Relativity 107b: General Relativity Basics - Manifolds, Covariant Derivative, Geodesics

You are free to continue watching to the next video, but if you feel you are getting confused, here are some other videos on geodesics and the covariant derivative:

0:00 Introduction
1:35 Equivalence Principle and Manifolds
6:15 Extrinsic vs Intrinsic views of Manifolds
10:29 Tangent Vectors on Manifolds
16:20 Covariant Derivative Notation
22:10 Levi Civita Connection
28:58 Geodesics
33:44 Summary

[nicknack]

It’s like the world’s most patient and thorough TA decided to hold recitation just for me. This is impressive and so helpful in terms of carefully explaining *all* of the pieces that every other lecture and many texts gloss over.

[luisaim]

Now I'm doing my final General Relativity exam. This video is the signal that everything will be okay.

[ammyvl]

I can admit when I'm not gonna understand something, and this is one of those times. Be back in 3 years after I learn differential geometry

[chimetimepaprika]

Always a pleasure. I usually have to watch them quite a few times so by this point I have viewed like hundreds of hours of Eigenchris.

[shaunmodipane]

Damn, im really impressed how far you are talking this series. Keep up the good work

[pinklady]

I am only an intermediate in maths and have never studied any maths in any university, yet I understand your great explanations. I have learned some notations including shorthands.
1:09 Einstein Summation Notation
1:38 Equivalence Principle
3:31 Manifolds
6:17 Extrinsic geometry vs intrinsic geometry
9:27 General Relativity (1915)
15:05 Tangent spaces — extrinsic view
15:49 Derivative operators = basic vectors
16:36 Covariant derivative in flat space
17:19 Christoffel symbols
22:11 Comparing vectors in flat space
22:26 Comparing vectors in curved space
25:45 Fact #1 — Metric compatibilty
26:42 Fact #2 — Torsion-free
27:03 Metric compatibility + torsion-free

[rickmcn]

This really explained some subtle points that I hadn't fully grasped before, thanks.

[rjaindia]

Best series of lectures. Much much better than any University lectures

[bobrieber]

This is so good. I just have enough mathematical training to be able to understand these concepts, though I am not that far in my studies at university, it is very interesting to get an overview of the topic in a way that is accessible. The explanations of the notational gotchas are particularly helpful

[mobilephil]

Wow. You've done it again. Brilliant deeply useful summary. Right on the nail.

[azeds]

One of the main channels that helped my mathematical intuition

[tcb]

I really like this series. It made my day.

[eelcj]

Any manifold can be embedded in a high dimensional space (like 2*N or 2N+1 D). So, extrinsic or intrinsic has little difference, at least in mathematics.

[BiswajitBhattacharjee-upvv]

In the intrinsic case, those three "like" vectors are indeed on a complex situation.
As you mentioned an 4-D manifold has its limiting appearance.

[yizhang]

Covariant Derivative finally makes sense to me. Thank you very much.

[ayansur]

nothing to say.just woww..one of the best video series in utube for understanding GTR.

[arunsahoo]

The unique channel covering all graduate topics

[lourencoentrudo]

It's 1 AM and I have a Calc II exam after tomorrow, what am I doing here :') Chris, you're like chocolate, you're bad for me but I still go on a rampage to watch your videos

[RichardAlsenz]

There are some inconsistencies with this. You can develop an understanding of this by reviewing Gauss's revelations on space:

Physics has to disregard the delusions of mathematicians and find a Physics Geometry that is consistent with the scientific method. The mathematics must be defined as Gauss attempted but found no one capable.

Here it is Gauss to Bessel Goettingen 9 April 1830 …

"The ease with which you delved into my views on geometry gives me real joy, given that so few have an open mind for such.

My innermost conviction is that the study of space is a priori completely different than the study of magnitudes; our knowledge of the former (space) is missing that complete conviction of necessity (thus of absolute truth)

that is characteristic of the latter;

we must in humility admit that if number is merely a product of our mind."

This can be resolved by creating the geometry by rotating an observer to establish the axis for north and south pole references. The perceived measurement is observed by humans using one of their perceiving senses which provide information to their brain. In sight it is the eye that yields the reality, in sound, it is the oscillation of the observers’ nerves in the ear or other parts of their body.

The Doppler effect establishes the change measured in time.
The Doppler effect is the derivative (the change of) the E-field in respect to time, not space.
Space is simply a mathematical delusion:?)

Space does not exist in physics, it exists as delusion in the mind of mathematicians who do not require observation.

The inconsistency in mathematics exists in the first assumption of Euclid. It is responsible for the generation of irrationality:?) Gauss may well have understood the issue. It is evident in Bessel's response to Gauss that Bessel did not understand what Gauss was talking about:?)

I hope this information allows you to sort out how the delusion of space came into being. I will answer any questions you have. I can be reached privately if you prefer at 713 922 3227. I am preparing a redefinition of geometry that clarifies the mistaken assumption proclaimed by Euclid and perpetuated by Newton as well as others including Einstien who followed Euclid's mistaken first assumption.

[nettewilson]

It's taken me many YouTube videos to understand why gen relativity never made any sense to me. But I finally realized I was trying to visualize a 4 dimensional phenomenon.