Constructive Axiomatics for Spacetime Physics

The programme of 'constructive axiomatics', promulgated by Hans Reichenbach in 1924, seeks to build up the architecture of our best theories of physics from basic axioms supposedly imbued with immediate and indubitable empirical content. Taking inspiration from Reichenbach, Hermann Weyl proposed his own 'causal-inertial' approach to the constructive axiomatization of Einstein's general relativity, according to which a relativistic spacetime can be constructed solelyfrom the trajectories of light rays and freely-falling particles; this project, however, came to fruition only in 1972, with the constructive axiomatization of general relativity due to Ehlers,Pirani, and Schild ('EPS').One century since Reichenbach, and fifty years since EPS, Constructive Axiomatics for Spacetime Physics is a celebration of the constructive axiomatic methodology. It achieves four main tasks. First, it provides a thoroughgoing presentation of the EPS axiomatization, closing missing loopholes, identifying problematic axioms, and so forthDLin this way, one gains a much-improved appreciation of the extent to which a causal-inertialapproach to general relativity might succeed, and of what such an approach might offer. Second, it synthesizes and assesses the vast but disparate literature on constructive axiomatics which has arisen over the pastcentury and sets the methodology in its proper philosophical context. Third, it generalizes the approach to apply to quantum spacetimes. And fourth, it applies the approach to the context of non-relativistic spacetime physics. All in all, the book demonstrates that constructive axiomatics is live-and-kicking; the book will become the go-to resource for this way of philosophizing about the nature of space and time.

Emily Adlam is a philosopher of physics focusing on the foundations of quantum mechanics and the philosophy of time. She did her PhD in theoretical physics at the University of Cambridge, and was a postdoctoral associate at the University of Western Ontario before moving to Chapman University. Niels Linnemann is a philosopher of physics at the University of Geneva. After completing degrees in physics, maths, and philosophy at theUniversities of Münster, Oxford, and Cambridge, he earned his doctorate in philosophy under supervision of Christian Wüthrich at the University on Geneva for his work on theory construction in quantum gravity. His interests beyond thephilosophy of spacetime include the fields of scientific discovery and theory construction, as well as that of the metaphysics of sciences. He co-runs an initiative to help make the philosophy of physics more known in German-speaking countries. James Read is an associate professor at the University of Oxford. He studied physics and philosophy at Oxford, and mathematics at Cambridge, before completing a doctorate in philosophy from Oxford in 2018. He works in the philosophy ofphysics, in particular on the foundations of spacetime theories and symmetries. His work has won various international awards, including the Hanneke Janssen Prize and Clifton Memorial Prize.

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