Deformed Heisenberg algebra with minimal length and equivalence principle

Abstract

Studies in string theory and quantum gravity lead to the Generalized Uncertainty Principle (GUP) and suggest the existence of a fundamental minimal length which, as was established, can be obtained within the deformed Heisenberg algebra. The first look on the classical motion of bodies in a space with corresponding deformed Poisson brackets in a uniform gravitational field can give an impression that bodies of different mass fall in different ways and thus the equivalence principle is violated. Analyzing the kinetic energy of a composite body we find that the motion of its center of mass in the deformed space depends on some effective parameter of deformation. It gives a possibility to recover the equivalence principle in the space with deformed Poisson brackets. and thus GUP is reconciled with the equivalence principle. We also show that the independence of kinetic energy on composition leads to the recovering of the equivalence principle in the space with deformed Poisson brackets.

11 pages

References in corpus (13)

• Universality of Quantum Gravity Corrections
• The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field
• Hydrogen-atom spectrum under a minimal-length hypothesis
• Minimal Length Uncertainty Relation and gravitational quantum well
• Minimal Length in Quantum Gravity, Equivalence Principle and Holographic Entropy Bound
• Minimal Length and Bouncing Particle Spectrum
• The Casimir Effect in Minimal Length Theories based on a Generalized Uncertainity Principle
• Corrections to the ns-levels of hydrogen atom in deformed space with minimal length
• Dilaton Cosmology, Noncommutativity and Generalized Uncertainty Principle
• Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background
• Scattering problem in deformed space with minimal length
• Quantum gravity, minimum length and Keplerian orbits
• The quantum N-body problem with a minimal length

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