  It is commonly accepted that the combination of quantum mechanics and general
relativity gives rise to the emergence of a minimum uncertainty both in space
and time. The arguments that support this conclusion are mainly based on
perturbative approaches to the quantization, in which the gravitational
interactions of the matter content are described as corrections to a classical
background. In a recent paper, we analyzed the existence of a minimum time
uncertainty in the framework of doubly special relativity. In this framework,
the standard definition of the energy-momentum of particles is modified
appealing to possible quantum gravitational effects, which are not necessarily
perturbative. Demanding that this modification be completed into a canonical
transformation determines the implementation of doubly special relativity in
position space and leads to spacetime coordinates that depend on the
energy-momentum of the particle. In the present work, we extend our analysis to
the quantum length uncertainty. We show that, in generic cases, there actually
exists a limit in the spatial resolution, both when the quantum evolution is
described in terms of the auxiliary time corresponding to the Minkowski
background or in terms of the physical time. These two kinds of evolutions can
be understood as corresponding to perturbative and non-perturbative
descriptions, respectively. This result contrasts with that found for the time
uncertainty, which can be made to vanish in all models with unbounded physical
energy if one adheres to a non-perturbative quantization.
