Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-03-17
Prog.Theor.Phys.102:169-179,1999
Physics
High Energy Physics
High Energy Physics - Theory
13 pages, Journal Version, PTPTeX
Scientific paper
10.1143/PTP.102.169
We propose an uncertainty relation of space-time. This relation is characterized by GhT \lesssim \delta V, where T and \delta V denote a characteristic time scale and a spatial volume, respectively. Using this uncertainty relation, we give qualitative estimations for the entropies of a black hole and our universe. We obtain qualitative agreements with the known results. The holographic principle of 't Hooft and Susskind is reproduced. We also discuss cosmology and give a relation to the cosmic holographic principle of Fischler and Susskind. However, as for the maximal entropy of a system with an energy E, we obtain the formula \sqrt{EV/Gh^2}, with V denoting the volume of the system, which is distinct from the Bekenstein entropy formula ER/h with R denoting the length scale of the system.
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