Theory and phenomenology of relativistic corrections to the Heisenberg principle

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. Arguably the equivalence principle and Heisenberg’s uncertainty principle are the two most important aspects of our current description of nature, since they are the pri-mary principles on which general relativity and quantum mechanics are built. Any progress in reaching a deeper understanding of the equivalence principle and of the uncertainty principle investigating the conceptual incompatibility between general relativity We residual uncertainty is still small but special-relativistic corrections could be appreciated, which is also the regime best suited for testing experimentally our understanding of the interplay between special relativity and the uncertainty principle.