Speaker
Description
The plethora of conceptual and technical problems of Quantum Gravity (QG) does not indicate the futility of this quest per se or non-existence thereof. Rather, we face multiple incomplete approaches that have been developed, all reflecting some expected aspects of QG. The absence of a unique theory is especially evident in the renormalization approach to gravity, where coarse-grained effective physics cannot determine a single theory due to the infinite-dimensional critical surface. These difficulties call for a more constrained framework built on strong, selective principles. We propose Pure Shape Dynamics (PSD) as one such approach. Motivated by the idea that local physical data refer only to relations within material structures, PSD posits scale-invariant, purely relational configurations (shapes) as the sole physical degrees of freedom from which gravity and geometry emerge. This imposes non-trivial constraints on the formalism. The PSD formulation of dynamical geometry^1 shows how absolute scale and time can be removed to yield a fully relational description. Starting from the ADM formulation of GR, we derive a decoupled dynamical system governing the evolution of spatial conformal geometry and relational matter degrees of freedom, while eliminating the scale factor as an independent variable. Crucially, this autonomous system fully recovers the empirical content of GR and, remarkably, is derived purely algebraically without solving the non-linear Lichnerowicz-York and lapse-fixing differential equations. This demonstrates gravity as emergent from the dynamics of 3D spatial conformal geometry and, more importantly, suggests a suitable kinematics for a QG. The strategy is as follows. We posit a finite number of points, each equipped with Weyl spinors, within a conformal geometry. Relational reference structures arise from conformal geodesics – namely, generalized circles – requiring tangent and acceleration vectors, encoded in the spinor pairs at each vertex. The transport of this system with a conformally covariant connection reveals the conformal curvature, which can be explored analogously to the spatial curvature using the Ashtekar connection in LQG. Hence, a construction parallel to the kinematic Hilbert space of LQG is expected to ground the dynamical Hilbert space of Quantum PSD. Such a model with finite, yet arbitrarily large, degrees of freedom describes a regularized quantum gravity. To address the classical limit, under a suitable coarse-graining procedure, this model is expected to describe an effective dynamical system of conformal geometry – the very framework developed in PSD for classical gravity.
(1) P. Farokhi, T. Koslowski, P. Naranjo (2025): “Pure Shape Dynamics: Relational Dynamical Geometry”. arxiv:2503.00996
