This is the upper limit of information that, with a given energy, a region can hold.

Make sense? Wait, there's more.

This information is due to different Quantum states. Because of uncertainty, one can develop a bound of the form for use with a sphere:

I <= (2 Pi E R)/(hbar c ln2)

I ==information
E ==energy
hbar ==Plank's constant
c ==, of course, the speed of light

Also be written as

I <= k M R

M == mass in the region
k == constant of ~2.57686*10^43 bits/(m kg)

This was developed by J.D. Bekenstein (aka Jacob Bekenstein, an Israeli physicist), having to do with entropy in a black hole related to their area.

Got it? Now, this is all well and good, but what does it mean? It means that all systems have a finite complexity. This is a natural consequence of Heisenbergâ€™s Uncertainty Principle. How this occurs is rather weird and I really don't understand it.

You can use this bound to determine how much memory you would need to store a person in, for example, a computer. (For reference, the avg. person would take up 10^45 bits, a lump of sugar: 10^20 bits.{I have since read that 10^45 would be enough to hold ALL humans. I'll try and clear this up soon.) This replication wouldn't be really good, it would be perfect. (For issues w/r/t this, see ontological free will and emulated quarks.)

The Bekenstein Bound has implications for our existence here as well - if, admittedly, distant ones. There is currently a great debate underway about whether the universe's expansion is accelerating, decelerating or remaining exactly constant. The three states corresponding to these outcomes are known as the Open universe, Closed universe and Flat universe models.

The Flat universe will continue to expand at a constant rate forever. If the density of the universe at 1 nanosecond after the Big Bang was precisely 447,225,917,218,507,401,284,016 gm/cc, then the universe has critical density. If so, then the expansion of the universe (decrease in the mass/cubic spatial unit) is offset perfectly by the gravity of that mass.

An Open universe has a negative curvature; if the density of the universe at 1ns age was a mere 1 gram/cc less than the value above, then (theory states) we should have already lost track of the more distant objects in the universe, as they should be receding from us at a relative speed greater than that of light, making the edges of our universe an event horizon of sorts through which no information returns. In an Open universe, the rate of expansion is increasing; why is debated.

Finally, a Closed universe (which has, say, a 1ns density of just 1 gram/cc more than the value above) has a density high enough that gravitation is greater than the energy represented by the expansion of the universe. In this case, the expansion is and has always been negatively accelerating; eventually it will hit stasis at a point of maximum expansion. At this point it will begin to contract until the Big Crunch occurs. This is a rough check on our knowledge of the 1-ns universe; If that density was 2 g/cc higher, not only would we definitely have a Closed universe but the math says that such a crunch should have already taken place.

What does this have to do with Bekenstein bounds? Look at it this way: our universe is a three-dimensional space plus time. Thus, our universe (according to the Bekenstein bound) can have a specific amount of information contained within it depending on its size. If the universe is closed, then we can compute the total four-dimensional volume of the universe as a finite number, since it will expand to a finite maximum before collapsing. In this case, as it shrinks, its maximum informational capacity will shrink with it, meaning that the number of available quantum states for everything contained within it (like, say, us) shrinks as well. Yuck. Talk about predestiny.

If it's flat, then the expansion of the universe will continue at a rate such that we will always be able to 'see' all of it from present (at our location) back through the past to the moment of creation (as we venture further out). In such a case, there will be an infinite number of potential quantum states (amount of information) due to expansion, and we will always be able to retrieve said information.

If it's open, then we have a whole new set of problems. In this case, the increasing speed of the expansion means that it is possible for information to be 'lost' as it travels towards the edge of the universe; the expanding edge means that it cannot reach the edge nor can it reach 'back inward' to us, due to Doppler limitations. In such a case, our world could be viewed as a lonely outpost, around which our scouts continuously are dispatched and fail to return. We will 'lose' information; eventually, the 'center' of this space (defined by the observer's position) will be completely devoid of information able to reach the observer as all information is rushed outwards by expansion ( I believe but am not sure that this state is the proper definition of de Sitter space nope, I'm wrong - TC).

At least, that's how I understand it. Heh. I'm not an astrophysicist, nor do I play one on TV.