How arithmetic generates the logic of quantum experiments

January 14, 2011

Indeterminate scalars under the Field Axioms: foundation for Reichenbach’s quantum logic

Filed under: Uncategorized — steviefaulkner @ 3:25 pm

Paper newly posted at:


Inherent within quantum measurement experiments is a decision process which current theory fails to express and does not explain. Each act of measurement indeterminately decides on one outcome from a spectrum of values. Nature executes this decision, but evidence indicates that the elected outcome is not caused by any physical influence.

The discrepancy between experiment and theory is traceable to a logical detail of arithmetic, not encoded in mathematical physics. Mathematical physics deals in semantic theories. These disregard this logical detail. For classical physics, no discrepancy is evident; in that domain, semantic truth and logical validity coincide. Happily, a logical implementation of the arithmetic, rather than a semantic one, does encode the indeterminate details .

The arithmetic in question is that of scalars. These are mathematical objects whose rules of algebra are the Field Axioms. Mathematical physics assumes the a priori existence of scalars. But in this article, apriority is transferred to the Field Axioms themselves. This step elevates the semantic theory to a logical one. Model Theory, a branch of mathematical logic, sets the Field Axioms within a rigorous environment that naturally differentiates between scalars they derive, distinct from scalars that satisfy them. A theorem is proved which isolates scalars whose existence is neither provable nor disprovable. These are the scalars which satisfy Axioms, but are not derivable; they are mathematically undecidable and logically indeterminate. Examples are worked through. The scalars’ modes of existence furnish the 3-valued logic which is foundation for Hans Reichenbach’s quantum logic.



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