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Quantum States: An Analysis via the Orthogonality Relation

Zhong, Shengyang (2021) Quantum States: An Analysis via the Orthogonality Relation. Synthese. ISSN 1573-0964

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From the Hilbert space formalism we note that five simple conditions are satisfied by the orthogonality relation between the (pure) states of a quantum system. We argue, by proving a mathematical theorem, that they capture the essentials of this relation. Based on this, we investigate the rationale behind these conditions in the form of six physical hypotheses. Along the way, we reveal an implicit theoretical assumption in theories of physics and prove a theorem which formalizes the idea that the Superposition Principle makes quantum physics different from classical physics. The work follows the paradigm of mathematical foundations of quantum theory, which I will argue by methodological reflection that it exemplifies a formal approach to analysing concepts in theories.

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Item Type: Published Article or Volume
Zhong, Shengyangzhongshengyang@163.com0000-0001-5538-0002
Keywords: Orthogonality relation, Mathematical foundations of quantum theory, Quantum logic, Concept analysis
Subjects: Specific Sciences > Physics > Quantum Mechanics
Depositing User: Dr. Shengyang Zhong
Date Deposited: 28 Oct 2021 03:52
Last Modified: 28 Oct 2021 03:52
Item ID: 19757
Journal or Publication Title: Synthese
Publisher: Springer (Springer Science+Business Media B.V.)
Official URL:
DOI or Unique Handle: 10.1007/s11229-021-03453-5
Subjects: Specific Sciences > Physics > Quantum Mechanics
Date: October 2021
ISSN: 1573-0964

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