H Atmanspacher
Contextual emergence in physics and cognitive neuroscience

The concept of contextual emergence has been proposed as a non-reductive, yet well-defined relation between different levels of description of physical and other systems. It is illustrated for the transition from statistical mechanics to thermodynamical properties such as temperature. Stability conditions are shown to be crucial for a rigorous implementation of contingent contexts that are required to understand temperature as an emergent property.

Are such stability conditions meaningful for contextual emergence beyond Physics as well? An affirmative example from cognitive neuroscience addresses the relation between neurobiological and mental levels of description. For a particular class of partitions of the underlying neurobiological phase space, so-called generating partitions, the emergent mental states are stable under the dynamics. In this case, mental descriptions are (i) faithful representations of the neurodynamics and (ii) compatible with one another.

Quantum approaches to consciousness

It is widely accepted that consciousness or, more generally, mental activity is in some way correlated to the behavior of the material brain. Since quantum theory is the most fundamental theory of matter that is currently available, it is a legitimate question to ask whether quantum theory can help us to understand consciousness. Several approaches answering this question affirmatively, proposed in recent decades, will be surveyed. It will be pointed out that they make different epistemological assumptions, refer to different neurophysiological levels of description, and use quantum theory in different ways. For each of the approaches discussed, problematic and promising features will be equally highlighted.

E Binz
A Basic Non-Commutative Structure: Heisenberg Algebras in Minkowski Space, Signal Analysis Optics, Quantization and Field Quantization.

An oriented Minkowski space carries the structure of a skew field of quaternions and vice versa. The quaternions, a Clifford algebra, naturally decompose into a family of three-dimensional Heisenberg algebras and Heisenberg groups causing in particular the Hopf fibration. These algebras, vice versa, determine the quaternions uniquely. The Schrödinger representation of the Heisenberg group generates the Wigner- and the ambiguity function both playing a major role in signal analysis. Either one determines Fresnel optics. On the other hand Fresnel-optics is also caused by intertwiners of the Schrödinger representation. The infinitesimal version of this pictures yields the quantization of quadratic polynomials. A deformation quantization of fields is obtained by an infinite dimensional analogon of the simply connected Heisenberg group converted into a C*- algebra.

B Coecke
Shaping classical behaviors.

What are classical processes as opposed to quantum processes, and what is their structure? We analyse this question in terms of *resource-sensitive information-flow*. Given a basic framework with composition of systems and operations, which we conceive as the background *quantum* structure, we extract classical structures by imposing different kinds of constraints on the way states can be processed. Mathematically, for any symmetric monoidal category we extract classical stochastic theory, convex shapes, informatic majorization ordering, and deterministic functional and non-deterministic relational behaviours. All this gives a novel and profoundly qualitative view on the classical limit question. All the above still fits within the purely graphical calculus I have presented at several occasions. If time permits I would also like to discuss how mutually unbiased quantum observables such as position and momentum which make up a *true* quantum structure look within this graphical language.

T Filk
Quantum mechanics in a relational space

In recent years, the pressing need to unify our theory of space-time with the fundamental concepts of quantum theory led to a revival of models of “relational space” or “relational space-time” in the sense of Descartes and Leibniz. I will argue that many weird aspects in the formalism of quantum mechanics, including the “particle-wave duality”, the “sum over histories”, the double slit experiment, and, in a natural extension of the model, the quantum non-locality as expressed in EPR-type experiments, find a much more natural explanation when the position of particles is interpreted in terms of a relational picture.

M de Gosson
Remarks on the fact that the uncertainty principle does not determine the quantum state

Abstract. We discuss the relation between density matrices and the uncertainty principle from the point of view of Hardy’s theorem on the concentration a function and its Fourier transform. This allows us to justify and expalin some recent statements by Man’ko, Marmo, Sudarshan, and Zaccaria. In addition we discuss our results in terms of the “symplectic camel”, which allows a symplectic and coordinate free formulation of the Robertson-Schrödinger uncertainty principle. Part of this talk is joint work with F. Luef (Vienna).

B Hiley
Four roads to Bohm’s quantum reality.

Einstein’s reaction to Bohm’s original proposals concerning his ‘causal’ interpretation of quantum mechanics was that “he got it too cheap”. This essentially reflects the simplicity of the approach. No great new principles, just a simple polar decomposition of the wave function and splitting of the Schrödinger equation into its real and imaginary parts. Out pops a quantum Hamilton-Jacobi (QHJ) equation, essentially a conservation of probability equation, together with a conservation of probability equation. The QHJ looks like the classical HJ equation but introduces a new quality of energy, the quantum potential energy. Is this introduced ad hoc as Heisenberg claimed? No! There are no additions: it simply emerges from the formalism. Is it just fortuitous? I have examined three other approaches to QM and they produce exactly the same structure. They all produce the same two equations, including a quantum potential. I will examine and compare these three approaches. They are the Wigner-Moyal approach, the generalised Heisenberg approach and the approach through the Clifford algebra, using essentially quaternions. They link with the work of Ernst Binz and Maurice de Gosson. I am left with a puzzle, namely although they look very different, are they really different or is there a deeper link between them?”

F van Oystaeyen

Two presentations:-

1. Quantization of relations and process evaluation

2. A really noncommutative manifold

No abstracts sent.

T Palmer
A Novel Perspective on the Free Will Theorem: The Invariant Set Hypothesis.

If experimenters have free will, then, by Conway and Kochen’s recent theorem, so do elementary particles. If experimenters don’t have free will, then, by Bell’s analysis, the evolution of the world seems incomprehensibly conspiratorial. In an attempt to resolve this dilemma, a “third way” is presented here: that states of the world lie on the fractionally-dimensioned invariant set of some underlying deterministic chaotic dynamics. It will be explained how the non-computable measure-zero properties of such an invariant set, lead to a novel non-spooky interpretation of the Bell and Conway-Kochen theorems. Going further, entanglement is described as a reduction in the dimension of the world-system’s invariant set under sub-system synchronisation. Using this, implications of the Invariant Set Hypothesis are linked to some of Penrose’s speculations about the non-computability of the laws of physics and the role of gravity during measurement.

P Pylkkanen
The implicate order and consciousness

David Bohm proposed the notion of implicate order initially as a way of characterizing physical phenomena and later extended it to biological and psychological phenomena. In this talk I will provide an overview of the way the implicate order applies to the mind. This involves discussing both phenomenological aspects, such as time consciousness, as well as ontological issues, such as the relationship of mind and matter, and the problem of mental causation.

Reference: Pylkkänen, P. (2007) Mind, Matter and the Implicate Order. Heidelberg and New York: Springer.

I Stubbe
Dynamic logic: a noncommutative topology of truth values

The naive idea of (deterministic, non-destructive, non-typed) ‘processes’ can be formulated as a monoid action. To account for non-determinism and possible destructiveness, one can replace the (functional) action by a relational one. But simple manipulations then suggest to replace the ‘action’ (of a monoid) by an ‘enrichement’ (in a quantale, or a quantaloid to account for types).

Taking this stance, we build a “mathematical universe” (a category of ordered sheaves, technically speaking) which is governed by a logic whose truth values form a noncommutative topology (namely a quantaloid). Examples include sheaves on a locale (i.e. localic toposes) but also metric spaces (viewed as sheaves on the real numbers).

Georg Wikman

Approaches to the Notion of Order through Similarity and Difference

With A Case study of the Concept of Indistinguishable “Twins”