You're not boring. The math presentation is fascinating. I'm a physics teacher who answers questions. I'm very busy. That means that there is a tremendous hunger to know about these things - at least in a few people. Keep up your good work. The world of physics awaits new students. I want to live to see the wonderful theories they make and new mathematics invented. The universe is better than any science fiction movie. Thank you for your video series.
Three late nights watching misleading and confusing Tensor videos - and finally i find the series that rules them all.. Simply excellent. My journey towards understanding is back on track thanks to you. Well done and thank you.
This approach is far above any I've seen before - specifically, your use of real numbers in the vectors and matrices with examples using elementary concepts is excellent.
This is my second time watching your playlist. I want ensure that my algebra's set before starting your calculus series. You're a UA-cam math hero, +eigenchris, so thank you! Best wishes!
When your teacher casually says "I'm just gonna throw some equations here." And that equation is the Einstein field equation 😂😂😂 Just kidding...keep up the good work!
Oh my I tried to learn General Relativity on my own using Wikipedia, but this channel is the perfect guide to get things rolling for me!! THANK YOU THANK YOU THANK YOU!!
Dude.... you legitimately blew my mind when you talked about the tensor product and how you apply that operator to create a more complicated space / "entangled space"
Simple and elegant way to explain complicated terms such as Superposition (as vectors multiplication and addition)and Entanglement( as Tensor Dot or Cross Product type operations!!) - working on Stress Energy Tensors and came across your videos!! awesome, something you have to go to the basics to clarity.
Great vid. Not enough tuition in mathematics is properly motivated. It starts at early childhood and continues throughout the education system. Those who love receiving a load of abstract rules and algorithms prospering, those who don't, who need a reason, a purpose, less so. I've always been middle ways. But always loved teaching and found I couldn't feel honest unless I 'really' understood all the connections and 'motivations' behind fields of mathematics and problems in those fields.
Your presentation is phenomenal, and filling in a huge gap in mathematical material on-line. Thank you! I find tensors difficult to comprehend, but if I were to boil down my work-in-progress understanding to some quick summary, I'd say that at their ultimate computational level, they are a bunch of dot products that are eventually multiplied, yielding a real number. Dot products measure the similarity between vectors, and therefore, the larger the ultimate value of the tensor, the more similar (aligned, co-directional, along gradient lines, etc.) the different vectors absorbed into the tensor happen to be. The closet intuition is the idea of a directional derivative, where a gradient is dotted with a vector. Since dot-products are also real numbers, and multiplication is commutative, the whole thing is multi-linear. Different dot products are valued differently (coefficients). Is this a good hacker's intuition?
The mathematically formal way of saying "they are a bunch of dot products that are eventually multuplied, yielding a real number" is the term "multilinear map". Saying that tensors are multilinear maps is a pefectly good way of viewing them--many people accept it as thr main definition. If you watch ahead in my tensor calculus series, you'll ser the directional derivative is really just a covector acting on a vector (which is basically like a dot product). I'd say you're on the right track.
I've watched all playlist and it's the best approach i've seen so far, with excellent geometrical meaning and very intuitive. Congratulations for the playlist! Is there any textbook or something with pratice problems? Greetings from Brazil.
Sir I am a second year Of Bachelor of Science Student...at this level , our syllabus is having only Linear Algebra and vector calculus..but I have lot of interest in the studying the outside the syllabus things ...I hope I will get satisfaction after Doing the Tensor Mechanics, Relatively from your channel... I will comment after doing all these things on the Last topic of relativity... approximately 1 month later ...stay tuned
'It's simple to make something complex, but complex to make it simple.' Jazz Musician. Anon. You make it so simple. Thank you. My students tell me I do the same. Stay Safe 🌺 +igenchris
Thanks alot I was searching for a video that dont use calculus and thats really great that you'd explain tensors according to the General Relativity and thats what i am searching
thanks for the excellent and helpful video. Just one thing, I didn't see what is the special feature of geometry compared to the one learned in high school from the examples.
Thank you these amazing (!) videos-both this and the Tensor Calculus! They are very clear, helpful, educational and explain things well. Could I convince you that it would be helpful if you considered putting the text with figures in a book (say like Schwichtenberg's books to help those of learn better from printed page and can refer back and re-work the equations Thank you Jay
Correction: when particles are not entangled that's when total state of system is direct product state. Entangled states are not direct product states.
Could you please explain mathematically how the g sub mn matrix if formed using ds^2=dr^2 + r^2 d (theta)^2 ? What was presented was g sub mn = [1 0, 0 r^2]. Note [1 0, 0 r^2] is a two by two matrix
@@eigenchris Oh really? Here I thought it was some complex LaTeX set-up with some weird plug-in to make slideshows. Well that simplifies things... How long does something like a 10-minute video take to make?
@@AnarchoAmericium Most Microsoft products (word, powerpoint, etc) have an equation editor in the "insert" tab that lets you make nice-looking equations without fussing with LaTeX. You can also record powerpoint presentations with audio and export them to video. (edit starts now) This video I was probably able to get done in a weekend. Been over 2 years though, so hard to remember.
Great video ! Could you please share some reference on geometrical view of tensor product as discussed at 5:55 ? I am quite interesting on this part. Thanks a lot !
That little scribble I did was pretty vague. I'm not sure how seriously you want to take it. I'm sorry, but I don't really have any references on visualizing it. The key is that the tensor product takes two vector spaces and multiplies their dimensions. So the tensor product of a 2-dimensional space (with basis e1,e2) and a 3-dimensional space (with basis f1,f2,f3) results in a 6-dimensional space. A basis for this 6-dimensional space would be (e1#f1, e1#f2, e1#f3, e2#f1, e2#f2, e2#f3), where # is the tensor product. This means that any vector in this space can be written as a linear combination of these 6 vectors. I don't have a convenient way to draw this as a picture though.
Wikipedia has a page Tensor Product. About 40% way down is an example. Vector u= 0 3 column vect. Vect w= -5 3 column. Vect prod of u and w = 0 15 0 -9 square matrix. COOL We transform two 2x1 matrices into a square matrix. We have ascended to a higher level of math. It's a powerful tool. It's more fun to play with than any computer game for me.
This course is brilliant! I dropped my masters degree because I don't get anything, because teacher was incomprehensible. And he drew covectors just like vectors! But now, when you said what covector actually is, I feel like I can get my textbook and finally understand what the fuck is going on there! Thanks! After watching, I think I should go through this course once again, but with textbook in hand and do exercises, and stuff, to get it once and for all
@Paul Wolf Clifford Algebra is good but at times its not very convenient. Especially for relativity, it's much better a first approach with the usual method..
Hi in reference to your slides about COVECTORS, let's say I have v1 that pierces two lines of the stack. alpha(V1) = 2. Now let assume I draw a V2 much longer than V1. However V2 also pierces the same two lines of the stack. Then what is alpha (V2) = ? Thank you.
Is this aplicable for google's library for A.I. called tensorflow? It would be nice if you show math for data science algorythms (linear algebra and calculus). You would gain a lot of subscribers
Unfortunately these videos are basically not related to tensorflow. Tensorflow just considers a tensor to be an array of numbers and doesn't worry about any of the mathematical properties that are important for physics applications like general relativity.
eigenchris thank you for answer. Nevermind I find your tutorial and way of teaching very understandable and interesting. Just keep doing it! You're great
Hmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm You just said that general relativity & quantum mechanics as well as !Dreaded Tensors! are all simple/easy. Well those were the three classes I hated the most. Anyways I'm going to carefully watch all your videos in this playlist. If my brains melt/explode again like in college a few decades ago, it's your fault. Thks though
Hi ! I'm physics undergraduate student and I watch this video for studying tensor. I think it is helpful to study it. By the way, I want to know what kind of book that I can study more about tensor? If you can, I want to know how can I study tensor for physics
I don't know of many books. I read parts of "Gravitation" by Misner, Thorne and Wheeler, but it is a very thick book that is sometimes hard to understand.
Are there any motivations for using tensors in subjects outside of pure math and physics? For example, could biology, chemistry, psychology, economics, or sociology benefit from using tensors?
Unfortunately, math and physics are the only areas where I have much experience, so this answer mainly comes from me googling. Chemistry has ties to quantum mechanics, and multi-particle systems in QM are described by the tensor product of quantum states. Sometimes fluid flow is measured by tensors, so that can come up in biology when dealing with fluids... "Diffusion Tensor Imaging" or DTI is a type of brain scan you can google. I think if you're dealing with statistics, at the more advanced levels you can talk about data point existing on "curved surfaces", at which point it might be useful to talk about a "metric" for measuring distances. Stuff like that might come up in economics. These all seem like pretty specific/advanced applications though, so I'm not sure if the average biologist, chemist or economist cares about tensors much. But for relativity, tensors are the "bread and butter" of the subject.
@Paul Wolf Ah yes, I see that tensors have some application in material science and engineering. en.wikipedia.org/wiki/Anisotropy#Materials_science_and_engineering
@Paul Wolf I suspect the "all models are wrong but some are useful" aphorism applies in many of the sciences. It is understandable for people to come up with ideas that attempt to explain how the world works, but in the long run they should be useful in predicting future data. Newton's F=ma is a great model in this way, while various string theories are not. en.wikipedia.org/wiki/All_models_are_wrong
@Paul Wolf Relativity has some evidence, and it makes practical predictions in satellite communication. I don't think it is as unsubstantiated as Everett's interpretation of QM (i.e. many-worlds interpretation). en.wikipedia.org/wiki/Theory_of_relativity#Experimental_evidence en.wikipedia.org/wiki/Theory_of_relativity#Modern_applications en.wikipedia.org/wiki/Many-worlds_interpretation
You'll probably want to watch up to video 6 in this series, and then watch the Tensor Calculus series to learn the GR stuff. I'm working on a relativity series now, but I'm still at the beginning don't think I'll get to GR until June 2020.
@@dharmanshah1239 If you're willing to do that for a few videos, that would be awesome. I should honestly start doing that myself. My channel is getting to a size where I should try and make it more accessible.
You're not boring. The math presentation is fascinating. I'm a physics teacher who answers questions. I'm very busy. That means that there is a tremendous hunger to know about these things - at least in a few people. Keep up your good work. The world of physics awaits new students. I want to live to see the wonderful theories they make and new mathematics invented. The universe is better than any science fiction movie.
Thank you for your video series.
Great comment. I agree.
The universe is better than ANY myth or fiction.
Love the simple, clear way you teach! this is gold!
This is exactly what I've been looking for in a long time after hearing a ton of popular quantum stories!
Three late nights watching misleading and confusing Tensor videos - and finally i find the series that rules them all.. Simply excellent. My journey towards understanding is back on track thanks to you. Well done and thank you.
This approach is far above any I've seen before - specifically, your use of real numbers in the vectors and matrices with examples using elementary concepts is excellent.
This is my second time watching your playlist. I want ensure that my algebra's set before starting your calculus series. You're a UA-cam math hero, +eigenchris, so thank you! Best wishes!
Clear, simple and easy.
I'd been waiting in youtube for a simple explanation for the Tensors, many thanks for your kindness to share this.
When your teacher casually says "I'm just gonna throw some equations here." And that equation is the Einstein field equation 😂😂😂
Just kidding...keep up the good work!
@Paul Wolf "science fiction religion"? lol. tell me you don't know anything about physics without telling me you don't know anything about physics.
Oh my I tried to learn General Relativity on my own using Wikipedia, but this channel is the perfect guide to get things rolling for me!! THANK YOU THANK YOU THANK YOU!!
Dude.... you legitimately blew my mind when you talked about the tensor product and how you apply that operator to create a more complicated space / "entangled space"
This is awesome. I wish I know this earlier! This just explains why we need Tensor for Relativity in a simple way.
Voice is not boring. The problem is the vocal fry. Wonderful lessons !!!!!!!
sir. you made my heart beat faster. cant wait to learn this. thank you.
Your voice is fine. I speed it up to 1.25. Great stuff!!
Simple and elegant way to explain complicated terms such as Superposition (as vectors multiplication and addition)and Entanglement( as Tensor Dot or Cross Product type operations!!) - working on Stress Energy Tensors and came across your videos!! awesome, something you have to go to the basics to clarity.
True gold. Actually makes complex math understandable.
your voice is not boring sir
This is a good idea to explain where tensors are used first.
Great vid. Not enough tuition in mathematics is properly motivated. It starts at early childhood and continues throughout the education system. Those who love receiving a load of abstract rules and algorithms prospering, those who don't, who need a reason, a purpose, less so. I've always been middle ways. But always loved teaching and found I couldn't feel honest unless I 'really' understood all the connections and 'motivations' behind fields of mathematics and problems in those fields.
Really appreciate the work you have dome on this. You are concise and complete - a pleasure to follow. Any plans to turn this series into a book?
Congratulations ! This is the best of the best of all!
Very unique and very interesting videos. I want to see more.
you are a legend (to me) +great jokes, thank you so much; the best educational content I've come across since Corey Schafer's python vids
Your presentation is phenomenal, and filling in a huge gap in mathematical material on-line. Thank you!
I find tensors difficult to comprehend, but if I were to boil down my work-in-progress understanding to some quick summary, I'd say that at their ultimate computational level, they are a bunch of dot products that are eventually multiplied, yielding a real number. Dot products measure the similarity between vectors, and therefore, the larger the ultimate value of the tensor, the more similar (aligned, co-directional, along gradient lines, etc.) the different vectors absorbed into the tensor happen to be. The closet intuition is the idea of a directional derivative, where a gradient is dotted with a vector. Since dot-products are also real numbers, and multiplication is commutative, the whole thing is multi-linear. Different dot products are valued differently (coefficients). Is this a good hacker's intuition?
The mathematically formal way of saying "they are a bunch of dot products that are eventually multuplied, yielding a real number" is the term "multilinear map". Saying that tensors are multilinear maps is a pefectly good way of viewing them--many people accept it as thr main definition.
If you watch ahead in my tensor calculus series, you'll ser the directional derivative is really just a covector acting on a vector (which is basically like a dot product).
I'd say you're on the right track.
Simple , and to the point . Excellents . . . Thanks .
New favorite math channel.
I am looking forward you eventually go into the general relativity , the mainstream application of tensor calculus.
The reason it was developed, too
@@מידןטמיר It wasn't developed for general relativity, it was developed far before even special relativity.
I've watched all playlist and it's the best approach i've seen so far, with excellent geometrical meaning and very intuitive. Congratulations for the playlist! Is there any textbook or something with pratice problems? Greetings from Brazil.
Sir I am a second year Of Bachelor of Science Student...at this level , our syllabus is having only Linear Algebra and vector calculus..but I have lot of interest in the studying the outside the syllabus things ...I hope I will get satisfaction after Doing the Tensor Mechanics, Relatively from your channel...
I will comment after doing all these things on the Last topic of relativity... approximately 1 month later ...stay tuned
Thanks for the great class here from Brazil!
“Superposition is a fancy way of saying linear combination of” - and just like that things clicked in a new way. Thank you.
You're not boring.
This feeling is so good! This is what UA-cam for!!
You are just an amazing guy!
Wow! Excellent explanation of quantum buzzwords! :)
Thank you for the nice explanation. Which is the textbook that you would recommend?
Awesome series. Really helps for someone dumb like me
Excellent JOB. Thank YOU.
'It's simple to make something complex, but complex to make it simple.' Jazz Musician. Anon. You make it so simple. Thank you. My students tell me I do the same. Stay Safe 🌺 +igenchris
Your tutorial is awesome! Will you share your slices?
Great video, thank's a lot! I learned the quantum tensor networks, and second part of video is great!
I have a calculus background but know no linear algebra :( I hope I will understand your series.
Thanks alot I was searching for a video that dont use calculus and thats really great that you'd explain tensors according to the General Relativity and thats what i am searching
Absolutely Fantastic !
awesome series!!! Thanks!!
thanks for the excellent and helpful video. Just one thing, I didn't see what is the special feature of geometry compared to the one learned in high school from the examples.
This is awesome !
Hello! Does your course cover Tensor Decomposition as well? Thanks!
Thank you for this series!
Thank you these amazing (!) videos-both this and the Tensor Calculus! They are very clear, helpful, educational and explain things well. Could I convince you that it would be helpful if you considered putting the text with figures in a book (say like Schwichtenberg's books to help those of learn better from printed page and can refer back and re-work the equations
Thank you
Jay
I have the original powerpoint slide files here: github.com/eigenchris/MathNotes
You're off to a good start. :-)
Thank you so much you really saved my ass, it's the best explanation of tensors i have seen :) Thumbs up!!!
Wonderful! Thank you
Geometry for an unproven theory. How many angels dance on the head of a pin? Oh my.
Which books are this series based on? If there's none, can i have some suggestions. Thanks
Correction: when particles are not entangled that's when total state of system is direct product state. Entangled states are not direct product states.
That's true. The states live in the tensor product of the two state spaces, though. That's what I was trying to say.
@@eigenchris got it, thanks.
Hi
Do anybody have detailed notes of this lecture series?
Actually, I lost my notes.
Thanks for the video! Can we get a copy of your slides somewhere?
You are my hero man
Very simple and interesting ❤️
The holy grail of nerdy humour
Crisp and clear!
Could you please explain mathematically how the g sub mn matrix if formed using ds^2=dr^2 + r^2 d (theta)^2 ?
What was presented was g sub mn = [1 0, 0 r^2].
Note [1 0, 0 r^2] is a two by two matrix
"you only need linear algebra, no calculus"
SIGN ME UP MAN
Very good
excellent videos !!
I like this series. Do you explain the Christofel symbols? THank you.
I'll probably get to those in the next month or two.
Your voice is alike the present THREE DAYS GRACE vocalist👍or undistored Batman voice
Hi sir this is really impressive have u any lecture Of maxwell equations in 4 vector form
I talk about them a little in Relativity 103e on "the problems with galilean relativity".
@@eigenchris sr I m following u here is all my related data except that if u can i ll be thnkful
Hey Chris, thanks for the nice videos. Can you please mention the book name you follow. Regards.
Unfortunately, I'm not following any one particular book. I can't really recommend any particular source for learning about tensors.
its a bit late but u can prefer mathematical methods for physicists by arfken
@eigenchris
What software are you using to make your videos?
Microsoft Powerpoint
@@eigenchris
Oh really?
Here I thought it was some complex LaTeX set-up with some weird plug-in to make slideshows.
Well that simplifies things...
How long does something like a 10-minute video take to make?
@@AnarchoAmericium Most Microsoft products (word, powerpoint, etc) have an equation editor in the "insert" tab that lets you make nice-looking equations without fussing with LaTeX. You can also record powerpoint presentations with audio and export them to video.
(edit starts now)
This video I was probably able to get done in a weekend. Been over 2 years though, so hard to remember.
Edited my response above; made a mistake about which video this comment was on.
all right folks, i am gona teach you about tensors, dont be intimidated, it is easy, but first lets mention some quantum phyisics.
Great video ! Could you please share some reference on geometrical view of tensor product as discussed at 5:55 ? I am quite interesting on this part. Thanks a lot !
That little scribble I did was pretty vague. I'm not sure how seriously you want to take it.
I'm sorry, but I don't really have any references on visualizing it.
The key is that the tensor product takes two vector spaces and multiplies their dimensions. So the tensor product of a 2-dimensional space (with basis e1,e2) and a 3-dimensional space (with basis f1,f2,f3) results in a 6-dimensional space. A basis for this 6-dimensional space would be (e1#f1, e1#f2, e1#f3, e2#f1, e2#f2, e2#f3), where # is the tensor product. This means that any vector in this space can be written as a linear combination of these 6 vectors. I don't have a convenient way to draw this as a picture though.
Wikipedia has a page Tensor Product. About 40% way down is an example. Vector u= 0 3 column vect. Vect w= -5 3 column. Vect prod of u and w = 0 15 0 -9 square matrix. COOL We transform two 2x1 matrices into a square matrix. We have ascended to a higher level of math. It's a powerful tool. It's more fun to play with than any computer game for me.
It very helpful
This course is brilliant! I dropped my masters degree because I don't get anything, because teacher was incomprehensible. And he drew covectors just like vectors! But now, when you said what covector actually is, I feel like I can get my textbook and finally understand what the fuck is going on there! Thanks!
After watching, I think I should go through this course once again, but with textbook in hand and do exercises, and stuff, to get it once and for all
Actually I just realized, this teacher didn't even explained the Einstein's notation properly, just started to use it at the first lesson...
@Paul Wolf Clifford Algebra is good but at times its not very convenient. Especially for relativity, it's much better a first approach with the usual method..
very good
Your voice is not boring but sounds like speaking over an old telephone line. Hihi!
so lovely! wow!
Tnx form Bangladesh 🇧🇩
do u teach quantum mechanic and general relativity?
I plan to make videos on relativity toward the end of 2018. I don't know quantum that well and probably won't make videos on it.
You might want to check Leonard Susskind lectures for that. He also has a series on string and M theory.
@@MrSidney9 the Leonard Susskind lectures aren't that serious, and as far as I know he only had 2 lectures on general relativity.
Hi in reference to your slides about COVECTORS, let's say I have v1 that pierces two lines of the stack. alpha(V1) = 2.
Now let assume I draw a V2 much longer than V1. However V2 also pierces the same two lines of the stack.
Then what is alpha (V2) = ? Thank you.
If V2 pierces 2 stack lies of alpha, then alpha(V2) = 2. The only situation where this is possible is if V2 is at a very large angle compared to V1.
Are there any assignments to this and other courses?
Sorry, no. I haven't uploaded any practice problems.
@@eigenchris it would be cool if there were some. Maybe I can find some in the internet which more or less match your course?
Thanks
Is this aplicable for google's library for A.I. called tensorflow? It would be nice if you show math for data science algorythms (linear algebra and calculus). You would gain a lot of subscribers
Unfortunately these videos are basically not related to tensorflow. Tensorflow just considers a tensor to be an array of numbers and doesn't worry about any of the mathematical properties that are important for physics applications like general relativity.
eigenchris thank you for answer. Nevermind I find your tutorial and way of teaching very understandable and interesting. Just keep doing it! You're great
you are really awesome ,thank u very much
Hmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
You just said that general relativity & quantum mechanics as well as !Dreaded Tensors! are all simple/easy. Well those were the three classes I hated the most. Anyways I'm going to carefully watch all your videos in this playlist. If my brains melt/explode again like in college a few decades ago, it's your fault. Thks though
I didn’t even know I already knew what linear combination was. I used it all the time in calculus and they never gave it a name.
I've heard of matrices, but I've never seen one solved.
Hi !
I'm physics undergraduate student and I watch this video for studying tensor. I think it is helpful to study it.
By the way, I want to know what kind of book that I can study more about tensor?
If you can, I want to know how can I study tensor for physics
I don't know of many books. I read parts of "Gravitation" by Misner, Thorne and Wheeler, but it is a very thick book that is sometimes hard to understand.
@@eigenchris I see..
Thanks for replying !!
Have a nice day!!
WAIT WAIT I may've seen the field eq. In Iron man movie
What is your educational qualification?
I have an undergraduate degree in Engineering Physics and a graduate degree in Computer Engineering.
Are there any motivations for using tensors in subjects outside of pure math and physics? For example, could biology, chemistry, psychology, economics, or sociology benefit from using tensors?
Unfortunately, math and physics are the only areas where I have much experience, so this answer mainly comes from me googling. Chemistry has ties to quantum mechanics, and multi-particle systems in QM are described by the tensor product of quantum states. Sometimes fluid flow is measured by tensors, so that can come up in biology when dealing with fluids... "Diffusion Tensor Imaging" or DTI is a type of brain scan you can google. I think if you're dealing with statistics, at the more advanced levels you can talk about data point existing on "curved surfaces", at which point it might be useful to talk about a "metric" for measuring distances. Stuff like that might come up in economics. These all seem like pretty specific/advanced applications though, so I'm not sure if the average biologist, chemist or economist cares about tensors much. But for relativity, tensors are the "bread and butter" of the subject.
@@eigenchris I appreciate you brainstorming some possibilities, thank you.
@Paul Wolf Ah yes, I see that tensors have some application in material science and engineering.
en.wikipedia.org/wiki/Anisotropy#Materials_science_and_engineering
@Paul Wolf I suspect the "all models are wrong but some are useful" aphorism applies in many of the sciences. It is understandable for people to come up with ideas that attempt to explain how the world works, but in the long run they should be useful in predicting future data. Newton's F=ma is a great model in this way, while various string theories are not.
en.wikipedia.org/wiki/All_models_are_wrong
@Paul Wolf Relativity has some evidence, and it makes practical predictions in satellite communication. I don't think it is as unsubstantiated as Everett's interpretation of QM (i.e. many-worlds interpretation).
en.wikipedia.org/wiki/Theory_of_relativity#Experimental_evidence
en.wikipedia.org/wiki/Theory_of_relativity#Modern_applications
en.wikipedia.org/wiki/Many-worlds_interpretation
Is this lecture series enough to start learning General relativity?
You'll probably want to watch up to video 6 in this series, and then watch the Tensor Calculus series to learn the GR stuff. I'm working on a relativity series now, but I'm still at the beginning don't think I'll get to GR until June 2020.
@@eigenchris alright, thank you!
thank you!
I want to give a love react to this :D
Covectors eat vectors and spit out numbers.
Do you want me to add english captions on your videos so that deaf people or who are not familiar with english can really understand your lectures
Your lectures are gold, I'll be Happy to work for you
@@dharmanshah1239 If you're willing to do that for a few videos, that would be awesome. I should honestly start doing that myself. My channel is getting to a size where I should try and make it more accessible.
@@eigenchris ya I'll do it for free when I got some spare time sir!! thanks
What you're doing for students is beyond awesome
thanx a lot, auto captions are a nightmare
Your voice ain't that bad yo
I am not illiterate in maths but i am totally baffled and bewildered ....................
You might be more interested in my more recent videos on relativity. I go through things more slowly.
@@eigenchris great sir....i always had this question in mind which knowledge came to us first physics or maths.......or 777
❤❤