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Lorentz transformation conclusion with rotation of axis

  1. Nov 13, 2007 #1
    Hi Guys,

    I've attached 2 pages from the book of landau "The Classical Theory of fields", I have a question about the lorentz transformations in pages 10,11

    after reaching the step:

    tanh(psy)= V/c

    How did he split the latter into sinh(psy) and cosh(psy) and added the "gamma" constant which is 1/sqrt(1-V^2/c^2) ????

    Can we add any constant we want? of course there is a reason

    anyone can explain?

    I know the Einsteins way of concluding these transformations but I want to understand the rotation of axes method

    thanks in advance, please reply as soon as possible :)
     

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  2. jcsd
  3. Nov 13, 2007 #2

    robphy

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    Think about a [Minkowski-] right-triangle... and its associated Pythagorean theorem [the square-interval]:

    write:
    [tex]\cosh^2 \psi - \sinh^2\psi = 1 [/tex]
    as:
    [tex]\cosh^2 \psi(1 - \tanh^2\psi) = 1 [/tex]
     
    Last edited: Nov 13, 2007
  4. May 30, 2008 #3
    Thanks
    :approve:
     
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