Natural topography of Hilbert Spaces as a generator of free will?

There is a theory that goes by the name Margenau’s Theory, which tries its hand at reducing human consciousness to a field of probabilities in what is termed a Fock Space, which is an algebraic construction in quantum mechanics to construct the quantum states space of a variable or an unknown number of identical particles from a single particle Hilbert Space, H.

jb_slides-010-fock-space

Hilbert space extends the notion of Euclidean geometry from a two-dimensional space to a three-dimensional space, and is talked about as an abstract vector space possessing the structure of an inner product that allows the length and the angle to be measured. Now, such a space could be created by an electrical activity at the synaptic level. Normal behaviour could therefore be seen as the elasticity of the field, and free will as a rupture within it. But, in what topology begs the question? Since, there is nothing in the natural topography of Hilbert Spaces that could be the generator of free will….

fig-4-three-states-of-the-hilbert-space-of-the-quantum-dimer-model-there-are

Three states of the Hilbert space of the quantum dimer model. There are off-diagonal matrix elements in the effective Hamiltonian which connect state ͑ a ͒ to state ͑ b ͒ , and state ͑ a ͒ to state ͑ c ͒ , by a resonance between pairs of horizontal and vertical dimers around a plaquette. The latter matrix element differs from the former because only the latter has a diagonal link across the resonating plaquette. Also shown are the corresponding values of the heights h a on the sites of the dual lattice. Credit

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