  The problem of emergence in physical theories makes necessary to build a
general theory of the relationships between the observed system and the
observing system. It can be shown that there exists a correspondence between
classical systems and computational dynamics according to the Shannon-Turing
model. A classical system is an informational closed system with respect to the
observer; this characterizes the emergent processes in classical physics as
phenomenological emergence. In quantum systems, the analysis based on the
computation theory fails. It is here shown that a quantum system is an
informational open system with respect to the observer and able to exhibit
processes of observational, radical emergence. Finally, we take into
consideration the role of computation in describing the physical world.
