Inference concerning physical systems

Abstract

The question of whether the universe "is" just an information-processing system has been extensively studied in physics. To address this issue, the canonical forms of information processing in physical systems-observation, prediction, control and memory-were analyzed in [24]. Those forms of information processing are all inherently epistemological; they transfer information concerning the universe as a whole into a scientist's mind. Accordingly, [24] formalized the logical relationship that must hold between the state of a scientist's mind and the state of the universe containing the scientist whenever one of those processes is successful. This formalization has close analogs in the analysis of Turing machines. In particular, it can be used to define an "informational analog" of algorithmic information complexity. In addition, this formalization allows us to establish existence and impossibility results concerning observation, prediction, control and memory. The impossibility results establish that Laplace was wrong to claim that even in a classical, non-chaotic universe the future can be unerringly predicted, given sufficient knowledge of the present. Alternatively, the impossibility results can be viewed as a non-quantum mechanical "uncertainty principle". Here I present a novel motivation of the formalization introduced in [24] and extend some of the associated impossibility results. © 2010 Springer-Verlag Berlin Heidelberg.