8. Lie transport, Killing vectors, tensor densities.

MIT 8.962 General Relativity, Spring 2020
Instructor: Scott Hughes
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Discussion of a second notion of transport, 'Lie' transport, and the associated Lie derivative. Use of this derivative to discuss spacetime symmetries, as encapsulated by Killing vectors. Also discusses 'tensor densities,' volume elements in general spacetimes, and certain tricks and identities that use the determinant of the spacetime metric.
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[@brendawilliams8062]

Thank you. You are such a magnificent teacher. Appreciated.

[@meowwwww6350]

He is

[@MrFischvogel]

Thank you so much, Sir ! Please keep motivating math definitions as you did in this lecture and make it avaiable to everybody =)

[@redrum41987]

39:12 Lie Derivative

[@KipIngram]

19:00 - It seems like that was awfully round-about, to just come up with the "new derivative" being the same as the covariant derivative. Why didn't we just start with that?

[@benbarberian1701]

for the sake of general case

[@lleozin96]

So basically every next class is in Thursday

[@meowwwww6350]

Then why are you reporting him to the classroom and I don't want to go to sleep at night and I

[@meowwwww6350]

Then why are you reporting him to the classroom and I don't want to go to sleep at night I

[@lleozin96]

@@meowwwww6350 what

[@naturematters08]

@@lleozin96 yech

[@mikikaboom9084]

57:20 My teacher would get offended if it were wrong though

[@ujjwalb1729]

What is the difference between connection coefficients and Christoffel symbols?

[@sagittarius284]

Connection coefficients represent a certain kind of connection on a manifold. Christoffel symbols are also connection coefficients but associated to a special kind of connection called "Levi Civita Connection".

[@NothingMaster]

Here is the problem with time: GR is essentially a classical field theory and QM is driven by QFT. But if you think about it, in QM time behaves in a classical background parameter fashion; meaning the flow of time is universal and absolute. In GR, on the other hand, time is a component of the four-dimensional spacetime, and the flow of time changes according to the curvature of spacetime, as well as the spacetime trajectory of the observer. Why is there such a discrepancy regarding the nature and the behavior of time between these two (falsifiable and experimentally confirmed/validated) theories that supposedly describe the same physical Universe?!

[@almanacization]

That isn't correct. In QFT time no longer plays any kind of significant role in comparison to space. This is conventionally done not by promoting time to an observable, but instead demoting position to a label (although successful formulations exists with the other approach as well). Afterwards, multiple quantization schemes are available to the interested individual. If you go along with canonical quantization, you'll find that superficially time is indeed treated differently than space, but once you move to Heisenberg picture all the equations are relativistically covariant. The symmetries are even more obvious if you use path integral quantisation instead - there Lorentz covariance is absolutely central to the whole endeavour.

[@NothingMaster]

Rūdolfs Treilis : Please stop talking nonsense, and try to reach beyond your intellectual capacity, when you obviously didn’t even understand the gist of the problem.

[@almanacization]

@@NothingMaster Ahhh, don't you just love it when all the crackpots start sweating profusely and become rude assholes whenever any mathematical detail is brought out :)

[@ekaingarmendia]

Have you ever tried to predict the probability distribution of the state of an electron after a measurement by watching mercury do it's thing? It's kind of hard.

[@iziskin123]

I think NothingMaster was getting at the fact that QFT depends on a static Minkowski spacetime. GR says matter/energy deform spacetime away from plain Jane Minkowski.

[@studywitharii]

Is any indian here studying in MIT, I just wanna ask that how much percentage is needed in 12th to get into MIT as in field of experimental physicist. I am currently 14, and have studied all of these things which aint of my level and i understand it. I want to study in MIT after my 12th, thats why i want to ask.

[@brendawilliams8062]

Then you have the 101. 102. Ect. Is that right

[@brendawilliams8062]

Would you use the 4 value of 243

[@brendawilliams8062]

Is this no. 91314

[@monstersp8331]

Respected MIT university professor in India country's MHRD minister ramesh pokhariyal told in corona situation INDIA's biggest exam JEE MAIN and NEET is starting 1st September 2020.but India's majority students says that please our exam conduct after2 months because india's sop is to weak and people not obey social distance and many state in heavy rain. therefore those states in very highly spread poor.and majority peoples exam centre very far like 100km to 300km how can they journey in lockdown state.I request to MIT UNIVERSITY HEAD PROFESSOR please write to email our mhrd minister to exam continue ofter 2 months because corona situation we are very afraid and how can we journey in corona viruses situation this situation very bad and headache situation. Please support domestic India's majority students oppose exame in current situation. Thank you for reading.please as soon possible as reply.