L2 transformation reduces to the L1 transformation

[Pyrokenesis]

Hello.

I am having trouble answering the following question:

"Show that the L2 transformation reduces to the L1 transformation when the two reference frames are in standard configuration."

Am I wrong to assume that r = xi + yj + zk

Any help would be beautiful!

Thanx much

 

[mathman]

"Show that the L2 transformation reduces to the L1 transformation when the two reference frames are in standard configuration."

I assume that the source of this question defines what the L2 and L1 transformations are, as well as what two reference frames are being compared. Please elaborate.

 

[Pyrokenesis]

The L2 transformations are as follows:

r' = r + γv^[(1 - 1/γ)(r.v^) - βct];

ct' = γ(ct - r.β);

where β = v/c & v^ is the unit vector in the direction of v.

The L1 transformations are:

x' = γ(x - βct);
y' = y;
z' = z;

ct' = γ(ct - βx);

where β = v/c.

All are viewed in the S' frame.

 

[HallsofIvy]

We should also require that you define "standard configuration" but I'm going to assume that is with both reference frames moving in the direction of the x-axis .

Yes, you are correct to right r= xi+ yj+ zk. Notice that the difference is that "xi+ yj+ zk" assumes some particular coordinate system ("standard configuration") while "r" does not.

You may also assume ("standard configuration") that v= vi+ 0j+ 0k and that v^= i+ 0j+ 0k.

 

[Pyrokenesis]

Sorry. Yes standard configuration is when both reference frames move in the direction of the x-axis.

Thanks I think I can solve it now.