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

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

In: 1 A bit could be encoded on something like the spin of an atomic particle…particles which could be near pin-points in space. So no, I would not say there is a physical limitation (ie you need at least x amount of space to encode a bit). However once you’re getting down at the atomic level now you also have to deal with weird quantum effects such as the bit randomly changing or measuring the bit causing it to change… A bit is a mathematical concept, which can be represented by anything that can have two states. In theory, a bit can be represented by a single atom or even an electron. In quantum computing a qubit can be represented by the spin of an electron or the polarization of a photon. I don’t believe that “size of a photon” means anything, much less “size of the polarization of a photon”. If we can write to it, and read from it, and it can be in at least 2 states, it can be thought of as a bit. If we can consistently and reliable represent it in more states we can use it to represent multiple bits.

With current technology we can reliably (though not easily or cheaply) manipulate things on the atomic scale in such a way that we could read and write data that way. Getting below the atomic scale might be tough as you start to run into quantum effects, but in theory if we could set and read the states of quarks and leptons that would be even tinier storage. 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).