Observables in Table Top Quantum Gravity
Περίληψη: General relativity poses a long-standing puzzle: without a fixed spacetime to use as reference, it is notoriously challenging to define physical observables. [1] gave a first definitive result about this decades–long question, providing a very sharp formulation of the ‘problem of observables’: in a precise sense of ‘definable’, provided by a branch of logic called descriptive set theory, diffeomorphism-invariants are not definable. These difficulties notwithstanding, the problem of observables can be fully resolved for background independent theories defined on finite graphs, as we showed in [2]. Sets of complete observables can be constructed so that each seeks a connected subgraph structure — local correlations. Geometrical information is fully encoded in background independent observables through this subtle interplay of global and local graph notions, a behavior we term glocal. In this talk, we discuss the above results as to their relevance regarding: (i) notions of invariants under quantum coordinates, such as that appeared in [3] (ii) the epistemological relevance of Table Top Quantum Gravity protocols
[1] https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.131.171402
[2] https://arxiv.org/abs/2508.02346
[3] https://journals.aps.org/prl/abstract/10.1103/bnkn-4p3f