Covariant and contravariant

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

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  • #2
PeterDonis
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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.
 
  • #3
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If the OP is asking whether we could express Guv=8πTuv 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').
 
  • #4
WannabeNewton
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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
 

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