TITLE:
Fermions: Spin, Hidden Variables, Violation of Bell’s Inequality and Quantum Entanglement
AUTHORS:
Doron Kwiat
KEYWORDS:
Fermions, Spin, Hidden Variables, Bell’s Inequality Violation, Spin Entanglement
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.10 No.4,
October
10,
2024
ABSTRACT: Using real fields instead of complex ones, it was recently claimed, that all fermions are made of pairs of coupled fields (strings) with an internal tension related to mutual attraction forces, related to Planck’s constant. Quantum mechanics is described with real fields and real operators. Schrodinger and Dirac equations then are solved. The solution to Dirac equation gives four, real, 2-vectors solutions
ψ
1
=(
U
1
D
1
)
ψ
2
=(
U
2
D
2
)
ψ
3
=(
U
3
D
3
)
ψ
4
=(
U
4
D
4
)
where (
ψ
1
,
ψ
4
) are coupled via linear combinations to yield spin-up and spin-down fermions. Likewise, (
ψ
2
,
ψ
3
) are coupled via linear combinations to represent spin-up and spin-down anti-fermions. For an incoming entangled pair of fermions, the combined solution is
Ψ
in
=
c
1
ψ
1
+
c
4
ψ
4
where
c
1
and
c
4
are some hidden variables. By applying a magnetic field in +Z and +x the theoretical results of a triple Stern-Gerlach experiment are predicted correctly. Then, by repeating Bell’s and Mermin Gedanken experiment with three magnetic filters
σ
θ
, at three different inclination angles
θ
, the violation of Bell’s inequality is proven. It is shown that all fermions are in a mixed state of spins and the ratio between spin-up to spin-down depends on the hidden variables.