Speaker
Description
We propose a kinematical framework in which spacetime geometry is encoded directly in the Heisenberg commutators: the metric becomes an operator extracted from $[\,\hat x^\mu,\hat P_\nu\,]$, and the non-commutativity of translation generators follows from Jacobi closure. The construction naturally yields an operator analogue of metric compatibility and reproduces the familiar torsion/curvature structure once Lorentz generators are included. A worked Friedmann--Robertson--Walker example gives $[\,\hat P_0,\hat P_i\,]\propto H(t)\hat P_i$, making cosmic expansion an explicit source of non-commuting ``translations.'' Time is treated as an observable through a conservative POVM implementation, or as a self-adjoint operator on an enlarged Hilbert space organized by an antiunitary gravitational-conjugation symmetry. We highlight physical interpretations, limiting regimes, and several near-term avenues toward dynamics and phenomenology.