Is there constructed some set of physical laws from which we can logically obtain that any function that can be implemented in some device is Turing computable?


EDIT


I believe that if we restrict ourselves to classical mechanics (I mean if we suppose that any device obey just classical mechanics laws) then CT thesis can be proved.



Physics and Church–Turing Thesis
Just appeared on the arXiv today:
"The physical Church-Turing thesis and the principles of quantum theory,"
by Pablo Arrighi and Gilles Dowek.
<http://arxiv.org/abs/1102.1612>


**Abstract:**



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> Notoriously, quantum computation shatters complexity theory, but is innocuous to computability theory. Yet several works have shown how quantum theory as it stands could breach the physical Church-Turing thesis. We draw a clear line as to when this is the case, in a way that is inspired by Gandy. Gandy formulates postulates about physics, such as homogeneity of space and time, bounded density and velocity of information --- and proves that the physical Church-Turing thesis is a consequence of these postulates. We provide a quantum version of the theorem. Thus this approach exhibits a formal non-trivial interplay between theoretical physics symmetries and computability assumptions. 
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