I can’t wait to see your next video❤️

Btw I love the BGM, what is the name of it?

I just want to say, I mighta stuck with calculus had I had these videos in my life when I was learning it. You're doing god's work here, and I hope you get all the clicks and ad revenue from millions of math and physics students trying to understand and visualize what they've been told to learn in abstract number form.

I have dreams about motion, pure motion. Am I a weirdo?

This video is awsome

agreed

agreed

agreed

agreed

agreed

One of the...? Pls tell me the other once! :)

@@leonackermann3098 there are also Russian ones, since I am Russian, but this will certainly not help you. Check also Alex Flournoy videos for more technical details, he downloads lectures on GR right now. Famous Susskinds´ are also good

@@stevenmarshall1119 Ah I know already Susskind and Flournoy ;) also post the russian just because of random interest if I will understand a single word ^^ Greetings from Germany

@@leonackermann3098 kzfaq.info/love/yeF4TqSnmLDXWk-qRWTezQ, einfach LightCone. Ich bin ein Russe, aber seit langem ich lebe und arbeite in Deutschland. Schöne Grüße dir auch, lieber Unbekannte!

@@stevenmarshall1119 Okay dann check auch mal aus Physics Videos bei Eugene, für 3D Animationen.

Nice! Can you explain what's going on?

@@joseville Each basis vector e_i can vary in all coordinates, generally. Hence, we consider all possible deviations from the initial state of the basis vectors in all coordinates, i.e. the derivatives of all basis vectors with respect to all coordinates, x_j. The derivative d(e_i) /dx_j is our desired change. Now, the change of this basis vector e_i is more in the direction of the coordinate x_j if the velocity component in the direction x_j is larger. Hence, we have to add a velocity component v_j to our derivative here. That makes our term as ( d(e_i) / dx_j ) * (v_j). This right here is our 'component' for the deviation of our basis vectors. To get the direction part of the term, we multiply a basis vector to this term, which would indicate the directions of change of basis vectors, in terms of basis vectors (if you get what I mean). This, coupled with the initial derivative change consists the Christoffel Symbols (_gamma^i_kj v_j e_i). Hope you get what it means. I'm sorry, the math notation is a lot weird here. Feel free to ask if you have any problem.

​@@aaryanchokshi3862Is the spacetime being used here Euclidean?

@@tahamuhammad1814 No, the case discussed in this video is for any irregular grid.

​@@aaryanchokshi3862can you help me, I'm so freackin confused. It just doesn't make sense for the basis vectors to change along the grid, that's against definition. If our vector space is 2-dimensional (not necessarily Euclidean), there may exist many bases (plural of basis) but each basis is a unique set of two vectors. Now, when we give coordinates to that space (which is the same thing as making a grid on it) we choose a two vectors that can form a basis (let's call those vectors a and b). We will choose these vectors such that there is a unique way to write every point in that vector space as xa+yb where x and y are scalars.

Even though it is complicated, it doesn't hurt to go through all of the points he makes to see what you understand and what you don't. This is a good practice for the future as well if you ever want to study ahead for a class.

I'm a physics' student and I focus on GR. I need to tell you that it's hard to understand something like this.

@@sanath8483 I’ll try to do that! I still see someone who knows calculus like a superhuman or something. Just imagining that theoretically you could deduce the most important equations of all time by yourself is so impressive. I’m probably overestimating it, due to my anticipation to learn and habit to watch a lot of physics videos just for fun

Tbh only those with preliminary knowledge understand certain ascpects, as the vid will assume you know them. Othereise...it would have to teach several years of maths when explaining something lol E.g. anyone that hasn't done derivatives/differentiation (dy/dx) won't know that it denotes the gradient or rate of change. When dealing with velocity..rate of change is obviously acceleration or deceleration. Anyone that hasn't studied maths and physics to a sufficient academic level simply wont know that. ...I got thrown off the boat at those 8 Schileoochoff values whatever they're called. EDIT: he explains Chrystoffel symbols. So i got some understanding

It's great that you're using youtube/the web to learn about these interesting topics! I did the same in high school, fell in love with the creative thinking that goes into physics problems, and am now working on my physics phd. Don't worry about not understanding a topic or even about being wrong if you try to connect the dots with limited information, you are always laying the groundworks for a more complete, functional, and satisfying understanding.

Does he have a channel in another language?

@@joseville their primary channel, @ScienceClic, is in french. They also have a spanish channel.

I suggest you study eigenchris' playlists on tensors for beginners, tensor calculus and relativity by eigenchris. He taught me general relativity extremely well.

Thanks :)

Thanks !

Eso estaría de lujo!!

Thanks !

I struggled a bit there too. But I think it makes sense. There’s no reason we can’t relabel gamma, alpha, and beta to alpha, mu, and, nu respectively since we’re expanding them out anyway (it’s not like there’s any significance to alpha appearing in both the left and right side). If you accept that, then it’s a matter of accepting that if two vectors are equal, then their components are equal too. Helps to recognize that the basis vectors are linearly independent since they form a basis

Thank you ! Love your videos by the way !

@@ScienceClicEN Cheers!

If it helps, it's just the relativistic or curved spacetime analog of Newton's First Law/Law of inertia for flat spacetime.

Thanks! The "vertical" component of the vector (which here is almost zero which is why it seems we measure the thickness)

Thanks ! I animate the videos on After Effects

We rename the indices on the right such that the basis vectors match on both sides (with index alpha), and then we project the equation onto the basis vector (we consider only the alpha component of the vectors on both sides)

Thanks ! It's a personal creation you can find it on my SoundCloud : soundcloud.com/aroussel

@@ScienceClicEN cool, thanks a lot