Harald Atmanspacher

Complementarity in Classical Dynamical Systems

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an ad hoc partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.

Epistemic and Ontic Quantum Realities

Quantum theory has provoked intense discussions about its interpretation since its pioneer days. One of the few scientists who have been continuously engaged in this development from both physical and philosophical perspectives is Carl Friedrich von Weizsaecker. The questions he posed were and are inspiring for many, including the authors of this contribution. Weizsaecker developed Bohrs view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einsteins ontically oriented position.

Extending the Philosophical Significance of the Idea of Complementarity

We discuss a specific way in which the notion of complementarity can be based on the dynamics of the system considered. This approach rests on an epistemic representation of system states, reflecting our knowledge about a system in terms of coarse grainings (partitions) of its phase space. Within such an epistemic quantization of classical systems, compatible, comparable, commensurable, and complementary descriptions can be precisely characterized and distinguished from each other. Some tentative examples are indicated that, we suppose, would have been of interest to Pauli.

Positive-Operator-Valued Measures and Projection-Valued Measures of Noncommutative Time Operators

Some relationships between two differentconcepts of noncommutative time operators are discussed.One is the concept of a Hermitian, but not self-adjointtime operator TB based on apositive-operator-valued measure for a dynamical observable B. The otheris the concept of a self-adjoint time operatorTL obtained in the Liouville representation,a special case of the standard representation of quantumtheory. Conditions are indicated under which aself-adjoint extension of TB leading toTL can be constructed. Similarities with thenotions of consistent and inconsistent histories areindicated. Conceptual issues as to the interpretation of the different timeoperators are outlined with particular emphasis on thenotion of temporal nonlocality.

Stability criteria for the contextual emergence of macrostates in neural networks

More than thirty years ago, Amari and colleagues proposed a statistical framework for identifying structurally stable macrostates of neural networks from observations of their microstates. We compare their stochastic stability criterion with a deterministic stability criterion based on the ergodic theory of dynamical systems, recently proposed for the scheme of contextual emergence and applied to particular inter-level relations in neuroscience. Stochastic and deterministic stability criteria for macrostates rely on macro-level contexts, which make them sensitive to differences between different macro-levels.

Can classical epistemic states be entangled

Entanglement is a well-known and central concept in quantum theory, where it expresses a fundamental nonlocality (holism) of ontic quantum states, regarded as independent of epistemic means of gathering knowledge about them. An alternative, epistemic kind of entanglement is proposed for epistemic states (distributions) of dynamical systems represented in classical phase spaces. We conjecture that epistemic entanglement is to be expected if the states are based on improper phase space partitions. The construction of proper partitions crucially depends on the system dynamics. n nAlthough improper partitions have a number of undesirable consequences for the characterization of dynamical systems, they offer the potential to understand some interesting features such as incompatible descriptions, which are typical for complex systems. Epistemic entanglement due to improper partitions may give rise to epistemic classical states analogous to quantum superposition states. In mental systems, interesting candidates for such states have been coined acategorial states, and among their key features are temporally nonlocal correlations. These correlations can be related to the situation of epistemic entanglement.

From the Dynamics of Coupled Map Lattices to the Psychological Arrow of Time

Stable neuronal assemblies are generally regarded as neural correlates of mental representations. Their temporal sequence corresponds to the experience of a direction of time, sometimes called the psychological time arrow. We show that the stability of particular, biophysically motivated models of neuronal assemblies, called coupled map lattices, is supported by causal interactions among neurons and obstructed by non‐causal or anti‐causal interactions among neurons. This surprising relation between causality and stability suggests that those neuronal assemblies that are stable due to causal neuronal interactions, and thus correlated with mental representations, generate a psychological time arrow. Yet this impact of causal interactions among neurons on the directed sequence of mental representations does not rule out the possibility of mentally less efficacious non‐causal or anti‐causal interactions among neurons.