***The limits of mathematical computability have been set solely by mathematical logic and reasoning until now. Taking the view that information is after all physical, however, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics in {\em intrinsic randomness} and {\em implied infinity}. We then outline a quantum mechanical "algorithm" for one of the insoluble problems of mathematics, the Hilbert's tenth and equivalently the Turing halting problem. The key element of this algorithm is the {\em computability} and {\em measurability} of both the values of physical observables and of the quantum-mechanical probability distributions for these values. The algorithm, as it stands, has its limit as it cannot solve non-computable problems of other classes different than that of Turing halting problem. But it provides an interesting and new perspective that computability, and with it the limits of Mathematics, ought to be determined not solely by
Mathematics itself but also by Physical Principles.***


This looks quite interesting, but it has to do with computers rather than reality. Unfortunately I cannot download the paper on the library computer.