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True gold. Actually makes complex math understandable.

Why is this on yt music 😊

I like the array definition better

1番わかりやすい

Great stuff. Great series.

Wonderful, wonderful

i love your videos. You present all the mathematical steps and the intuition. I have 300 math and physics books. Your explanations are much better than the explanations in any of my books. I bought you a cup of coffee and will continue to support you.

It is called phasor in EE😊

I have a question that’s been gnawing at me for awhile: After finding the z+ projector (P+) in Cl(3,0) would it not be more obvious to write the basis spinors as simply P+ and P-, where P- is defined as the orthogonal version of P+? In other words, would it be more straightforward to use P- to describe the “down state” rather than using another multiple of P+ to describe the “down state”? Likewise for Cl(3,1) or Cl(1,3) (I use the alternative metric signature (-,+,+,+). For this, we need two projectors in a similar style to Cl(3,0) to form a minimal left ideal if we won’t use the pseudo scalar term. Since we need two of them, each of those two has an orthogonal pair, so we can imply that the basis required for spinors in this algebra are formed from these four projectors. Is there any advantage or disadvantage to simply defining the basis this way, compared to multiplying the algebra on the left and finding the basis spinors to be multiples of one or two projectors? I hope that question makes sense 😅, because it’s a lot of words when I can’t just simply point to my scrap paper!

Hey, I recognise that tensor algebra, that's a Fock space (for bosons). This is making my QFT lectures make a lot more sense in retrospect.

Great visualisation and explanation of the Lorentz transform. Personally, I need to become clearer on the distinction between time delays caused by spacetime transformations and those caused by time-of-arrival differences. Due to the finite speed of light, changing positions cause differences in time-of-arrival (for a non-moving observer), also affecting perceived simultaneity, but those effects need to be kept apart from the core of special relativity.

this video series on covariant derivative is a must !!!

Maybe this is a silly question, but when we hear about the equations for hyperbolas we always hear about them equaling one. So, why in this case can we have s in the equation for a hyperbola this value may be larger than one?

oh my god this is amazing

If we use an epsilon in front of h_{ij} in the definition of g_{ij} and claim that epsilon<<1 and epsilon ^2 =0, then we don't have to bother about the combinations of "h" which will become<<1 and zero.

Sir, thank you for this series of videos. And also, thank you for your series on general a d special relativity. I've seen them all, and they make Peskin and Schroeder, and Wheeler, Thorne (Gravitation) so much clearer. I will now re-read these texts in light of the clarity you provided in these videos. Bless you sir.

why cant one save this to a playlist of their liking (i.e. Lacan) ?

Thanks a lot. I am doing self study on GR and I was only able to get the first Ricci tensor on my own, but I needed your video to get the other 3. You did a fantastic job of organizing the work. I could not get it without your help. Please keep doing videos that show all the mathematical steps. I greatly appreciate it.

at minutes 7.48 you said that the distance it’s c2/alpha,,, which is true you are illustrating the diagram with the speed of light c=299792458 but since you are using c=1 you have to make also the distance consistent..it would be 1/alpha

If this is a joke, then my degree in applied mathematics is a joke... and unfunny one 😭

As a High School Physics Teacher, I always preface everything I say with "This isn't the actual truth, but..."

I don't understand why the gamma factor has to be there, like, if v=c, then gamma will go to infinity, of what use will then be gamma to properly scale the coordinate axis'. I would be thankful, if someone explained it to me!

Excelent series of videos, thank you for it

I read through some of the your replies to comments. god damn you know how to argue

Damn from calculus to cs..

my brain is not big enough to comprehend this fully. i've been watching this video and for the past two weeks trying to understand, but alas i am not this comfortable with linear algebra and complex numbers to throw them together so casually. gotta study up, i hope i can understand this video and the rest of the series soon.

one in a million? you would need 137 billion people on earth for that to be true. you mean so much to so many more people than you think. <3

Wait. How can we subtend lesser area compared to flat circle? I can only imagine area getting bigger due to a bulge. How come in negative curvature, the area is decreasing?

My guesses for the characters depicted: Founders of quantum mechanics: Einstein Dirac Oppenheimer? Pauli? Lecturer at the start: Sidney Coleman

I have learnt so much.... thank you!

I think you're falling into the trap that science these days isn't political. Given we struggle with things like the replication crisis (especially a problem in medicine and psychology), I think it it's further naive to assume such. Academia, by in large, has a certain political sway. It is interested in promoting certain things, and also interested in making sure certain things don't get investigated at all. Say I wanted to conduct a study asking children undergoing any form of transition to define the term "informed consent". Good luck, lol otherwise people like Chloe Cole wouldn't exist. Science is a tool, used by humans. It isn't this equalizing arbiter of truth, and it can be abused to catastrophic effect. Of course there are more studies in favor of these kind of treatments for children, transgenderism as a point of scientific study is still in its infancy, and it's HUGE money. Medicine isn't even willing to acknowledge sugar for the problem that it is because of the nice scam they have going on with the food industry. WPATH is notorious for churning out tons of bunk studies that can't be replicated or are otherwise unsound according to the scientific method. You can write a million papers about a topic, but it only takes one to debunk them all if it is the truth. Why did EU roll back trans health care for minors literally a month after you published this video? Bigotry? Lol, no, Long term studies (which you don't talk about) show an overall net negative past six years. The number of long term studies are few, again, because it's a NEW FIELD. I think it's important that scientists like you and Sabine chime in on these issues, as "science" is what is being used to push these cultural agendas. However, your video is as equally misleading as Sabine's. There are nuanced cultural and financial forces that all these studies ignore. I read one the comments in this video that taught me something, that transgender dissatisfaction with surgery is actually a result of the quality of surgery, not the surgery itself. Wow, I didn't understand it like that and want to see unhappy people happy. Ok. Let's take it the next logical step, if we aren't currently capable due to lack of scientific progress, why are we carrying out these procedures on children? The technology is new and thus far unsatisfactory, so we should adamantly stay the course?? What I am I missing from this equation other than the implications that treating children as guinea pigs is fine? I feel like I am taking crazy pills. Just to clarify, I think consenting adults should be able to do whatever they want with their bodies! And as long as they respect my identity, I can respect theirs. I can see and respect the amount of effort you put into this video, but you're endlessly treading water at the surface without spending any time diving down into the dark void of truth. So yeah, gobedlygook here, gobedlygook there, remind yourself that humans are more than the particles that sum them up and there is more to life than numbers on a page. Look at the hard truth, and yourself in the mirror and really think about it.

Damn, this was really nice. I think all physics students who are taught GR should first be taught these things rather then just making them learn index gymnastics of the tensor. This was really insightfull and i probably would come back to these lectures again and again (since i binged watched it from the start without carefully following the calculations). Thank you so much for taking your time to do this. I am following lectures on GR by Susskind and I couldn't digest covariant derivative. Someone in the comments suggested your playlist, and i am glad to have followed it. I wont continue from here on, as i only needed to understand covariant derivatives. But if i ever require the concepts from later lectures, surely i would continue. Edit: After typing this comment, i checked the topics of other lectures, and now i really want to watch them all (I really dont have time, as i have planned to finish a lot lectures before my holiday ends.)

I am crying like hell. I am now asking who am I 😢😢

In the Galilean example, you don't explicitly bring up a medium. But the "velocity of the car according to Einstein" is the cars velocity relative to the medium, right? Since Einstein is "stationary" and the speed of sound is different for different observers. Does this make a relevant difference or would a simple Galileo Transformation still do the trick if Einstein was moving relative to the medium? In the Galilean Doppler formula, we explicitly have the velocities of the source and receiver relative to the medium. f0(c+-v1)/(c-+v2)

It's funny how Sabine said academia fell out of her favor so she turned to making videos on RUclips. Yet the accuracy of her videos is on a decline. Someone mentioned their disappointment on her video on autism in the comments and I also find her video on capitalism to be completely wrong. I wonder if academia really failed her or the other way around. Surely the community has little tolerance if you sound like you don't know what you're talking about(she doesn't).

😂😂😂😂😂😂😂

Arent there infinite number of lines in a contour? What decides the density of the stacks, or the spacing between stacks?

Would be correct to say the following: given some linear map that transforms a vector v from V into w from W, that can be represented by a matrix. The column basis vectors of the matrix span a subspace; the column space of the matrix. The set of all linear maps that meet compatibility properties (what you call linearity) forms a vector space itself: Hom(V,W). Can we say that Hom(V,W) is a tensor product space?

I'm in Topology right now. Others may not know how strangely accurate and well-paced this video is.

To define Tensor as a collection of vectors and covectors combined toghether using the Tensor Product is actrually problematic: Both vectors, and Covectors are Tensors themselves, and it is not particularly usefull to define a vector in terms of a collection of vector-coventors... bla bla..

Personally, I see the scientific consensus on transgender anything as worth about as much as a net for holding water. For one, gender is a social construct, and studying transgender anything will inherently be fairly unclear, messy, and subject to interpretation. For two, it's a very divisive culture war issue, and any scientific results that are remotely conclusive will be heavily attacked one way or the other as coming from bigotry or criticized for contradicting "settled science" or some other nonsense that is unscientific in nature. For three, scientists are biased too, and that will influence what they choose to research and what makes it past peer review. Vaccines are far more conclusively understood scientifically and yet they're not conclusively agreed upon by the general public. This is far less clearly understood scientifically, so expecting it to be remotely agreed upon by the general public is somewhat absurd imo.

Thank you!

😂 good

Are there any particular textbooks that you used for these videos (or that you would recommend in general)? Amazing series btw.

I quote "Hooray! A task!" About once a week

What's a good textbook for mathematical vector and tensor analysis at the undergraduate level? I've been trying to find one, but usually I only find vector calculus textbooks (i.e late part of calc 3.) or a book written mostly for physicists and engineers.

In your previous video on spinors you have introduced two concept ,in case of two sphere alike , they are positive by Nature and in video of spin as spinor in SG experiments outcome oriented in different axis of space orientation an and probabilistic distribution of states an element " i" to make a sense of different dimension. A member of complex projective line , those spinor a special transformation unknown to to known.

❤

Awesome content even for my graduate students Thanks

🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉😮