But why one is co- and the other contra-?
Is it because the covariant varies without the need of the metric (ie you just do a lorentz transformation) and the contravariant need the metric (ie you first lower the indices and then you transform)? If yes, the introduction of contravariant vectors is only motivated by the fact that it simplifies the wrtitting of things like the scalar product etc?
And here comes he most stupid question (here I shouldn't say that I'm doing the master in physics
) :
what is exactly meant by euclidian covariance (or lorentz covariance)? Just the way it transforms(ie in the euclidian case adding the speed of the new reference system and in the lorentz one just making a lorentz transformation with the betas and gammas).
I'm sure that you are right when you say that it is so trivial that nobody ever says it. That's why now that I started to ask myself now what's actually underneath it (and making my own hypothesis), I have nobody to ask to as this things seem now to be taken as granted from every prof...
