(1) This derivation is very similar to the one for the conservation of energy equation in section 4.1.2, except this time we are considering the flow of particles rather than energy into the cube.

(2) The components of the energy momentum tensor in a general frame (say the lab) are given by

where the matrices take you from the MCRF to the lab frame.

The rest of the problem is just filling in the algebra in section 4.1 of the lecture notes.

(3) Again, this is just filling in the algebra in section 4.2 of the lecture notes.

(4) This is how you start the this problem. The components of the four- current vector are given by . We can therefore write the four- force as