Recent content by zn52

yes it might be that the speed of light squared is in the denominator and it is considered as 1 ...

I see . But how can we derive this expression ? why is it defined in the velocity space ? sometimes I wonder from where similar expressions come from ...

well as you can see in the same line, the vx and vy are velocities since they are equal to P over E in the 4-momentum . the px and py are momentum in the x and y directions of the incoming photos I guess ?

hello, Please attached snapshot of an answer to an Ex. I was stunned at the formula for the derivative of the solid angle which is : d(solid angle) = dvx * dvy I would appreciate if somebody can provide some hints on how one can find it ? Thank you,

I thank you so much Ben. Now everything falls in place including the pressure term above and got my confusion cleared up since I had not payed much attention to that instantaneous frame indeed. I'm now so happy and I can sleep at night :) My warm regards.

I think , please correct if I'm wrong that there is a misunderstanding perhaps . The rod is not in a translational motion along the y axis, but rather it is rotating around its center, the z axis. In this case the frame K of the rod has its axis also rotating around the lab frame K'. In this...

Indeed I also had the same questions as you...it is indeed weird... the order of coordinates is t,x,y,z . I'm wondering, why you mentioned that the transformation should mix t and y ? what would differentiate x from y since the rotation is around z? Also , why in the matrix for the rotation, we...

hello, Please see attached Ex and its Answer. I'm surprised that the pressure Txx has the same value as that in the instantaneous frame of the rotating rod Tx'x'. I believe this could be a typo isn't it ? Isn't the Lorentz transform the following matrix for the rotating rod around the z axis...

Oops look what we have. It seems since dv' = Jacobian * dv and since dv = dtdxdydz and because dt and dt' are related by Gamma which means that dx'dy'dz' = Gamma * dxdydz Yuppy ! now I'm convinced and can sleep at night happily. By the way I have just seen that the chapter in Schutz' Intro...

I thank you so much for your clarification. Indeed I would have thought that the volume represents the same set of points but I was wrong. I had done an excercise in the book : "Problem book in relativity and Gravitation" from which I have attached one solution. As you can see volumes are...

I agree . But I still have some nagging points which I would appreciate if you could clarify them to me and the reader , please correct me if I'm wrong: 1 - You mentioned that nbr density in lab frame = nbr density in particles' frame * Gamma This means : n/v = (N/V) * Gamma where n is...

hey Folks, Please see attachment. I'm in doubt about the equation 5.15a. Indeed, it is said on the line just above it that : "in a frame where particles have velocity Va" which means the lab frame , say. Then in this frame the time component of 4-velocity is the Lorentz contraction factor...

I thank you so much for your assistance. after several weeks deep into tensors I have now realized that these are dummy indices. It is not obvious for anyone at the beginning to spot that...Now I can sleep happily at night... Cheers,

I thank you so much for your clarification and guidance. Now I have moved on after having worked intensively on the Levi-civita and determinants. I had to work through simple cases in 3D and 2D in order to understand these mathematical identities...

The issue in this very example is that on the LHS, if you would expand the Levi-Civita symbol using the antisymmetrisation you mentioned above, you will end up with the same symbol which is on he RHS. This would mean that the 1/2 has no place ! I'm may be confused or I'm I missing something ? I...