Is another definition of sum useful?

[jk22]

Von neumann and bell pointed out that basically the non isomorphic fact that the spectrum $$\sigma(A+B)!=\sigma(A)+\sigma(B)$$ leads to contradictions.

If we but replace the sum by $$A\otimes 1+1\otimes B$$ then the above inequality becomes an equality.
This would make things much easier.

We would get as eigenvalues for chsh integer values for example.

 

[Simon Bridge]

Note: The inequality sign is \neq to give $\neq$.

It is always possible to define a problem away - but adopting the definition in general leads to other problems in other places.
In this case, the observation is about something of Nature. You don't get to make Nature something else by changing the definitions of the words used to describe Her.

 

[jk22]

But in our case with the usual sum of operators Bell's theorem could be rephrased as $$1+1+1-1=2\sqrt{2}$$ ? (if we compute the values that are afterwards averaged)

Where we need to find the operation + between measurement results.

 

[jk22]

My last post is confusing, in fact what I mean is that There seem to be a discrepancy between measurement results (0,2,4) and eigenvalues (0,2sqrt 2) ?