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formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished].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:	Creators Email ORCID Cocco, Lorenzo Lorenzo.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:	https://philsci-archive.pitt.edu/id/eprint/17141

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• A system of axioms for Minkowski spacetime. (deposited 03 May 2020 17:21) [Currently Displayed]
  • A system of axioms for Minkowski spacetime. (deposited 26 Jul 2020 14:36)

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