  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. $S/E < 2\pi k R/\hbar c$, 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.

General Physics