A revision of the Generalized Uncertainty Principle

Abstract

The Generalized Uncertainty Principle arises from the Heisenberg Uncertainty Principle when gravity is taken into account, so the leading order correction to the standard formula is expected to be proportional to the gravitational constant $G_N=L_{Pl}^2$. On the other hand, the emerging picture suggests a set of departures from the standard theory which demand a revision of all the arguments used to deduce heuristically the new rule. In particular, one can now argue that the leading order correction to the Heisenberg Uncertainty Principle is proportional to the first power of the Planck length $L_{Pl}$. If so, the departures from ordinary quantum mechanics would be much less suppressed than what is commonly thought.

6 pages, 1 figure

References in corpus (21)

• The Cosmological Parameters 2006
• Big-Bang nucleosynthesis (Particle Data Group mini-review)
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Lorentz invariance with an invariant energy scale
• A Generalized Uncertainty Principle in Quantum Gravity
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• The Generalized Uncertainty Principle and Black Hole Remnants
• Testable scenario for Relativity with minimum-length
• Generalized Lorentz invariance with an invariant energy scale
• On Gravity and the Uncertainty Principle
• Minimal Length Uncertainty Relation and Hydrogen Atom
• The Effect of the Minimal Length Uncertainty Relation on the Density of States and the Cosmological Constant Problem
• Signatures in the Planck Regime
• Black-hole thermodynamics with modified dispersion relations and generalized uncertainty principles
• The Generalized Uncertainty Principle in (A)dS Space and the Modification of Hawking Temperature from the Minimal Length
• Natural extension of the Generalised Uncertainty Principle
• Some Consequences of the Generalised Uncertainty Principle: Statistical Mechanical, Cosmological, and Varying Speed of Light
• Self-consistency in Theories with a Minimal Length
• String Balls at the LHC and Beyond
• Thermodynamics of a black hole based on a generalized uncertainty principle
• Generalized Uncertainty Principle, Modified Dispersion Relations and Early Universe Thermodynamics

Cited by in corpus (18)

• Generalized Uncertainty Principle: Approaches and Applications
• Black hole thermodynamics with generalized uncertainty principle
• Effects of quantum gravity on the inflationary parameters and thermodynamics of the early universe
• Comparing two approaches to Hawking radiation of Schwarzschild-de Sitter black holes
• Lorentz Invariance Violation and Generalized Uncertainty Principle
• Entropy bound of local quantum field theory with generalized uncertainty principle
• Gravitational Effects in Quantum Mechanics
• Black hole thermodynamics and modified GUP consistent with doubly special relativity
• Modified Newton's Law of Gravitation Due to Minimal Length in Quantum Gravity
• Entropy In The Present And Early Universe: New Small Parameters And Dark Energy Problem
• On entropic uncertainty relations in the presence of a minimal length
• Effects of the Generalized Uncertainty Principle on the Inflation Parameters
• Modified clock inequalities and modified black hole lifetime
• Dangerous implications of a minimum length in quantum gravity
• Quantum Theory at Planck Scale, Limiting Values, Deformed Gravity and Dark Energy Problem
• Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics
• Entropic uncertainty relations for successive measurements in the presence of a minimal length
• Generalized Uncertainty Principle, Modified Dispersion Relation and Barrier penetration by a Dirac particle