Theory and phenomenology of relativistic corrections to the Heisenberg principle

TL;DR

This paper explores relativistic corrections to the Heisenberg uncertainty principle, proposing a new approach based on worldline crossing that could lead to experimentally testable modifications in the intermediate velocity regime.

Contribution

It introduces a novel perspective on relativistic effects on the uncertainty principle using worldline crossing, addressing an intermediate velocity regime lacking prior analysis.

Findings

Proposes a new relativistic uncertainty principle framework.

Identifies the intermediate velocity regime as key for testing.

Suggests experimental avenues for validation.

Abstract

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.