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Proper Time

  1. Oct 1, 2008 #1
    I know what the equation for proper time is in basic Euclaiden space. But when space-time is concerned, I get a bit confused.

    The equation is: [tex]\Delta\tau=\sqrt{g_{\mu\nu}dx^{\mu}dx^{\nu}}[/tex]

    I realise that [tex]g_{\mu\nu}[/tex] is the Metric tensor. However i dont understand the dx's and their indices.

    Would someone be able to explain these features to me?


  2. jcsd
  3. Oct 1, 2008 #2


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    Hi Ben! :smile:

    It means dtau² is the linear combination of the dxidxjs, with coefficients gij.

    So, for example, if gij is the usual (1,-1,-1,-1) diagonal tensor, then dtau² = dt² - dx² - dy² - dz². :smile:
  4. Oct 1, 2008 #3


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    The indexes on the dx's are tensor indexes, which run over the 4 dimensions so that for instance,
    [tex]x^0 = t, x^1 = x, x^2 = y, x^3 = z[/tex]

    When indexes are repeated high and low, it means take the sum ( as Tiny-Tim has done ).

  5. Oct 1, 2008 #4


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    can be thought of as
    [tex]\Delta\tau=\sqrt{ d\vec x \cdot d\vec x }[/tex]
    In the original form, the metric-tensor is explicit.
  6. Oct 3, 2008 #5
    Thanks Tiny Tim, Mentz 114 and Robphy.

    Appreciate your help and I understand this equation alot better.



    P.S. Nice secret message Robphy!
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