How Would Physics Change Without Covariant and Contravariant Tensors?

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Without covariant and contravariant tensors, the formulation of physical laws, such as Einstein's equations, would lose their essential properties of coordinate independence and tensoriality. While it is possible to express these equations without using tensors, the underlying distinctions between covariant and contravariant forms remain crucial for accurately describing physical phenomena. The discussion emphasizes that both types of tensors are necessary for a complete understanding of the geometry of spacetime. Even in alternative formulations, the tensorial nature of classical equations cannot be eliminated. Ultimately, the absence of these tensor concepts would fundamentally alter the framework of modern physics.
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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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extrads said:
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.
 
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').
 
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
 

Thread 'EPR revisited'

In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A## and B has ##|b>_B## simultaneously, i.e., when their synchronized clocks both read time T However, in other inertial frames, due to the relativity of simultaneity, the moment when B has ##|b>_B##...
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