This is what I understood about 4-vectors in relativity.
We define the contravariant and covariant vectors like this : Aμ=[A0A1A2A3]
Aμ=[A0A1A2A3]
The relationship between them will be :
Aμ=ημνAν
In +--- convention it will lead to :
Aμ=[A0−A1−A2−A3]
Great.
But it doesn't give me information on the "absolute" sign of 4-vectors. For example if I take the 4-position.
I have an even at time t at space coordinates (x,y,z).
Will I have Xμ=[txyz]
Or
Xμ=[txyz]
I think it is the first answer because Aμ should transform the same way that the "real" coordinates (t,x,y,z) transform, but I am not totally sure ?
Thank you.
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