Recent content by Unown

Thanks! I understand now.

Okey. But why is that? Why is my calculation wrong? How to show, that ds dt is given by J(f) dx dy?

Hey, I tried to do this in this way: I use V for potential energy and T for kinetic energy. Given equation reads: V=-2T V+T=-T Now you see that the left hand site is a total energy: E_{tot}=-T Differentiate the whole thing: dE_{tot}=-dT So if the total energy is...

In the second to last expression, you just take dt' dx' dy' and dz' from the third and place 'em there. I also took out \gammas, to simplify things. Well thanks for the try. Just be sure you didn't get suggested by my derivation and did the same mistake. Any other ideas?

Yes, sorry about that. I corrected this issue. But the equation still gives 0.

Yes, if we use Jacobian this becomes trivial. But the question doesn't include Jacobian, we have to do this the normal way. I think my problem can be somewhere when I am writing \frac{dz}{dt} and \frac{dt}{dz}. Maybe there should be metric tensor somewhere that gives additional minus sign...

Homework Statement Prove that the element dt\ dx\ dy\ dz is invariant under Lorentz boost with velocity \beta along z axis. Homework Equations Convention c=1 Lorentz boost in z direction: L(z)=\left[ \begin{array}{cccc} \gamma & 0 & 0 & -\gamma\beta \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\...