# Bekenstein Bound

This info is from Wikipedia

In physics, the Bekenstein bound is an upper limit on the entropy S, or information I, that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximum amount of information required to perfectly describe a given physical system down to the quantum level.

Upon exceeding the Bekenstein bound a storage medium would collapse into a black hole.This finds parallels with the concept of a kugelblitz, a concentration of light or radiation so intense that its energy forms an event horizon and becomes self-trapped: according to general relativity and the equivalence of mass and energy.

My question is is there a known quantity of info or anything that is the limit of Bekenstein Bound or needed to overcome it?

• Is the question what the limit is (in terms of bits per meter per kilogram), or whether there are limits to the limit? Jun 21 '18 at 15:16
• The former, what is the limit for the Bekenstein Bound Jun 21 '18 at 16:01

The Bekenstein bound states that the maximum number of bits that can be stored inside a sphere of radius $R$ with total energy $E$ is $$I\leq \frac{2\pi}{\hbar c \ln(2)}RE = 2.8672\cdot10^{26} \, \mathrm{bits/J~m}$$ or, when expressed for mass, $$I\leq \frac{2\pi c }{\hbar \ln(2)}RM = 2.5769\cdot10^{43} \, \mathrm{bits/kg~ m}.$$

This bound is valid if self-gravity isn't too extreme and the spacetime is not curved so much that $R$ or $E$ becomes hard to define.

• Interesting, Thanks, so I would know what to do to find answers, Just to ask though, How would I type this equation into calculators like Google Calc? like, how to turn some of those symbols into numbers? Jun 21 '18 at 23:43
• You just multiply the constants above with the energy or mass (depending on which equation you use) and the radius. Jun 22 '18 at 7:34
• ok, thanks, one last question, what if I want to find out the energy/mass? Do I just do the same equation again but divide it by the number of bits/J/kg/m? Jun 22 '18 at 17:21
• Also I meant like what is the number for that (h) reduced Planck constant and what unit would be used for th speed of light? (Meters per second?) Jun 22 '18 at 17:22
• Also what would the “I <“ be in a calculator? Jun 22 '18 at 21:39

I am trying to put the formula for the Bekenstein Bound for energy into the calculator, and this is how I did it. I am trying to solve for energy.

((2*pi)/1.054571800(13)e−34*299792458*log(2))*1737400/2.8672e+26

• 1.054571800(13)e−34 = h-bar
• 299792458 = m/s speed of light
• 1737400 = meters radius of the moon
• log(2) = ln(2)

That is what I did, can someone verify If that is the correct way of doing it?