/sci/ - Science & Math

>>12082967
https://vixra.org/author/jonathan_w_tooker

I showed that Bell's inequality relies on a not-too-good assumption that fermionic spin eigenfunctions are universally orthonormal. When we write spin eigenfunctions with Pauli matrices, they are orthonormal, but it remains a goal in physics to find analytical eigenfunctions which don't have matrix parts. More likely those functions would be "Dirac orthonormal" where Dirac orthonormality is a characteristic of things that are not orthonormal.

NO!!! Bell's theorem assumes sin eigenstates are orthonormal when it is not known that the states are orthonormal. In a theory with orthonormal spin states, hidden variables are ruled out by Bell's theorem. However, in a theory in which they are only "Dirac orthonormal," which is a subset of things that are "not orthorormal," as in
[eqn]\big\{\text{Dirac orthonormal things} \big\}\subset \big\{\text{Things that are not orthonormal} \big\}[/eqn]
then local hidden variables are allowed. To see why this is so important, note that the most unsatisfactory feature of the quantum theory is the inability to find analytical functions for spin eigenstates. The need to introduce spinors is where the whole discrepancy between the intuitive formalism of classical theory breaks down. One expects that a "more complete" quantum theory would have analytical eigenstates for bosons and fermions. As it is, we have an unsavory workaround with the multiplectic Pauli and Dirac spinors.

In his theorem, Bell treat non-orthogonal states as if they were orthogonal.

>>10944506
Nah. That chart showed that "a" and "e" are Latin letters, not Hebrew letters. While you're revising history, maybe you could tell us about the hollow cost?