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GRAVITATION, by MTW, Exercise 2.7

  1. Jul 28, 2010 #1
    (i) reference frames - who's who??
    I don't get the Lorentz transformation conceptually. E.g. the mathematical transformation is:


    [tex]
    x^\mu = \Lambda^{\mu}_{\alpha'} x^{\alpha'}
    [/tex].

    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,


    [tex]
    u^\mu = \Lambda^{\mu}_{\alpha'} u^{\alpha'}
    [/tex].

    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:


    [tex]
    u^{i} = \Lambda^{i}_{\alpha'} u^{\alpha'}
    [/tex]?

    or is it found by simply setting [tex]\gamma[/tex] equal to 1 and then computing the above?
     
    Last edited: Jul 28, 2010
  2. jcsd
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