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Special relativity, summation agreement

  1. Jun 23, 2010 #1

    Uku

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    1. The problem statement, all variables and given/known data

    [PLAIN]http://www.hot.ee/jaaniussikesed/valem_kovar_erlt.bmp [Broken]

    The first half of the equation is okay, but, after the second equal sign I started to improvise, did I mess up or is it correct? Trying to understand the indexes.

    ds being the differentially small distance between events, dx the location vector? (not a 4 vector, I'm not sure on the English here) with covariant and contra-variant components present and the g is the metric tensor with its components marked by the indexes.

    Regards,
    Uku
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jun 23, 2010 #2

    lanedance

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    Homework Helper

    so i think you have got your indicies a little mixed up, a reapeted indicex, means to sum over the index, so start with
    [tex] dx_{\mu} = g_{\mu \nu} dx^{\nu}[/tex]

    so in this case the sum is over the repeated [itex] \nu [/itex], teh sum would then become a double sum
    [tex] ds^2 = dx^{\mu} dx_{\mu} = dx^{\mu} g_{\mu \nu} dx^{\nu}[/tex]

    see this for more
    http://en.wikipedia.org/wiki/Raising_and_lowering_indices
     
  4. Jun 24, 2010 #3

    Uku

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    Thanks!
     
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