**Authors:** Steve faulkner

Abstract:

I Follow up on the 2008 experiments of Tomasz Paterek et al, which link quantum randomness with logical independence. Analysis reveals, that the Paterek formalism (unwittingly) relaxes a Quantum Postulate. That relaxation denies the axiomatic imposition of unitary, Hermitian and Hilbert space mathematics, while allowing these to arise freely, as logically independent structures. Surprisingly, the Paterek formalism demands a non-unitary environment — where unitary structures may freely switch on or off. The unitary environment is necessary in the formation of superposition states, but not eigenstates. This unitary condition is sustained by self-referential logical circularity around cyclic sequences of transformations. Amongst all possible self-referential systems, these generate stable, persistent structures we recognise as quantum mechanical vectors and operators. Circularity explains indeterminacy's non-causedness. Non-definiteness, stems from geometric amb
iguity — typically, left|right handedness in the Bloch sphere. Collapse is caused when the unitary symmetry is deformed by some agency, such as a magnetic field or polariser.

Keywords:

foundations of quantum theory, axiomatised quantum theory, quantum mechanics, quantum randomness, quantum indeterminacy, quantum information, linear algebra, elementary algebra, imaginary unit, prepared state, measured state, eigenstate, superposition state, Hilbert space, unitary, redundant unitarity, orthogonal, scalar product, inner product, mathematical logic, logical independence, self-reference, logical circularity, mathematical undecidability.

**Comments:** 21 Pages.

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[v1] 2017-10-02 12:41:10

[v2] 2017-10-10 07:37:11

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