What is it about?
This paper shows that the math (not the physics) of quantum mechanics is the mathematics of set parttitions linearized to Hilbert spaces. Since partitions (or equivalence relations) are the simple logical-level math concept to represent indefiniteness and definiteness, this shows that the key concept of superposition should be interpreted in terms of indefiniteness, not as the addition of "waves." The quantum world is Indefinite World, not Wave World.
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Why is it important?
For a century, quantum mechanics has been misinterpreted as being about waves since the complex vectors spaces are the natural math for waves. But we show that the way quantum math is developed and used really arises from the linearization of partitions (or, equivalently, equivalence relations).
Perspectives
This paper corroborates the objective indefiniteness interpretation of quantum mechanics first proposed (using different language) by Heisenberg and later by Shimony and otheres.
David Ellerman
School of Social Science, University of Ljubljana, Slovenia
Read the Original
This page is a summary of: Follow the Math!: The Mathematics of Quantum Mechanics as the Mathematics of Set Partitions Linearized to (Hilbert) Vector Spaces, Foundations of Physics, September 2022, Springer Science + Business Media,
DOI: 10.1007/s10701-022-00608-3.
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