Bekenstein and the Holographic Principle: Upper bounds for Entropy

摘要: Using the Bekenstein upper bound for ratio of entropy $S$ any bounded system, with energy $E = Mc^2$ and effective size $R$, to its $E$ i.e. $S/E < 2\pi k R/\hbar c$, we combine it holographic principle (HP) ('t Hooft Susskind) which is $S \le \pi c^3R^2/\hbar G$. We find that, if both bounds are identical, such system a black hole (BH). For that not BH two different. The must obey lowest bound. If proportional, result proportionality between mass M $R$. When constant $2G/c^2$ in question BH, identical. analyze case universe. Then universe sense $M$ Hubble $R \approx ct$, t age universe, follow Schwarzschild relation $2GM/c^2 R$. Finally, Hawking Unruh temperatures same. Applying this they define quantum $\sim 10^{-66} g$ our