On an algebraic definition of laws

An algebraic definition of laws is formulated, motivated by analyzing points in Euclidean geometry and from considerations of two physical examples, Ohm’s law and Newton’s second law. Simple algebraic examples constructed over a field are presented. •Laws of nature can be formalized as many-sorted a...

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Bibliographic Details
Published in:Journal of mathematical psychology 2014-01, Vol.58, p.13-20
Main Authors: Simonov, A.A., Kulakov, Y.I., Vityaev, E.E.
Format: Article
Language:English
Subjects:
Cancellation conditions
Groups
Measurement theory
Physical laws
Transitive groups
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Summary:An algebraic definition of laws is formulated, motivated by analyzing points in Euclidean geometry and from considerations of two physical examples, Ohm’s law and Newton’s second law. Simple algebraic examples constructed over a field are presented. •Laws of nature can be formalized as many-sorted algebras of a special type.•Algebraic representations of the laws form a special type of groups.•For the case when measurement outcomes are real numbers an exhaustive classification of all possible laws can be achieved.
ISSN:0022-2496
1096-0880
DOI:10.1016/j.jmp.2013.11.003