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Contravariant Four-gradient ESN in Wikipedia appears wrong

  1. Oct 11, 2016 #1
    1. The problem statement, all variables and given/known data
    I am self studying relativity. In Wikipedia under the four-gradient section, the contravariant four-vector looks wrong from an Einstein summation notation point of view.

    https://en.wikipedia.org/wiki/Four-vector

    2. Relevant equations

    It states:

    E
    00-E11-E22-E33 = Eαα

    3. The attempt at a solution
    As it is it looks wrong to me. Is it wrong or is it NOT ESN or something else?
     
  2. jcsd
  3. Oct 11, 2016 #2

    TSny

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    Homework Helper
    Gold Member

    Welcome to PF!
    I agree with you that it doesn't look right. For the contravariant form of the 4-gradient they have
    upload_2016-10-11_22-11-0.png
    I don't think there should be any negative signs in the first four lines. The last four lines look correct to me. So, I believe the Einstein summation works as follows $$\partial = E_\alpha \partial^\alpha = E_0 \partial ^0 + E_1 \partial ^1 +E_2 \partial ^2 + E_3 \partial ^3$$ where $$\partial^1 \equiv \frac{\partial}{\partial x_ {_1}} = -\frac{\partial}{\partial x^1}$$ etc.
     
  4. Oct 13, 2016 #3
    Thanks so much for your comment and help!
     
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