The upper bound of the amount of information inside a spherical region with a given energy. Information in this context is to be understood as distinguishable (quantum) states. Due to the uncertainty relations it is possible to derive a bound of the form
I <= (2 Pi E R)/(hbar c ln2)
where I is the information, E is the energy, R is the radius, hbar Plank's constant, c the speed of light. It can also be written as
I <= k M R
Where M the mass in the region and k a constant having the value ~2.57686*10^43 bits/(m kg). This bound was derived by J.D. Bekenstein in another but equivalent form, relating the entropy of black holes to their area (S = A/(4 hbar G), where A is the area of the event horizon).
Text by Anders Sandberg in his Transhumanist Terminology
Initially published on 08 October 2001.