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About a Lorentz matrix and its inverse

  1. Feb 11, 2009 #1
    Hi you all.
    Please forgive my poor English;
    I will try to put my best foot forward!

    I'm studying special relativity mostly on Naber's
    "The geometry of Minkowski spacetime". Just after
    introducing the concept of Lorentz matrix L
    (by means of "M" I point its inverse) through
    the well known relation

    L^c_a L^d_b g_cd = g_ab

    he states (pag. 22 equation following 1.3.10) that

    L^4_i / L^4_4 = - M^i_4 / M^4_4

    As far as I see no other assumption is involved in.
    Please, can you give any hint about establishing
    this equation ?

    Best Regards
    Barbara Da Vinci
     
  2. jcsd
  3. Feb 11, 2009 #2

    Fredrik

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    If I understand your notation correctly, that equation is equivalent to saying that if the velocity of frame F' in F is [itex]\vec v[/itex], then the velocity of frame F in F' is [itex]-\vec v[/itex]. I don't know how to motivate that statement other than by saying that it makes some sense to think of it as an interpretation of Einstein's first postulate. ("The laws of physics are the same in all inertial frames").

    Let me know if you need more information to understand why those two statements are the same. Hint: What do you get when a Lorentz transformation acts on (t,x,y,z)=(1,0,0,0)?
     
  4. Feb 11, 2009 #3

    George Jones

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    Welcome to Physics Forums!

    Use equation (1.2.11).
     
  5. Feb 12, 2009 #4
    Thanks for replying: I got it !
    Have a great day !!
     
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