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.