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- W76259799 abstract "Using the Bekenstein upper bound for the ratio of the entropy $S$ of any bounded system, with energy $E = Mc^2$ and effective size $R$, to its energy $E$ i.e. $S/E < 2pi k R/hbar c$, we combine it with the holographic principle (HP) bound ('t Hooft and Susskind) which is $S le pi k c^3R^2/hbar G$. We find that, if both bounds are identical, such bounded system is a black hole (BH). For a system that is not a BH the two upper bounds are different. The entropy of the system must obey the lowest bound. If the bounds are proportional, the result is the proportionality between the mass M of the system and its effective size $R$. When the constant of proportionality is $2G/c^2$ the system in question is a BH, and the two bounds are identical. We analyze the case for a universe. Then the universe is a BH in the sense that its mass $M$ and its Hubble size $R approx ct$, t the age of the universe, follow the Schwarzschild relation $2GM/c^2 = R$. Finally, for a BH, the Hawking and Unruh temperatures are the same. Applying this to a universe they define the quantum of mass $sim 10^{-66} g$ for our universe." @default.
- W76259799 created "2016-06-24" @default.
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- W76259799 date "2012-12-06" @default.
- W76259799 modified "2023-10-15" @default.
- W76259799 title "Bekenstein and the Holographic Principle: Upper bounds for Entropy" @default.
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