Timeline for What does it mean to go from a co-variant vector to a contravariant vector?

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Jan 14, 2018 at 18:22	comment	added	Bellem		Square distance? In gr you don't get square dinstance by squaring a vector, you can do that obly in sr. Then you can obtain the same thing through the definition of the pairing product, which gives you exactly the same results. You simply want to stress the importamce of having a metric manifold, which I agree with you, but the question was different. Of course if you want to have a metric manifold raising and lowering indices are a consequence...
Jan 14, 2018 at 17:08	comment	added	Michele Grosso		By contracting a vector with its dual you get a scalar, the norm of the vector (its square in reality), which is an invariant. If the vector is given by the coordinates you get the squared distance in spacetime, which is fundamental in both special and general relativity. That is why you need both contravariant and covariant components, however the latter have a different meaning as they define a linear application.
Jan 14, 2018 at 12:56	comment	added	Bellem		This is just definitions
Jan 13, 2018 at 22:07	history	edited	Michele Grosso	CC BY-SA 3.0	added 6 characters in body
Jan 13, 2018 at 22:01	history	answered	Michele Grosso	CC BY-SA 3.0