# Should tensor sum be used in matrix mechanics?

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## Main Question or Discussion Point

Suppose the Bell operator $B=|AB(1,2)+AB(1,3)+AB(2,3)|$

With $AB\in{1,-1}$

Nonlocal realism implies $B\in{1,3}$

However using usual matrix sum one eigenvalues for the result of measurement can be smaller than 1, implying nonlocal realism cannot explain the quantum result.

However if the Kronecker sum is used this fact disappears.

So what would these eigenvalues mean experimentally ?

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hilbert2
Gold Member
Can't answer the question itself, but as a tip: in LaTeX code the set notation with curly brackets $\left\{1,-1\right\}$ is written as "\left\{1,-1\right\}".

Thanks for the tip. I thought a bit about my OP

I used "realism", which is a big word from philosophy, but technically I think it's a threshold switch that digitalizes or binarizes the results that makes that difference. So nothing deep.

As summary matrix mechanics were possible in this forbidden band $]1,-1[$ hence sub-local realistic ?

PeterDonis
Mentor
2019 Award
using usual matrix sum one eigenvalues for the result of measurement can be smaller than 1
What "matrix sum" and "eigenvalues" are you talking about? The formula you give in the OP only involves numbers, not matrices.

jk22
Good point, it is if the $AB$s are raised to the rank of covariance operators of two spin 1/2 particles.

I.e. $A\rightarrow \vec{n}\cdot\vec{\sigma}$ ?

But I could calculate the eigenvalue only with a CAS (computers are useful but it looks like acedia)

Why is that as there is a violation of locality there is also an under locality value ?

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