Transforming Four Velocities with the Lambda Matrix

[GarageDweller]

In SR, I know we transform three velocities using the einstein velocity addition law.
However, in the case of four velocities, do they simply transform the same way as four positions? With the lambda matrix?

 

[jcsd]

In SR, I know we transform three velocities using the einstein velocity addition law.
However, in the case of four velocities, do they simply transform the same way as four positions? With the lambda matrix?

They're Lorentz vectors, so they transform as vectors under a Lorentz transformation. I.e. yes.

 

[Chestermiller]

In SR, I know we transform three velocities using the einstein velocity addition law.
However, in the case of four velocities, do they simply transform the same way as four positions? With the lambda matrix?

Yes. Try transforming the 4 vector (c,0,0,0) and see what you get. Then try transforming the 4 vector (γc, γv, 0, 0) and see what you get.