Just to cause trouble, since we're straying far far from today's presentations (except arguably UCL's Z. Younsi in the ongoing ESO Q&A panel). :-) Can we write down the uncertainty principle in covariant form? Maybe! There is active theoretical work ongoing (e.g.) <https://arxiv.org/abs/2110.15951v2> ("... a geometric formalism for the generalised uncertainty principle which is covariant and connects features of the underlying geometry with the deformation of canonical commutator relations ... [and] an elegant interpretation for the standard dispersion relation p^2=−m^2: it describes flat spacetime in the Milne coordinates, with rest mass m giving the measure of geodesic length from origin").