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Whoops, sorry Ruth I had your last name spelled incorrectly on last letter when I entered it in my Iphone hit t rather than r.

The real issue is whether physical observables must be Hermitian operators. I think the answer is no because laser beams are essentially eigenstates of the non-Hermitian destruction operators a in second quantization. These generally arise in spontaneous symmetry breakdown SSB relative to some group in ground states of real on-mass-shell particles and in vacuum states of virtual off -mass-shell particles. Indeed these emergent order parameters no longer obey the Schrodinger equation in configuration space, so you are right to question whether we can still entangle them without some limit.

However consider, for example, the entangled non-Hermitian operator

a1b2 + a2b1

Does it have a physically realizable eigenstate

(a1b2 + a2b1)|z1w2 + z2w1> = (z1w2 + z2w1)|z1w2 + z2w1>

where z1, z2, w1, w2 are points on the complex plane?

PS crystals emerge from SSB of T3 in systems of atoms and molecules

ferromagnets emerge from SSB of O(3) in systems of magnetic spins

superfluids emerge from SSB of two kinds of U1 in helium and electron-phonon systems respectively

The Higgs field emerges from SSB of SU2 in the physical vacuum in the standard model.

Perhaps the mental field in our brains emerges from SSB of some group for some subsystem e.g. Hameroff, Vitiello?

We have Dean Radin's "Entangled Minds" for example.
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