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.

arXiv comment10 pages, 2 figures, revtex4. 2nd place award for the 2022 Gravity Research Foundation essay competition. To be published IJMPD

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Cited by in corpus (5)

• The minimal length is physical
• Minimal length scale correction in the noise of gravitons
• Lorentz-covariant sampling theory for fields
• GUP, Lorentz Invariance (Non)-Violation, and Non-Commutative Geometry
• A novel mechanism for probing the Planck scale with wavepackets following general distributions