Undergrad Definition of Tensor Identity Simplification

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The discussion centers on the simplification of the expression g^{\alpha \delta}g_{\beta \gamma}, questioning whether it can be reduced or equated to something else. It is noted that if all indices are different, no simplification is possible. The conversation also touches on the relevance of this expression to tensor densities, indicating a potential connection that remains unexplored. Overall, the participants seek clarity on the nature of the expression and its implications in tensor analysis. The topic highlights the complexities involved in tensor identities and their simplifications.
Arman777
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Is there a simplifcation of ##g^{\alpha \delta}g_{\beta \gamma} ## or what is equal to ?
 
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it's just a coordinate dependent number no? assuming your indices are not abstract or anything
 
Okay I got no worries
 
Arman777 said:
Is there a simplifcation of ##g^{\alpha \delta}g_{\beta \gamma} ## or what is equal to ?

Not if all the indexes are different.

Also, what does this have to do with a tensor density?
 

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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