General relaweedity 1:02:37

@muttleycrew

3 жыл бұрын

He was clearly thinking about the Bongkowski metric

@jlpl3291

2 жыл бұрын

The 20 seconds of theatrics leading up to it were also funny

What I learned: "Do weed"

Love the fact that 40 years after my undergraduate studies MIT professors are still using blackboards

@SSNewberry

Жыл бұрын

Or white board in a few cases.

@marcusrosales3344

Жыл бұрын

I'm a physicist and this is the case in almost all departments I've been to. The old guys do not want to move on!

@SSNewberry

Жыл бұрын

@@marcusrosales3344 To where?

@marcusrosales3344

Жыл бұрын

@@SSNewberry Moving on from the 60s... You know from where things USED to be.

@SSNewberry

Жыл бұрын

@@marcusrosales3344 kzread.info/dash/bejne/no5nxLKOe9KbqsY.html He isn't old.

Guys, you definitely made my day with these videos!

Thank you for that description of a one form( fluxes)!!! When you talked about how it is a mathematical object which is perfect for capturing fluxes I pretty much jumped in my chair and went "Holy S#@t! Ευρεκα!!" I've been struggling with that in class - then a bit later with how a metric given one vector is a one-form. Wow...nice!

1. Go to 1:02:35. 2. Thanks me later.

"Shut up and calculate," wasn't from Feynman, that was David Mermin.

I like this guy.

"One-forms and vectors are basically the same thing." Mathematician: **twists in despair inside an infinite dimensional space**

1:02:36... Well that would be embarrassing if it was put on youtube for the whole world to see......😂

@Originalimoc

3 жыл бұрын

LOL

@drdca8263

3 жыл бұрын

Thanks, I didn’t notice that at first, was good for a laugh

First time watching a proper lecture on General Relativity. With all the one-forms, tensors and vector, I must say it is just Linear Algebra (and Calculus) trying to be classy.

So wholesome that this dude says "oh butter" when he makes a mistake. 25:59

1:02:38, 🤣🤣🤣🤣🤣🤣🤣🤣

Did anyone solve the Problem set 1 completely?It should be completed before 4th lecture as indicated in Calender of the course. Couldn't solve even one question completely. I really need help with the problems.

For anyone confused about the 1-forms and what they have to do with gradients and a map and really what they are, I highly recommend this series: Tensors for Beginners by eigenchris (kzread.info/head/PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG). It starts a bit slow but quickly picks up and, less than an hour in, you should have a much better idea/ visualisation of what he is talking about!

“Taken into account the space of separation!” 😂😂😂 Don’t worry, just be entangled and metrically act at a distance. 😜

@meowwwww6350

3 жыл бұрын

@@monstersp8331 I feel sorry for you

Instructions unclear at 62nd minute, became a category theorist

👍🏻 great

When explaining basis one-forms at 25:40, how can we expand like that when we just established the contraction rule as p(A) = A^alpha p_alpha? Don't the upstairs and downstairs indices need to be the same here? how can we have p_beta but A^alpha? To me that seems to imply use of 2 different basis vectors, e_alpha and e_beta, for obtaining the components of A and p respectively.

@shubhamjain3093

3 жыл бұрын

The expression he has written down amounts to the same contraction rule you've mentioned. He goes on to establish that the basis one form w^\alpha acting on basis vectors e_\alpha is just the Kronecker delta (delta^\alpha_\beta). The Kronecker delta turns the beta on p to an alpha (or vice versa) and you get the standard expression for contraction.

@cryora

Жыл бұрын

My understanding is that he is taking two separate paths of logic. The expression p(A) = A^alpha p_alpha is the result of one path of logic that does not restrict us from writing p(A) using the second definition. The first path of logic: p_tilde(A) = p_tilde(A^alpha e_alpha) = A^alpha p_tilde(e_alpha) = A^alpha p_alpha In the second path of logic, he is defining an operator omega_tilde receives a slot, so in other words omega_tilde^beta(A) = omega_tilde^beta(A^alpha e_alpha): p_tilde(A) = p_beta omega_tilde^beta(A^alpha e_alpha) = p_beta A^alpha omega_tilde^beta(e_alpha) Now since both expressions are equal to p_tilde(A) you can compare the results of the two paths of logic and set them equal to one another to get A^alpha p_alpha = p_beta A^alpha omega_tilde^beta(e_alpha) so that this is only true when you set omega_tilde^beta(e_alpha) = delta_alpha^beta

Buckle up 🙈🙈

I dont get why use 2 set of basis vectors to get the metric tensor in another reference, what will be that 2 set of basis vector? or is it the same basis vectors twice?

@stefann6630

3 жыл бұрын

It's the same reference frame, but with respect to different observers that see things different, even though they are the same; so a third observer comes in place, and explains the "reality" with respect to both observers. Hope it helps.

❤

Average GR class - do weed @1:02:35

What are the entrance requirements for mit physics? And what are the interviews and exams for entrance?

@mitocw

3 жыл бұрын

mitadmissions.org/

I think I'm stuck on co-/contra- variant indices. They way tensors were explained, for e.g. A mu nu, mu and nu were supposed to be indices, valued t, x, y, or z. But when we must convert between observers, we are not just shuffling the values in a matrix around by swapping indices. Can someone tell me: - what is the actual meaning of superscript vs subscript? - how basis vectors factor into tensors and how to use them to convert? - what it means when we use indices that don't just stand in for a number because the two vectors have a different basis?

@kubih7255

2 жыл бұрын

Watch the video series on Tensors by eigenchris. He explains it wonderfully.

@cryora

Жыл бұрын

@@kubih7255 If he explained it wonderfully, why couldn't you have answered these questions

@kubih7255

Жыл бұрын

@@cryora didn't see the point of writing a lengthy response especially since I wouldn't say I'm very qualified to teach others. I would much rather direct someone to a trusted source as opposed to running the risk of incorrectly interpreting something and making myself seem like a fool.

@cryora

Жыл бұрын

My interpretation is since the superscript are used for 1-forms (row vectors) while subscripts are used for regular (column) vectors, the the superscript can be thought of as the row index, while the subscript can be thought of as a column index. If you have a subscript and a superscript, then that is a 4x4 matrix. If you have two superscript, then that is a row of 4 row vectors, each vector with 4 elements. If you have two subscripts, that is a column of 4 column vectors, each with 4 elements. If you add a third index, that index may be either a superscript or a subscript. If it is a superscript added to a tensor that has a subscript and superscript, then it can be thought of as a 4x4 matrix where each matrix element is a column vector of 4 elements. subscript-subscript-superscript then gives you a column of 4, 4x4 matrices superscript-superscript-superscript gives you a column, where each element is a column of column vectors. Done in this way, you don't need to extend into the third dimension. The third dimension would instead require a third type of index, say a "middle stairs" index. If you contract, say, a [1 2] tensor (column of 4, 4x4 matrices - but can also represent a row of 4 columns of column vectors but sticking with the former interpretation for now) with a [1 0] tensor (row vector), you will get a 4x4 matrix. Whether you multiply each element of the [1 0] tensor with each of the 4x4 matrices, and then sum the matrices, or whether you perform the "dot product" on each column of each 4x4 matrices, depends on which index of the [1 2] tensor you are contracting with the [1 0] tensor. If you've ever used MATLAB, it's like using cells. You can put whatever you want into the cells - matrices, cells of arbitrary dimension, cells of cells, cells of cells of cells, etc. Only in GR, you're only working with 4 elements per index. So contracting eta^{a,b} with A_{a} to get A^{b}, you are essentially taking a row of row vectors and dotting into it a column vector to get a row vector. It would look like, in matrix notation: [[-1,0,0,0], [0,1,0,0], [0,0,1,0], [0,0,0,1]] . [A0; A1; A2; A3] = [-A0, A1, A2, A3] where commas separate rows and semicolons separate columns The problem is the minus sign for A^{0} element. If the Lorentz invariant scalar product is defined such that the minus sign comes from the metric tensor, and not from deliberately putting a minus sign on the 0th element of the row vector, then to move indices, you wouldn't use the metric tensor, but an identity tensor where each diagonal element is 1.

@jackcochran2581

10 ай бұрын

The Wikipedia article on "Covariance and Contravariance of Vectors" is very good. In particular the diagram at the top. Imagine a set of coordinate axes that are skewed so they're not perpendicular with each other. You can have one set of basis vectors that follows each axis wherever it goes, and another set of basis vectors that stays perpendicular (normal, orthogonal) to the "planes" (3-surfaces in a 4-space; lines in a 2-space) formed by the other axes. In an orthornormal basis with orthogonal axes these two are the same thing, but not in the general case.

Is anybody else here doing this course with assignments? I just started but it get's kinda boring when you can't discuss the question or solution with anybody and I am not always sure I got it right. Does anybody want to compare the solutions or discuss the questions via zoom?

@mateotabernero1067

2 жыл бұрын

hi, I know I'm a little bit late, but I am doing this course with assignments too, so we can compare them if you want to

@asdfg7536

2 жыл бұрын

@@mateotabernero1067 I would love to, but unfortunatly I have some other projects right now I need to finish. Have fun though :)

Kindly vist Eigenchris youtube channel to better understand the idea of dual vectors or 1-form or differential forms

1:2:35

Tensors continued, or as it became known, the 420 lecture 🤣

@possiblepilotdeviation5791

3 жыл бұрын

DO WEED

Anyone else getting bugged about axes not being clockwise? lol

@thehoom8188

2 жыл бұрын

Same!

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.

COMPUTER

do weed Lol 😂😂😂😂😂

Hi mit can i study at mit in physics for free? Is there any scholarship like that?

@mitocw

3 жыл бұрын

mitadmissions.org/afford/

Very confusing

I can't read what h is writing on the board! And if he knows this stuff so well, why does he have to keep looking at his notes - and are they his notes or someone else's? I am not impressed with him.

camera angle is really irritating, the software used for tracing professor is zooming in quickly. In additon, the notations are not proper at places very confusing whether it is multiplication or is the variable being raised to the power? Also please in future notes try to refer to previous equation, and mark any all results as eqn 1, 2, .... so that when in future it is being used, it can be said (from eqn2 we have) ....;some suggestion from a guy with double masters from department of mathematics