The Mathematical Description of a Generic Physical System

When dealing with a certain class of physical systems, the mathematical characterization of a generic system aims to describe the phase portrait of all its possible states. Because they are defined only up to isomorphism, the mathematical objects involved are “schematic structures”. If one imposes t...

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Bibliographic Details
Published in:Topoi 2015-10, Vol.34 (2), p.339-348
Main Author: Zalamea, Federico
Format: Article
Language:English
Subjects:
Education
Hilbert space
History, Philosophy and Sociology of Sciences
Humanities and Social Sciences
Identity formation
Ontology
Philosophy
Philosophy of Science
Philosophy of Technology
Physicists
Quantum physics
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Summary:When dealing with a certain class of physical systems, the mathematical characterization of a generic system aims to describe the phase portrait of all its possible states. Because they are defined only up to isomorphism, the mathematical objects involved are “schematic structures”. If one imposes the condition that these mathematical definitions completely capture the physical information of a given system, one is led to a strong requirement of individuation for physical states. However, we show there are not enough qualitatively distinct properties in an abstract Hilbert space to fulfill such a requirement. It thus appears there is a fundamental tension between the physicist’s purpose in providing a mathematical definition of a mechanical system and a feature of the basic formalism used in the theory. We will show how group theory provides tools to overcome this tension and to define physical properties.
ISSN:0167-7411
1572-8749
DOI:10.1007/s11245-015-9322-7