How Would Physics Change Without Covariant and Contravariant Tensors?

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SUMMARY

The discussion centers on the necessity of covariant and contravariant tensors in the formulation of Einstein's equations, specifically Guv = 8πTuv. It is established that while one could express these equations without tensors, the essential property of coordinate independence, or 'tensoriality', remains intact. The distinction between covariant and contravariant tensors is crucial for understanding their roles in physics. Additionally, the concept of spinors is introduced as an extension of tensors, highlighting the complexity of physical representations.

PREREQUISITES
  • Understanding of Einstein's field equations (EFE)
  • Knowledge of tensor calculus
  • Familiarity with covariant and contravariant tensor definitions
  • Basic concepts of spinors in physics
NEXT STEPS
  • Research the implications of tensoriality in general relativity
  • Study the differences between covariant and contravariant tensors in detail
  • Explore the mathematical framework of spinors and their applications
  • Examine alternative formulations of Einstein's equations without tensors
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Physicists, mathematicians, and students of theoretical physics who are interested in the foundational concepts of general relativity and the mathematical structures that underpin physical theories.

extrads
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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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