I think the square symbol or 'box operator' at the end 18:35 is this d'Alembert operator en.wikipedia.org/wiki/D%27Alembert_operator?wprov=sfla1 And down the rabbit hole we go weeee....
Hello Amit, and thank you for that question. Given dV = dtdxdydz in frame S and dV' = dt'dx'dy'dz' in frame S' moving with constant velocity with respect to the former frame S. We want to show dV = dV'. Lets start with the volume element moving along the common x,x' axes so that dy = dy' and dz = dz'. Now we know that dx' = 𝛾dx and dt' = dt/𝛾 so that, dV' = dt'dx'dy'dz' = dt/𝛾𝛾dxdydz = dtdxdydz = dV.
![I.N "HALLUCINATION" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/n5B5q1Hwt_U/mqdefault.jpg)
Your short lectures on general relativity are unmatched. Watching them with joy and gratitude.
Thanks again David!
This is incredible. Great explanation of a very difficult subject. Thank you.
Hello Kevin. Thank you for your encouraging comment, it is appreciated.
Super clarity, thank you so much!
Hello David. Thank you very much for your generous comment.
Even though it is short video, this video has incredible quality.
Thank you! Your comment is much appreciated.
"That's in violation of the law of Lorentz Invariance, baby."
Too good thank you! 👌
Hello Miguel and thank you for that.
I think the square symbol or 'box operator' at the end 18:35 is this d'Alembert operator
en.wikipedia.org/wiki/D%27Alembert_operator?wprov=sfla1
And down the rabbit hole we go weeee....
They are the same, differing in sign convention only.
can you please suggest me a book for tensor ??
Hello Pradeep. Try here: inis.jinr.ru/sl/vol2/Mathematics/_%D0%B0%D0%BC%D0%B1%D0%B0%D1%80/G.H.Heinbockel,_Tensor_Calculus&Coninuum_Mech/Heinbockel_Tensor_Calc.pdf
@@TensorCalculusRobertDavie thank you Sir
Volume element 4D dxdydzdt how is Lorentz invariant... Help please
Hello Amit, and thank you for that question.
Given dV = dtdxdydz in frame S and dV' = dt'dx'dy'dz' in frame S' moving with constant velocity with respect to the former frame S. We want to show dV = dV'.
Lets start with the volume element moving along the common x,x' axes so that dy = dy' and dz = dz'. Now we know that dx' = 𝛾dx and dt' = dt/𝛾 so that,
dV' = dt'dx'dy'dz' = dt/𝛾𝛾dxdydz = dtdxdydz = dV.
Thank you sir
You're welcome.
dpxdpydpz/E is lorentz invariant. Help sir🙏
Hello Palwinder. Try using E = hf = h/T then show that you end up with the 4-volume element which is invariant.