Covariant and contravariant

[extrads]

If the notions of covariant and contravariant tensors were not introduced,what would happen?E.g. what form will the Einstein E.q. G_uv=8πT_uv be changed into ?

 

[PeterDonis]

If the notions of covariant and contravariant tensors were not introduced,what would happen?

I'm not sure what you mean by this. Covariant and contravariant tensors represent distinct kinds of physical things; if you know the metric, you can compute correspondences between them, but they are still distinct concepts. So if you're going to use tensors at all, you need both kinds.

 

[Mentz114]

If the OP is asking whether we could express G_uv=8πT_uv without tensors, I would have to say that it can be done, but the central property of coordinate independence would still be there ( ie 'tensoriality').

 

[WannabeNewton]

The notion of contravariant and covariant is always there. It is made explicit in index notation but you can just as well write it in index-free notation as $G = 8\pi T$ but you cannot get rid of the tensorial nature of the classical EFEs. The extension of the concept of a tensor is a spinor: http://en.wikipedia.org/wiki/Spinor