# Contravariant Four-gradient ESN in Wikipedia appears wrong

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1. Oct 11, 2016

### SpecialEd

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. Oct 11, 2016

### TSny

Welcome to PF!
I agree with you that it doesn't look right. For the contravariant form of the 4-gradient they have

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.

3. Oct 13, 2016

### SpecialEd

Thanks so much for your comment and help!

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