The co is the one that varies with the coordinates, i. e. geometrically. The contra is the one that varies the other way, or "against" so to speak. Of course, which is the change of coordinates and which is the other is arbitrary from a mathematical point of view, whereas physically you measure space and time coordinates of each event.
Covariance means that, if you write p
µ = m u
µ and you change the coordinate axes, the components of
p will change but so will the those of m
u because they are the same type of tensor object. It's exactly the same notion as with euclidean 3-vectors, p
i = m v
i, except that in this case the metric is all +1 and no -1 so there's no contra. Of course, the trick of using an imaginary time coordinate allows the use of euclidean metric for space-time (or space-itime you might call it). It just gains the same result in a different way, the minus sign is "split between" the two vectors in the scalar product.
In short, it's just a way of getting that darn '-' in dx^2 - dt^2.
Quote:
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Originally Posted by sanctus
here I shouldn't say that I'm doing the master in physics
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Don't worry, we all found these things terribly confusing and mysterious and the professors all fail to spell them out more, because they become so obvious once you have reached enlightenment...
At that point you see the light but don't have the faintest idea how to get it across to the newbie.
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Inutil insegnŕ al mus, si piart timp, in plui si infastiděs la bestie.
Hypography Forum PITA...... er, Administrator.
