  The Heisenberg position-momentum uncertainty principle shares with the
equivalence principle the role of main pillar of our current description of
nature. However, in its original formulation it is inconsistent with special
relativity, and in nearly a century of investigation not much progress has been
made toward a satisfactory reformulation. Some partial insight has been gained
in the ultra-high-velocity regime but a full description is still missing and
in particular we have no clue about the intermediate regime of particles whose
speeds are much smaller than the speed of light but still high enough for
tangible departures from the Heisenberg formulation to be present. As we stress
here, that intermediate regime is also our best chance for testing
experimentally our understanding of the implications of special relativity for
the uncertainty principle. We here introduce a new approach to these
challenges, based mainly on the observation that the only operative notion of
position of a particle at a given time involves the crossing of the worldline
of that particle with the worldline of a test particle. We find that the
worldline-crossing perspective opens a path toward a special-relativistic
version of the uncertainty principle, which indeed could be tested
experimentally.
