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Quantum Mathematics




A chapter from Steve Faulkner's book:

The Underlying Machinery of Quantum Indeterminacy

Knowing precisely what drives necessity for the imaginary unit's presence in Quantum Theory resolves the question of quantum indeterminacy.

The Vienna Experiments show that quantum indeterminacy has mathematical origins, rather than originating in any unknown physics. This chapter sets the tone for mathematical discipline needed in exposing those origins; and demonstrates an example of easy-to-access logic, visibly manifest in Quantum Mathematics, which textbook theory ignores.

Emphasis is on Quantum Mathematics: the mathematics representing Quantum Mechanics; because quantum indeterminacy originates in mathematical processes. The mathematics permits semantical freedom for pure states, not permitted for mixed states; possible unitarity applying to pure states, and necessary unitarity applying to mixed states. A priori unitarity, imnposed across all states of a quantum system, is not truly or faithfully representative. The traditional formalism of Applied Mathmeatics is inadequate in exposing the semantical freedoms; the formalism of quantifier logic is needed.