We explore a possible connection between two aspects of loop quantum gravity which have been extensively studied in the recent literature: the blackhole areaentropy law and the energymomentum dispersion relation. We observe that the original Bekenstein argument for the areaentropy law implicitly requires information on the energymomentum dispersion relation and on the positionmomentum uncertainty relation. Recent results show that in first approximation blackhole entropy in loop quantum gravity depends linearly on the area, with small correction terms which have logarithmic or inversepower dependence on the area. And it has been argued that in loop quantum gravity the dispersion relation should include terms that depend linearly on the Planck length, while no evidence of modification of the positionmomentum uncertainty relation has been found. We observe that this scenario with Plancklengthlinear modification of the dispersion relation and unmodified positionmomentum uncertainty relation is incompatible with the blackholeentropy results, since it would give rise to a term in the entropy formula going like the square root of the area.
