hey Parth, great video! I'd love to see a video about the alcubierre drive and how it could allow FTL travel and violate causality.
Very good video...
Just earned yourself a new sub! Amazing explanation!
Can you also do a video on the Riemann Curvature Tensor?
Just how perfect an explanation can be, I used your video to explain all this to my dad who doesn't even know english and still got it
Most of it 😅
Nice explanation Parth.. I really like theory of relativity
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Thanks for giving that information brother
Bhai maje aagye
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I want more , I am hungry
Thank you - that was really clearly explained. I always felt short changed by my BSc in Astrophysics as we never dealt with GR properly using tensors, just simplified using Gaussian curvature. Would you recommend any textbooks?