The Mathematical Description of a Generic Physical System
 Citation data:

Topoi, ISSN: 01677411, Vol: 34, Issue: 2, Page: 339348
 Publication Year:
 2015

 EBSCO 30

 EBSCO 2

 EBSCO 1
 Repository URL:
 http://philsciarchive.pitt.edu/id/eprint/12201; http://philsciarchive.pitt.edu/id/eprint/11533
 DOI:
 10.1007/s1124501593227
 Author(s):
 Publisher(s):
 Tags:
 Arts and Humanities
article description
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.