Images and Logic of the Light Cone: Tracking Robb’s Postulational Turn in Physical Geometry

Jordi Cat

Abstract


Previous discussions of Robb’s work on space and time have offered a philosophical focus on causal interpretations of relativity theory or a historical focus on his use of non-Euclidean geometry, or else ignored altogether in discussions of relativity at Cambridge. In this paper I focus on how Robb’s work made contact with those same foundational developments in mathematics and with their applications. This contact with applications of new mathematical logic at Göttingen and Cambridge explains the transition from his electron research to his treatment of relativity in 1911 and finally to the axiomatic presentation in 1914 in terms of postulates. At the heart of Robb’s physical optics was the model of the light cone. The model underwent a transition from a working mechanical model in the Maxwellian Cambridge sense of a pedagogical and research tool to the semantic model, in the logical, model-theoretic sense. Robb tracked this transition from the 19th- to the 20th-century conception with the earliest use of the term ‘model’ in the new sense. I place his cone models in a genealogy of similar models and use their evolution to track how Robb’s physical researches were informed by his interest in geometry, logic and the foundations of mathematics.

 

Keywords


Robb; axiomatics; postulates; postulationism; light cone; relativity theory; geometry; foundations of mathematics; space-time; model; logical model; Russell; Hilbert; Veblen; Huntington; Peano; Minkowski; Cambridge; Göttingen

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DOI: http://dx.doi.org/10.22370/rhv.2016.8.498

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