Quantum-gravity-slingshot: orbital precession due to the modified uncertainty principle, from analogs to tests of Planckian physics with quantum fluids

TL;DR

This paper proposes using quantum fluids as experimental analogs to test the effects of the modified uncertainty principle at the Planck scale, demonstrating orbital precession effects similar to general relativity.

Contribution

It introduces a novel approach to emulate quantum gravity effects in laboratory settings using quantum fluids and analyzes the resulting orbital precession due to the modified uncertainty principle.

Findings

Quantum fluids can simulate Planck-scale quantum gravity effects.

Orbital precession analogous to Mercury's perihelion is observed.

Simulations validate the predicted quantum gravity-induced orbital dynamics.

Abstract

Modified uncertainty principle and non-commutative variables may phenomenologically account for quantum gravity effects, independently of the considered theory of quantum gravity. We show that quantum fluids enable experimental analogs and direct tests of the modified uncertainty principle expected to be valid at the Planck scale. We consider a quantum clock realized by a long-lasting quantum fluid wave-packet orbiting in a trapping potential. We investigate the hydrodynamics of the Schr\"odinger equation encompassing kinetic terms due to Planck-scale effects. We study the resulting generalized mechanics and validate the predictions by quantum simulations. Wave-packet orbiting generates a continuous amplification of the quantum gravity effects. The non-commutative variables in the phase-space produce a precession and an acceleration of the orbital motion. The precession of the orbit is strongly resembling the famous orbital precession of the perihelion of Mercury used by Einstein to validate the corrections of general relativity to Newton's theory. In our case, the corrections are due to the modified uncertainty principle. The results can be employed to emulate quantum gravity in the laboratory, or to realize human-scale experiments to determine bounds for the most studied quantum-gravity models and probe Planckian physics.