# 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? – Anders Sandberg Jun 21 '18 at 15:16
• The former, what is the limit for the Bekenstein Bound – C. Jordan Jun 21 '18 at 16:01

## 2 Answers

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? – C. Jordan 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. – Anders Sandberg 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? – C. Jordan 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?) – C. Jordan Jun 22 '18 at 17:22
• Also what would the “I <“ be in a calculator? – C. Jordan 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?