Vectors on Curved Space

In this paper I provide an ontology for the co-variant vectors, contra-variant vectors and tensors that are familiar from General Relativity. This ontology is developed in response to a problem that Timothy Maudlin uses to argue against universals in the interpretation of physics. The problem is tha...

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Bibliographic Details
Published inDialectica Vol. 63; no. 4; pp. 491 - 501
Main Author FORREST, Peter
Format Journal Article
LanguageEnglish
Published Oxford, UK Blackwell Publishing Ltd 01.12.2009
Subjects
Algebra
Curved space
Dialectic
Electric fields
Mathematical differentiation
Mathematical vectors
Scalars
Spacetime
Tensors
Vector fields
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Summary:In this paper I provide an ontology for the co-variant vectors, contra-variant vectors and tensors that are familiar from General Relativity. This ontology is developed in response to a problem that Timothy Maudlin uses to argue against universals in the interpretation of physics. The problem is that if vector quantities are universals then there should be a way of identifying the same vector quantity at two different places, but there is no absolute identification of vector quantities, merely a path-relative one. My solution to the problem is to use the mathematical characterization of vectors as differential operators on scalar fields. On the proposed hypothesis a scalar field is a conjunctive state of affairs, and vector and tensor fields are relations instantiated by scalar fields.
Bibliography:ark:/67375/WNG-6XWF6X2J-Z
istex:F68D726F2CBA06A9357F3D827DA2FBE91BB4C541
ArticleID:DLTC1219
ISSN:0012-2017
1746-8361
DOI:10.1111/j.1746-8361.2009.01219.x