Modeling observers as physical systems representing the world from within: Quantum theory as a physical and self-referential theory of inference

In 1929 Szilard pointed out that the physics of the observer may play a role in the analysis of experiments. The same year, Bohr pointed out that complementarity appears to arise naturally in psychology where both the objects of perception and the percieving subject belong to `our mental content'. Here we argue that the formalism of quantum theory can be understood from two related intuitive principles: (i) inference is a physical process performed by physical systems, observers, which are part of the experimental setup---this implies non-commutativity; (ii) experiments must be described from a first-person perspective---this leads to self-reference, complementarity, and a quantum dynamics that is the iterative construction of the observer's subjective state. We argue that Planck constant can be determined from available data on conscious-access experiments carried out within the framework championed by Nobel laureate Francis Crick. Finally, we discuss how this approach can be understood from information-theoretic principles.