Now this is how physics is explained!!! I don't know why a coordinate free, geometric, approach is not often encouraged. Or better, best of both worlds like your explanation demonstrated. Thank you so much!!!
Thanks, Robert! It was very difficult to find this demonstration. The main problem that me and my friends found is that you couldn't deduce this general transformation using the same ideas to demonstrate only for a x Boost, for example. We got frustrated, and then recognized that it should have another way to do this, probably using vectors, and it would be a lot 'cleaner'. Anyway, thanks again!
Hello Chirag. Note v/|v| is just a unit vector like any other unit vector that points in the same direction as v. Vectors are geometric objects and so all unit vectors have a magnitude of one and point in some direction. We just need to choose the one that points in the direction we are interested in. In the video r_(parallel) points in the same direction as v and so when we want to write r_(parallel) as a vector we can take its magnitude |r_(parallel)| and multiply it by a unit vector that points in the direction we are interested in, which is v. So we have, r_(parallel) = |r_(parallel)| v/|v|
This is very nice! I do have one question: the position vector r' in S' frame is expressed in terms of velocity vector v and position vector r in S-frame. To compare both sides (at 10min-ish of the video), one has to assume the unit vector ex'=ex, ey'=ey, ez'=ez, etc. What is the justification here?
Yes it is because we will need to consider the Lorentz contraction which is more easily achieved if the parallel part of the vector is parallel to the velocity vector.
Hello Naveed and thank you for your comment. I didn't include the inverse transformation because the focus of the video was on deriving the forward transformation and not its inverse which can be easily found using a software package.
Can I suggest you have a look at these links, physics.stackexchange.com/questions/142419/recommended-books-for-advanced-undergraduate-electrodynamics www.physicsforums.com/threads/graduate-electrodynamics-books.337872/
6 лет назад+3
This derivation is slightly different from that proposed by Albert Einstein himself in his book "relativity" : ruclips.net/video/koPnW0mXcvI/видео.html
Thank you Sir. Have been scratching head and pages to find an elegant general Lorentz boost. Your work is truly elegant.
Thank you for saying that, it is greatly appreciated. Cheers!
Actually, is very hard to find this demonstration in regular EM books. In most of them, the boost matrix is just shown for one axis. Thank you!
Thank you Gabriel. Glad you found it useful.
The easiest explanation yet elegant. Thanks sir
Hello Rikteem and thank you for your comment. It is great to hear you found the video helpful.
Now this is how physics is explained!!! I don't know why a coordinate free, geometric, approach is not often encouraged. Or better, best of both worlds like your explanation demonstrated. Thank you so much!!!
Thank you for your encouraging comment, I am glad that you found the video useful. Cheers!
Thank you very much. It's so useful.
Deigivan Física
Thank you.
You save my life from Relativistic EM homework.
Thank you Sirawut, glad my video was of use to you.
Thank you so much, Sir.
Hello Leicam and thank you for that! Cheers!
Thanks, Robert! It was very difficult to find this demonstration. The main problem that me and my friends found is that you couldn't deduce this general transformation using the same ideas to demonstrate only for a x Boost, for example. We got frustrated, and then recognized that it should have another way to do this, probably using vectors, and it would be a lot 'cleaner'. Anyway, thanks again!
Thank you Joao, I'm glad the video was useful to you.
Sir, Can you please explain the term v/|v| in the equation at 8:11. Sir shouldn't it be unit vector r.
Hello Chirag. Note v/|v| is just a unit vector like any other unit vector that points in the same direction as v. Vectors are geometric objects and so all unit vectors have a magnitude of one and point in some direction. We just need to choose the one that points in the direction we are interested in.
In the video r_(parallel) points in the same direction as v and so when we want to write r_(parallel) as a vector we can take its magnitude |r_(parallel)| and multiply it by a unit vector that points in the direction we are interested in, which is v. So we have, r_(parallel) = |r_(parallel)| v/|v|
Thank you so much Sir, you made my assignment easy
Thank you, I am glad to hear that you found it useful.
Thank you very much. It was very helpful.
Hello Rathindra and thank you very much for your comment.
This is very nice! I do have one question: the position vector r' in S' frame is expressed in terms of velocity vector v and position vector r in S-frame. To compare both sides (at 10min-ish of the video), one has to assume the unit vector ex'=ex, ey'=ey, ez'=ez, etc. What is the justification here?
Is it necessary for r parallel Vector to be parallel to velocity vector? 3:10
Yes it is because we will need to consider the Lorentz contraction which is more easily achieved if the parallel part of the vector is parallel to the velocity vector.
Thank you!
Hello Cas and thank you for your comment.
thank you so much 🤩
Glad it was helpful.
amazing
Thank you Vishnu.
Thanks. Very useful.
You're welcome.
thanks! very useful
Thank you Victor!
Thanks
You're welcome.
what is its inverse transformation?
Hello Naveed and thank you for your comment. I didn't include the inverse transformation because the focus of the video was on deriving the forward transformation and not its inverse which can be easily found using a software package.
Great
Thank you.
Can you suggest me a graduate level book for EM plz ??
Can I suggest you have a look at these links,
physics.stackexchange.com/questions/142419/recommended-books-for-advanced-undergraduate-electrodynamics
www.physicsforums.com/threads/graduate-electrodynamics-books.337872/
This derivation is slightly different from that proposed by Albert Einstein himself in his book "relativity" : ruclips.net/video/koPnW0mXcvI/видео.html
This is the general case where motion is in any direction and not aligned with a single axis.
Which book can i get this?
Hello and thank you for your question. I haven't seen this derivation in any textbook.