Contextual quantum process theory

Andrei Yu. Khrennikov

David Finkelstein

Barbara Drossel

Abstract Even though physicists often claim that their theories can, in principle, be reduced to the supposedly most fundamental theory, which is quantum physics, a look at how physics is practiced reveals that this reduction is almost never performed. Instead, effective models are built that include various types of contextual information and that are often incompatible with the supposedly fundamental theory. The phenomena described by these models can be characterized as contextually emergent. This chapter illustrates contextual emergence by means of examples from different fields of physics. In quantum physics, explanations of the measurement process require the assumption of a classical context that specifies the observable being measured and that induces the measurement event. In condensed matter theory, we find many types of quasiparticles that can only exist due to the solid that embeds them and the structure of which determines the properties of the quasiparticles. In thermodynamics, state variables such as the pressure and temperature of a system are given by its environment, and its phase transitions are triggered by changes in the environment. In the early universe, the degrees of freedom and the density and temperature determine the types of particles that are found in the universe. Later, the overall properties of the universe determine whether matter can condense to form stars. From all this it follows that processes and descriptions at different scales are equally important in physics. There are even contextual influences from outside physics. The chapter will thus conclude that physics is not causally closed.

Andrei Yu. Khrennikov

Quantum measurement theory is applied to quantum-like modeling of coherent generation of perceptions and emotions and generally for emotional coloring of conscious experiences. In quantum theory, a system should be separated from an observer. The brain performs self-measurements. To model them, we split the brain into two subsystems, unconsciousness and consciousness. They correspond to a system and an observer. The states of perceptions and emotions are described through the tensor product decomposition of the unconscious state space; similarly, there are two classes of observables, for conscious experiencing of perceptions and emotions, respectively. Emotional coloring is coupled to quantum contextuality: emotional observables determine contexts. Such contextualization reduces degeneration of unconscious states. The quantum-like approach should be distinguished from consideration of the genuine quantum physical processes in the brain (cf. Penrose and Hameroff). In our approach the brain is a macroscopic system which information processing can be described by the formalism of quantum theory. The paper is concluded with experimental test of contextual emotional coloring of conscious experiences based on Bell type inequalities which are treated in the contextual framework.

Rodrigo Iglesias, Fernando Tohmé, Marcelo Auday

An empirical model is a generalization of a probability space. It consists of a simplicial complex of subsets of a class 𝒳 of random variables such that each simplex has an associated probability distribution. The ensuing marginalizations are coherent, in the sense that the distribution on a face of a simplex coincides with the marginal of the distribution over the entire simplex. An empirical model is called contextual if its distributions cannot be obtained by marginalizing a joint distribution over 𝒳. Contextual empirical models arise naturally in quantum theory, giving rise to some of its counter -intuitive statistical consequences. In this paper, we present a different and classical source of contextual empirical models: the interaction among many stochastic processes. We attach an empirical model to the ensuing network in which each node represents an open stochastic process with input and output random variables. The statistical behaviour of the network in the long run makes the empirical model generically contextual and even strongly contextual.