Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partitions and Objective Indefiniteness in Quantum Mechanics   Classical physics and quantum physics suggest two meta-physical types of
reality: the classical notion of a objectively definite reality with properties
"all the way down," and the quantum notion of an objectively indefinite type of
reality. The problem of interpreting quantum mechanics (QM) is essentially the
problem of making sense out of an objectively indefinite reality. These two
types of reality can be respectively associated with the two mathematical
concepts of subsets and quotient sets (or partitions) which are
category-theoretically dual to one another and which are developed in two
mathematical logics, the usual Boolean logic of subsets and the more recent
logic of partitions. Our sense-making strategy is "follow the math" by showing
how the logic and mathematics of set partitions can be transported in a natural
way to Hilbert spaces where it yields the mathematical machinery of QM--which
shows that the mathematical framework of QM is a type of logical system over
the complex numbers. And then we show how the machinery of QM can be
transported the other way down to the set-like vector spaces over Z_2 showing
how the classical logical finite probability calculus (in a "non-commutative"
version) is a type of "quantum mechanics" over Z_2, i.e., over sets. In this
way, we try to make sense out of objective indefiniteness and thus to interpret
quantum mechanics.

36
The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
1
The categories of this paper are: cs