I understand that Turing completeness requires unbounded memory and unbounded time.
However there is a finite amount of atoms in this service thus making memory bounded. For example even though $\pi$ is irrational there is no way to store more than a certain number of digits even if all the atoms in the universe were used for this purpose.
What then are the limits of computability of an implemented Turing machine (which could use all the resources of the universe but no more) based on the limits of the universe? What is the maximum number of digits of $\pi$? Are there any papers on this subject that might be interesting to read?