An insightful argument for a linear relation between the entropy and the area of a black hole was given by Bekenstein using only the energymomentum dispersion relation, the uncertainty principle, and some properties of classical black holes. Recent analyses within String Theory and Loop Quantum Gravity describe blackhole entropy in terms of a dominant contribution, which indeed depends linearly on the area, and a leading logarea correction. We argue that, by reversing the Bekenstein argument, the logarea correction can provide insight on the energymomentum dispersion relation and the uncertainty principle of a quantumgravity theory. As examples we consider the energymomentum dispersion relations that recently emerged in the Loop Quantum Gravity literature and the Generalized Uncertainty Principle that is expected to hold in String Theory.
