Aristotelis Panagiotopoulos - Incompleteness theorems for observables - QISS 2025 Conference

Описание: Aristotelis Panagiotopoulos, Kurt Gödel Research Center

Incompleteness theorems for observables in general relativity, Invited Talk at QISS 2025 Conference - Vienna, Austria

Abstract: Formulating a theory of quantum gravity is a major open problem in mathematical physics. Some of the core technical and epistemological difficulties come from the fact that General Relativity (GR) is ‘generally covariant’, i.e. invariant under change of coordinates by the arbitrary diffeomorphism of the ambient manifold. The Problem of Observables is a famous instance of the difficulties that general covariance brings into quantization: no non-trivial diffeomorphism-invariant quantity has ever been reported on the collection of all spacetimes. It turns out that there is a good reason for this.
In this talk, I will present my joint work with Marios Christodoulou and George Sparling, where we employ methods from Descriptive Set Theory in order to show that, even in the space of all vacuum solutions, no complete observables can be Borel definable. That is, the problem of observables is to ‘analysis’ what the Delian problem is to `straightedge and compass’.
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The Quantum Information Structure of Spacetime (http://www.qiss.fr) is an interdisciplinary research initiative among several universities and research institutes all over the world, supported by the John Templeton Foundation through the grants https://www.templeton.org/grant/the-q... and https://www.templeton.org/grant/the-q..., coordinated from The Samy Maroun Center for Space, Time and the Quantum (http://www.spacetimeandquantum.com).

The goal of QISS is to explore and connect the research domains of Quantum Information/Computing, Quantum Gravity and Quantum Foundations. Main objectives are to found the physics of quantum spacetime on an information-theoretic basis, to bring within reach empirical access to quantum gravity in 'table-top' laboratory conditions by exploiting rapid advances in quantum computing related technologies and using quantum information theoretic concepts, and to promote an extensive interaction between physicists and philosophers on the conceptual role of information in spacetime physics.