Energy momentum tensor - 2

This video looks at some of the mathematical aspects of the energy-momentum tensor and how the momentum density vector can be extracted from it. It then goes on to show that matter, energy and momentum are conserved in the flat space-time of Special Relativity.

[@pomeron490]

Hello Robert, Thank you for your excellent videos on the energy-mometum tensor. At 17.03, should you not pull the c^2, gamma^2, and the n/V terms outside the integral? The latter 2 terms are constants characterising the swarm under inversigation. By leaving the1/V inside the integral, it would suggest that V is a variable to be integrated over. I do not think you actually meant that. Correct?

[@robertdavie1221]

Hello Po. The V needs to stay inside the first integrand because it is the variable being integrated over.

[@user-ok6hb1zr2o]

شكرا جزيلا :)

[@Mysoi123]

Hi Robert! I have a question. I remember if we calculate the stress-E tensor for a single particle, we can do as shown : V0P0 V0P1 V0P2 V0P3 V1P0 V1P1 V1P2 V1P3 V2P0 V2P1 V2P2 V2P3 V3P0 V3P1 V3P2 V3P3 where 0 , 1 , 2 , 3 are momentum and velocity in t, x, y ,z direction. then devided this matrix by the volume of the particle, we'll get the table T00 T01 T02 T03 T10 T11 T12 T13 T20 T21 T22 T23, but I do not remember the way to it with fluid of particles. Thanks for informative video!

[@TensorCalculusRobertDavie]

Fluids have a different approach which is not difficult. Perhaps I will make a video on this topic.

[@Mysoi123]

@@TensorCalculusRobertDavie Thank you so much!

[@pomeron490]

Thank you for your relply. If 1/v is the variable to be integrated over then we would have ln v. Am I missing something?

[@robertdavie1221]

The term n/V represents the density function of particles in the volume V. When we integrate over this same volume V we get the total number of particles, n.

[@ey3796]

Hi Robert, in the very first derivation in this video, the terms inside the 4x4 matrix are the products of normal velocities right? Since you’ve taken away the gammas to the front?. Thanks and great work!

[@TensorCalculusRobertDavie]

Hello Shashank and thank you very much for your comment. Yes, I have taken the gammas out front in order to not complicate the velocities inside the matrix.

[@nitram_1326]

Yeah mate

[@longsarith8106]

what is name of this book teacher?

[@TensorCalculusRobertDavie]

It is not from any book.