Is there a fundamental physical limitation to the amount of space needed to contain a single bit?

Question

Is there a fundamental physical limitation to the amount of space needed to contain a single bit?

In: 1

Answer 1

This is a bit ill-stated as a single bit can be stored in effectively zero space. Except that having zero space is not even a meaningful thing, you cannot just cut away the universe. A better question to ask is thus: how much information can be stored in a given volume of space?

Maybe unexpectedly, it turns out that the limit is the point where (information) density becomes so high, the volume turns into a black hole (which ironically seals all that information away forever). And counter-intuitively, this means that the maximal amount of information in a sphere is proportional to its _surface_, not the volume!

Lets finally quantify things a bit: a cubic centimeter of spherical volume can theoretically store about 10^^66 bits of data. [Some stackexchange discussion with all the gory details](https://physics.stackexchange.com/questions/2281/maximum-theoretical-data-density).