A Subtle Aspect of Minimal Lengths in the Generalized Uncertainty Principle
Michael Bishop, Joey Contreras, Douglas Singleton
Abstract
In this work, we point out an overlooked and subtle feature of the generalized uncertainty principle (GUP) approach to quantizing gravity: namely that different pairs of modified operators with the same modified commutator, [X^,P^]=iħ(1+βp2), may have different physical consequences such as having no minimal length at all. These differences depend on how the position and/or momentum operators are modified rather than only on the resulting modified commutator. This provides guidance when constructing GUP models since it distinguishes those GUPs that have a minimal length scale, as suggested by some broad arguments about quantum gravity, versus GUPs without a minimal length scale.
Topics & Concepts
CommutatorUncertainty principlePhysicsLength scaleQuantum gravityTheoretical physicsMomentum (technical analysis)Scale (ratio)QuantumPoint (geometry)Position (finance)Work (physics)Classical mechanicsQuantum mechanicsGeometryMathematicsLie conformal algebraLie algebraEconomicsFinanceNoncommutative and Quantum Gravity TheoriesBlack Holes and Theoretical PhysicsCosmology and Gravitation Theories