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R. G. Herb Condensed Matter Seminar
The Objective Indefiniteness Interpretation of Quantum Mechanics: Partition logic, logical information theory, and quantum mechanics
Date: Thursday, April 11th
Time: 11:00 am
Place: 5310 Chamberlin
Speaker: David Ellerman, University of California, Riverside
Abstract: Quantum mechanics (QM) is not compatible with the usual Boolean logic of subsets where elements have definite properties "all the way down." But there is a recently developed dual logic of partitions (subsets and partitions are category-theoretically dual) which models indefinite elements that become more definite as distinctions are made. If quantum mechanics was also incompatible with this unique dual logic of partitions, then one might "press the panic button" and postulate unknowable hidden variables to restore definiteness or soar off into the void with "many worlds" or the like.

But quantum mechanics fits perfectly with the dual logic of partitions. There is no need for (more) bizarre flights of fancy to "interpret" QM. This objective indefiniteness approach to QM does not restore our common sense assumption of definiteness down into the quantum realm. But it does restore sanity and understanding to the whole framework. That is, we now have the logic that precisely fits QM--a logic that was developed independently (i.e., without any thought of a QM connection) and that is the unique mathematical dual to ordinary Boolean subset logic, the logic assumed in classical physics. Moreover the normalized counting measure on partitions gives the quantum-relevant logical information theory--just as Boole developed logical probabilities as the normalized counting measure on subsets. Indeed, when the mathematics of partition logic and logical information theory is linearized and lifted to complex vector spaces, then it yields the mathematical framework of quantum mechanics (but not the specifically physical postulates).

The key concepts explicated by this approach are the old ideas of "objective indefiniteness" (emphasized by Abner Shimony), objective probabilities, and the objective realization of information, "its" from "dits" (= distinctions). Since partition logic, logical information theory, and the lifting program "derives" the mathematics of quantum mechanics, it shows how that QM framework can be interpreted--and this set of results gives what might be called the objective indefiniteness interpretation of quantum mechanics.
Host: Huber
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