Logical entropy – special issue

Manfredi, Giovanni

doi:10.1051/fopen/2022005

Cited by 6 publications

(2 citation statements)

References 10 publications

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“…The partitional approach to understanding the math of QM shows that the key organizing concepts are indistinctions versus distinctions and its cognates. Those concepts define the notion of logical entropy in the new partition-logical theory of information-asdistinctions ( [2,61]). When a particle in a superposition state undergoes an interaction, it is often asked "what characterizes whether it is a measurement or not?"…”

Section: Feynman's Treatment Of Measurementmentioning

confidence: 99%

A New Logic, a New Information Measure, and a New Information-Based Approach to Interpreting Quantum Mechanics

Ellerman

2024

Entropy

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The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of partitions. Or, putting it the other way around, the math of partitions is a skeletal version of the math of QM. The key concepts throughout this progression from logic, to logical information, to quantum theory are distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. The distinctions of a partition are the ordered pairs of elements from the underlying set that are in different blocks of the partition and logical entropy is defined (initially) as the normalized number of distinctions. The cognate notions of definiteness and distinguishability run throughout the math of QM, e.g., in the key non-classical notion of superposition (=ontic indefiniteness) and in the Feynman rules for adding amplitudes (indistinguishable alternatives) versus adding probabilities (distinguishable alternatives).

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Section: Feynman's Treatment Of Measurementmentioning

confidence: 99%

A New Logic, a New Information Measure, and a New Information-Based Approach to Interpreting Quantum Mechanics

Ellerman

2024

Entropy

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“…In the duality between subsets and partitions, distinctions of a partition are dual to elements of a subset. Hence, the quantitative notion of a partition is the normalized number of distinctions, and that is the first definition of logical entropy [16,17] with equiprobable outcomes:…”

Section: A New Information Measure: Logical Entropymentioning

confidence: 99%

A New Approach to Understanding Quantum Mechanics: Illustrated Using a Pedagogical Model over ℤ2

Ellerman

2024

AppliedMath

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The new approach to quantum mechanics (QM) is that the mathematics of QM is the linearization of the mathematics of partitions (or equivalence relations) on a set. This paper develops those ideas using vector spaces over the field Z2={0.1} as a pedagogical or toy model of (finite-dimensional, non-relativistic) QM. The 0,1-vectors are interpreted as sets, so the model is “quantum mechanics over sets” or QM/Sets. The key notions of partitions on a set are the logical-level notions to model distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. Those pairs of concepts are the key to understanding the non-classical ‘weirdness’ of QM. The key non-classical notion in QM is the notion of superposition, i.e., the notion of a state that is indefinite between two or more definite- or eigen-states. As Richard Feynman emphasized, all the weirdness of QM is illustrated in the double-slit experiment, so the QM/Sets version of that experiment is used to make the key points.

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The Mathematics of Quantum Mechanics: The Partition Analysis

Ellerman

2024

SpringerBriefs in Philosophy

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Logical entropy – special issue

Cited by 6 publications

References 10 publications

A New Logic, a New Information Measure, and a New Information-Based Approach to Interpreting Quantum Mechanics

A New Logic, a New Information Measure, and a New Information-Based Approach to Interpreting Quantum Mechanics

A New Approach to Understanding Quantum Mechanics: Illustrated Using a Pedagogical Model over ℤ2

The Mathematics of Quantum Mechanics: The Partition Analysis

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