A universal resolution limit

Scientific Essay from the year 2009 in the subject Physics - Theoretical Physics, Technical University of Berlin, language: English, abstract: Several approaches can be used to proof the assumption that an universal upper bound on the entropy to energy ratio (S/E) exists in bounded systems. In 1981 Jacob D. Bekenstein published his findings that S/E is limited by the "effective radius" of the system and mentioned various approaches to derive S/E employing quantum statistics or thermodynamics. It can be shown that similar results are obtained considering the energetic difference of longitudinal eigenmodes inside a closed cavity like it was done by Max Planck in 1900 to derive the correct formula for the spectral distribution of the black-body radiation. Considering an information theoretical approach this derivation suggests that the variance of an expectation value D is the same like a variance of the probability D

for measuring O : D = D

* . Implications of these findings are shortly discussed.