Modified commutators vs. Modified operators in a quantum gravity minimal length scale

Modified commutators vs. Modified operators in a quantum gravity minimal length scale

Ideas about quantum gravity often postulate that at some high energy/momentum scale there will be a fixed, minimal length. Such a minimal length can be phenomenologically investigated by modifying the usual Heisenberg Uncertainty Relation-ship, ΔxΔp≥ℏ2, which in turn means modifying the commutator between position and momentum operators, which in turn means means modifying these operators. We show that it is the modification of the position and momentum operators which is the key determining factor in the existence (or not) of a minimal length scale. By focusing on the primacy of the role of the operators we also show that one can avoid the implications from the observations of certain short gamma ray bursts which in certain cases seem to push a minimal length scale above the Planck scale.

conference paper