Astronomy - General Relativity (1 of 17) What is General Relativity?

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We will learn the difference between special relativity and general relativity.
Special relativity: as velocity approaches the speed of light, mass increases, distance shrinks, time slows down, and Einstein said: All observers see light moving at the speed of light.
General relativity: gravity is caused by a warping of space, The Equivalence Principle: light is affected by gravity.

Next video in this series can be seen at:

[diepieche]

Why my teacher & lecturer didn't explain like you? Glad you able to explain it in simple manner. Hopefully you can continue with Quantum physics.

[darkenergydoesnotexistbyjo]

Excellent lecture. I have a question. I understand that using a 2d sheet and a massive ball in the center is necessary to explain how mass bends time. Planet earth curves space around it and an object in orbit is actually just following the curvature of space. The problem I have is, if the two objects have equal mass, how can both masses orbit each other since the curvature of space is equal for both masses?

[alwaysdisputin]

11:20 _"If there's zero mass then there's no gravitational attraction. It's the mass that causes gravity, not energy. Or maybe both."_

IMO it's both because:
The main equation in general relativity is Einstein's field equation:

Rᵤᵥ - ½gᵤᵥ R + Λ gᵤᵥ = 8πG Tᵤᵥ
̅ ̅c ̅⁴ ̅ ̅
DrPhysicsA says in his vid 'Einstein's Field Equations for Beginners!' at 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."_

Wheeler summarised the theory: "Spacetime tells matter how to move. Matter tells spacetime how to curve."

Tᵤᵥ = the stress energy momentum tensor & it has 16 components.


| |⠀⠀ |⠀⠀ |⠀ ⠀ | 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 |



At 1:57:28 of 'Einstein's Field Equations for Beginners' DrPhysicsA says that T₀₀ has a kind of equivalence to the P₀ compoment of the 4-momentum vector from special relativity. You might recognise this component P₀
it is aka the rest mass energy, E = mc²

DrPhysicsA said: _"& 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."_

Leonard Susskind said:
_"We see that, in general, the source of the gravitational field is not just energy density, but it can involve energy flow; it can involve momentum density & they can even involve momentum flow. Now as a rule, the momentum flow or even the energy flow, certainly the momentum flow but even the momentum density, are much smaller than the energy density."_
_"Why do I say that? It has to do with the speeds of light in the formulas. If you put the speeds of light into the formulas, just like energy is always huge because it gets multiplied by: c² but on the other hand momentum is typically not huge because it's just mass times velocity, so velocity is slow if you're in the non-relativistic situation, when velocity is slow, energy is big; energy density is by far the biggest thing, the other components of the energy momentum tensor are much smaller typically decreased by powers of the speed of light."_
from 1:14:48 of the YT vid 'General Relativity Lecture 9'
from 11 Dec 2012 (not the 2009 video)

So gravity is caused by T₀₀ = the energy part of Tᵤᵥ
but it also caused by T₀₁ T₀₂ &⠀T₀₃ = the energy flow parts of Tᵤᵥ
& T₁₀ T₂₀ &⠀T₃₀ = the momentum density parts of Tᵤᵥ
So IMO all 16 components curve spacetime but the E = mc² part is much more noticeable because c² is huge.

So it seems if the Starship Enterprise somehow acquired enough energy to reach the speed of light it would collapse under the weight of it's own gravity & become a black hole. Get too close & it's a case of: "Resistance is futile. Prepare to be assimilated."

[akhileshkumar-mugb]

You are really incredible Sir ! Thanks for this series, much awaited by me

[saifahmed]

Will you go into detailed maths of this subject and what happens to black hole singularities when they collide

[zakirhussain-jsku]

The theory of relativity has great predictive power as its predictions have been tested & proven to be correct. Kindly explain followings for common viewers;
1. Contraction of spaceship is understandable. How spaceship moving close to speed of light contracts length b/w itself and point B?To influence length ahead of spaceship, any effect will have to travel faster than light as spaceship itself is moving at light speed. At light speed length will becomes zero, there will be no distance ahead of spaceship to travel.
2. Gravity can explain acceleration, how GR explains acceleration?
3. What is source of energy & momentum of spacetime.

[mathlover]

General theory is not for the faint of heart. Differential geometry is no joke. But it is a beautiful theory and a lot of fun to study. When you understand sensors it is a lot easier but tensors are HARD.

[highschoolphysics]

It has been a pleasure to see your channel grow, I have been an early subscriber and always highly recommended your channel to my students and fellow teachers. I was inspired to do my own, with a specific Canadian style. (Our variable use is different which was the complaint of my students)

[satyamkumar]

This series is going to be more interesting than a si fi movie 😁. Thank you so much sir

[johnholme]

Thank you Sir. I understand it now, it’s the warping of space into the fourth dimension which is time.

[juliopimenta]

The explanation, in fact an introduction to this subject, has the simplicity adequate for someone who is beginning to study. The idea of ​​distorting the fabric of space-time caused by objects with great mass is present in his explanation. There is no need to criticize.

[anupambiswas]

Spacetime warping is always represented as a 2 dimensional mesh....but how would you graphically explain or represent the warping of spacetime in 3 dimension?

[sabbirmarvel]

Waiting for this long time .Thank you sir ❤️🇧🇩

[kavitabani]

Sir how does this warping justify 3rd law of newton

[MandolinSunrise]

Thanks Michel, bringing interest to our lives! :)

[johnholme]

How does space being curved effect time?

[medtabernoust]

thank u so much for this amazing serie i've been waiting for it from along time hope u will cover all important thing about it <3

[aqilshah]

When your wonderful wife is Asking or talking with you, her voice is low so please Add subtitles of her voice so that we can also understand her. Thanks

[vgovind]

Thanks so much sir....glad that this video is out now...😀😀
Edit:I have a question..if gravity is simply the curvature of spacetime then there is no force actually right? So when we say that the Newtonian equation is a special case of general relativity does it mean that we are able to calculate that 'apparent force' as seen by us, using the Newtonian equation?
The video is so good, keep them coming...

[sailokesh]

Sir when will be viewers request video released??