The main formal structures of generalized quantum theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role of proposition observables), and the concept of generalized entanglement. Furthermore, the active role of the observer in the structure of observables and the partitioning of systems is emphasized.

A violation of Bell’s inequalities is generally considered to be the Holy Grail of experimental proof that a specific natural phenomenon cannot be explained in a classical framework and is based on a non-boolean structure of predications. Generalized quantum theory allows for such non-boolean predications. We formulate temporal Bell’s inequalities for cognitive two-state systems and indicate how these inequalities can be tested. This will introduce the notion of temporally non-local measurements. The Necker-Zeno model for bistable perception predicts a violation of (...) these temporal Bell’s inequalities. (shrink)

Science is always presupposing some basic concepts that are held to be useful. These absolute presuppositions (Collingwood) are rarely debated and form the framework for what has been termed paradigm by Kuhn. Our currently accepted scientific model is predicated on a set of presuppositions that have difficulty accommodating holistic structures and relationships and are not geared towards incorporating non-local correlations. Since the theoretical models we hold also determine what we perceive and take as scientifically viable, it is important to look (...) for an alternative model that can deal with holistic relationships. One approach is to generalise algebraic quantum theory, which is an inherently holistic framework, into a generic model. Relaxing some restrictions and definitions from quantum theory proper yields an axiomatic framework that can be applied to any type of system. Most importantly, it keeps the core of the quantum theoretical formalism. It is capable of handling complementary observables, i.e. descriptors which are non-commuting, incompatible and yet collectively required to fully describe certain situations. It also predicts a generalised form of non-local correlations that in quantum theory are known as entanglement. This generalised version is not quantum entanglement but an analogue form of holistic, non-local connectedness of elements within systems, predicted to occur whenever elements within systems are described by observables which are complementary to the description of the whole system. While a considerable body of circumstantial evidence supports the plausibility of the model, we are not yet in a position to use it for clear cut predictions that could be experimentally falsified. The series of papers offered in this special issue are the beginning of what we hope will become a rich scientific debate. (shrink)