There are actually physical laws somewhere in thermodynamics that place an upper bound on the existence of information within a space. Oddly enough, the maximum information in a space is proportional to the surface area, not the volume[1]. Black holes attain this maximum, although I'm not sure if non-black-holes are capable of attaining it as well.
In a related note, Bell's Theorem (along with a few experimental results) demonstrate that no theory of (local) hidden variables can account for quantum theory[2]. This means that the limit is not just on our ability to measure the information in an atom. It literally doesn't exist for us to measure. Quantum mechanics is confusing =P.
[1] Specifically, the information measured in binary bits is bounded by the surface area divided by four. I'm not 100% sure what the unit of surface area is, but I believe it's Plank units.
In a related note, Bell's Theorem (along with a few experimental results) demonstrate that no theory of (local) hidden variables can account for quantum theory[2]. This means that the limit is not just on our ability to measure the information in an atom. It literally doesn't exist for us to measure. Quantum mechanics is confusing =P.
[1] Specifically, the information measured in binary bits is bounded by the surface area divided by four. I'm not 100% sure what the unit of surface area is, but I believe it's Plank units.
[2] http://en.wikipedia.org/wiki/Bells_Theorem