The more things change the more they stay the same: Minimum lengths with unmodified uncertainty principle and dispersion relation
Abstract
Broad arguments indicate that quantum gravity should have a minimal length scale. In this essay we construct a minimum length model by generalizing the time-position and energy-momentum operators while keeping much of the structure of quantum mechanics and relativity intact: the standard position-momentum commutator, the special relativistic time-position, and energy-momentum relationships all remain the same. Since the time-position and energy-momentum relationships for the modified operators remains the same, we retain a form of Lorentz symmetry. This avoids the constraints on these theories coming from lack of photon dispersion while holding the potential to address the Greisen-Zatsepin-Kuzmin (GZK) puzzle of ultra high energy cosmic rays.
Keywords
Cite
@article{arxiv.2205.06624,
title = {The more things change the more they stay the same: Minimum lengths with unmodified uncertainty principle and dispersion relation},
author = {Michael Bishop and Joey Contreras and Douglas Singleton},
journal= {arXiv preprint arXiv:2205.06624},
year = {2022}
}
Comments
10 pages, 2 figures, revtex4. 2nd place award for the 2022 Gravity Research Foundation essay competition. To be published IJMPD