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I just want to share my curiosity

in the definition of 4-vector quantities such as world line 4-vector x^alpha, 4-velocity vect, gauge potential etc. the ones with subscript for indices usually have the first component with negative sign and the ones with superscript for indices have all positive. For position coordinate x, as far as i know, the former is called covariant coordinate while the latter is called contravariant.

Do these covariant -contravariant terminology apply to other 4-vectors (velocity, energy momentum,etc)?

What are actually the differences between the two? I just doubt if the covariant corresponds to Minkowskian space while the contravariant to Euclidean space, is it correct?

Please correct me if there are wrong points in my statements. Thanks

Another my question, the relativistic momentum is p = gamma*m*v, m is rest mass

One is likely to say that the relativisticity of momentum is because the mass is relativistic, that is m' = gamma*m. Can we see this point from other perspective (though I am not quite sure if it is right), that the speed has been transformed to gamma*v while m is unchanged?

these must be simple questions for many of you

thanks for any help

regards

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# Definition of 4-vector quantities

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