Lorentz Transforms: Question About Inverting LT Frames

[exmarine]

If I construct a LT from an un-prime frame to a prime fame: S':=LT(S,v') and another to a double prime system: S":=LT(S,v"), then invert the first: S:=LT(S',-v') and substitute it into the second: S":=LT([LT(S',-v')],v"), I do NOT get the same transform as going directly between the double and single prime frames: LT([LT(S',-v')],v") ≠LT(S',[v"-v']). Does this question make any sense? What am I missing?

Thanks.

 

[Doc Al]

When going from S' to S'', what velocity did you use?

Realize that if v' is the relative velocity of S and S' and v'' is the relative velocity of S and S'', then the relative velocity of S' and S'' is not simply v'' - v'.

 

[exmarine]

Oh? I thought it would be v"-v'. What is it then?

Thanks.

 

[exmarine]

Ok, I get it. I have to use the SRT addition of velocities. Thanks!

 

[Doc Al]

Ok, I get it. I have to use the SRT addition of velocities.

Right!