Minimal length estimation on the basis of studies of the Sun-Earth-Moon system in deformed space

Abstract

A space with deformed Poisson brackets for coordinates and momenta leading to the minimal length is considered. Features of description of motion of a body in the space are examined. We propose conditions on the parameters of deformation on which Poisson brackets for coordinates and momenta of the center-of-mass reproduce relations of deformed algebra, kinetic energy of a body is independent of its composition, and the weak equivalence principle is preserved in the deformed space. Influence of minimal length on the motion of the Sun-Earth-Moon system is studied. We find that deformation of the Poisson brackets leads to corrections to the accelerations of the Earth and the Moon toward the Sun, as a result the Eotvos-parameter does not vanish even if we consider equality of gravitational and inertial masses. The upper bound for the minimal length is estimated using results of the Lunar laser ranging experiment.

to appear in International Journal of Modern Physics D

References in corpus (6)

• Hydrogen-atom spectrum under a minimal-length hypothesis
• Lunar Laser Ranging Tests of the Equivalence Principle
• Composite system in noncommutative space and the equivalence principle
• Entropic Gravity, Phase-Space Noncommutativity and the Equivalence Principle
• Snyder dynamics in a Schwarzschild spacetime
• Macroscopic body in Snyder space and minimal length estimation