# GRAVITATION, by MTW, Exercise 2.7

1. Jul 28, 2010

### Living_Dog

(i) reference frames - who's who??
I don't get the Lorentz transformation conceptually. E.g. the mathematical transformation is:

$$x^\mu = \Lambda^{\mu}_{\alpha'} x^{\alpha'}$$.

Does this mean that if I am told the coordinates of the S' guy,
then I will see him at x(x') values in my S frame?

For velocities then,

$$u^\mu = \Lambda^{\mu}_{\alpha'} u^{\alpha'}$$.

Does this mean that if I am told the speed of the S' guy,
then I will record his speed as u(u') values in my S frame?

But how do I know u'?? All I see is u, and u' thinks he is motionless!

(ii) is his "ordinary" velocity:

$$u^{i} = \Lambda^{i}_{\alpha'} u^{\alpha'}$$?

or is it found by simply setting $$\gamma$$ equal to 1 and then computing the above?

Last edited: Jul 28, 2010