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A system of axioms for Minkowski spacetime

Cocco, Lorenzo and Babic, Joshua (2020) A system of axioms for Minkowski spacetime. [Preprint]

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Abstract

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future
use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness and a four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four
dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane - which obeys the Euclidean axioms in [Tarski and Givant, 1999] - and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagora’s theorem. We conclude with a Representation Theorem relating models of our system that satisfy second order continuity to the mathematical structure called ‘Minkowski spacetime’ in physics textbooks.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Cocco, LorenzoLorenzo.Cocco@unige.ch
Babic, Joshua
Keywords: Axiomatization; Minkowski spacetime; special relativity; nominalism; Field's program; synthetic mechanics and geometry
Subjects: Specific Sciences > Mathematics > Ontology
General Issues > Scientific Metaphysics
Specific Sciences > Physics > Relativity Theory
General Issues > Structure of Theories
Depositing User: Mr. Joshua Babic
Date Deposited: 03 May 2020 17:21
Last Modified: 03 May 2020 17:21
Item ID: 17141
Subjects: Specific Sciences > Mathematics > Ontology
General Issues > Scientific Metaphysics
Specific Sciences > Physics > Relativity Theory
General Issues > Structure of Theories
Date: 30 April 2020
URI: http://philsci-archive.pitt.edu/id/eprint/17141

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