Modified commutators are not sufficient to determine a quantum gravity minimal length scale
Michael Bishop, Jae-Yeong Lee, Douglas Singleton
Abstract
In quantum gravity it is generally thought that a modified commutator of the form [xˆ,pˆ]=iħ(1+βp2) is sufficient to give rise to a minimum length scale. We test this assumption and find that different pairs of modified operators can lead to the same modified commutator and yet give different or even no minimal length. The conclusion is that the modification of the operators is the main factor in determining whether there is a minimal length. This fact - that it is the specific form of the modified operators which determine the existence or not of a minimal length scale - can be used to keep or reject specific modifications of the position and momentum operators in theory of quantum gravity.
Topics & Concepts
CommutatorQuantum gravityMomentum (technical analysis)Scale (ratio)Length scalePosition (finance)QuantumMathematicsPhysicsTheoretical physicsMathematical physicsPure mathematicsQuantum mechanicsAlgebra over a fieldLie conformal algebraFinanceEconomicsNoncommutative and Quantum Gravity TheoriesBlack Holes and Theoretical PhysicsNeuroblastoma Research and Treatments