The
Bekenstein Bound is an 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).
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