6. The principle of equivalence.

MIT 8.962 General Relativity, Spring 2020
Instructor: Scott Hughes

Introduction to the principle of equivalence: freely falling frames to generalize the inertial frames of special relativity.  Two important variants of the equivalence principle (EP): The weak EP (one cannot distinguish free fall under gravity from uniform acceleration over 'sufficiently small' regions); the Einstein EP (the laws of physics in freely falling frames are identical to those of special relativity over 'sufficiently small' regions).

License: Creative Commons BY-NC-SA

[timpreece]

The title of this video should be "6. The Christoffel symbol and covariant derivatives"

[zenanchen]

Hi MIT! At 3:49, the equation for the basis vector e_phi has a little mistake in it. The L^alpha_phi term on the RHS is summed incorrectly with the basis vector e_phi term (it's supposed to be summed with the basis vector e_alpha term, as written correctly in the notes). Just a little mistake I've noticed, but in general, really nice lectures! Thanks MIT!

[rundong]

Physicists:
Perfect photonulator and re-rockulator ✅
Perpetual machine dEFiNeteLy
I'm dead of laughing

[LamontGranquist]

42:59 - I was about to flunk the whole class if nobody there caught that

[Dzjur.]

In coordinate basis the Christoffel symbols are symmetric in the 2nd and 3rd index, but it seems the definition used in the lecture does not match Schutz or wikipedia, it is the symmetry variant, which is not the same in non basis coordinates.

[jlpl]

I never really got a good idea of what the Christoffel symbols were from Susskind, but this lecture really explains it well.

[reinerwilhelms-tricarico]

Photonometer & Rerockulator. MIT® trademarks. ( Let's hope not the rest of GR depends on the existence of those patents ;-).

[jlpl]

Perhaps I'm missing something obvious, but why can one of two covariant derivatives easily be replaced by a regular partial derivative in a generalized representation?

[gizmo]

There is a point which is bothering : the lecturer uses the same notation "A.B" as well for the EUCLIDEAN scalar product as for the MINKOWSKI scalar product (that is : η(A, B)).
Another aspect of this non-distinction is that we are usually not 100 % sure what is meant by "normal vector"; in the EUCLIDEAN case, it means : A.A = 1. In the MINKOWSKI case, it would mean : A.A = + or - 1.
The perplexity may grow when you talk about "orthogonality", which gives rise to 2 rather different notions, both written : A.B = 0. (See, for example, PS01 for a short study of MINKOWSKI orthogonality).
Now that we begin changing bases, the things become even a bit more tricky.
I understand that we are supposed to pick the right meaning from the context. Nonetheless, having to check each time may be tiresome, and we could appreciate a notation which would eliminate any risk of confusion from the beginning.

[quantumphysics]

I'm a bit confused with the final thought experiment. Are we not considering the rock's kinetic energy before it hits the ground or are we trying to work in the rock's frame of reference? Wouldn't we say that the rock had some potential energy that converted to kinetic energy before entering the photonulator? Even if we allow the top of the hill to be at zero gravitational potential, wouldn't we then say that the energy of the rock at the bottom is it's rest energy - the potential energy + kinetic energy?

[MasterCivilEngineering]

Step by step video solutions of engineering questions

[ht]

Good lectures but notation convections are very bad. As an example, the A_alpha is a scalar because it's the alpha component of vector A. Should have used a better notation.

[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.