Abstract:
The new Process Physics models reality as self-organising relational information and takes account of the limitations of logic, discovered by Godel and extended by Chaitin, by using the concept of self-referential noise. Space and quantum physics are emergent and unified, and described by a Quantum Homotopic Field Theory of fractal topological defects embedded in a three dimensional fractal process-space.

Abstract:
The present paper is basically written as a non-apologetic strong defence of the thesis that computation is part and parcel of a physical theory and by no means a mere numerical evaluation of the prediction of a theory which comes towards the end. Various general considerations as well as specific examples are given to illustrate and support our arguments. These examples range from the practical aspect to almost esoteric considerations but at the end, everything converges towards a unity of theory and computation presented in the form of modern fractal logic and transfinite quantum field theory in a Cantorian spacetime. It is true that all our examples are taken from physics but our discussion is applicable in equal measure to a much wider aspect of life.

Abstract:
The need to find low power alternatives to digital electronic circuits has led to increasing interest in alternative switching schemes like the magnetic quantum cellular automata(MQCA) that store information in nanomagnets which communicate through their magnetic fields. A recent proposal called all spin logic (ASL) proposes to communicate between nanomagnets using spin currents which are spatially localized and can be conveniently routed. The objective of this paper is to present a model for ASL devices that is based on established physics and is benchmarked against available experimental data and to use it to investigate switching energy-delay of ASL devices.

Abstract:
In contrast to the Copenhagen interpretation we consider quantum mechanics as universally valid and query whether classical physics is really intuitive and plausible. - We discuss these problems within the quantum logic approach to quantum mechanics where the classical ontology is relaxed by reducing metaphysical hypotheses. On the basis of this weak ontology a formal logic of quantum physics can be established which is given by an orthomodular lattice. By means of the Soler condition and Piron's result one obtains the classical Hilbert spaces. - However, this approach is not fully convincing. There is no plausible justification of Soler's law and the quantum ontology is partly too weak and partly too strong. We propose to replace this ontology by an ontology of unsharp properties and conclude that quantum mechanics is more intuitive than classical mechanics and that classical mechanics is not the macroscopic limit of quantum mechanics.

Abstract:
Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum theory of computation has provided practical instances of this, and forces us to abandon the classical view that computation, and hence mathematical proof, are purely logical notions independent of that of computation as a physical process. Henceforward, a proof must be regarded not as an abstract object or process but as a physical process, a species of computation, whose scope and reliability depend on our knowledge of the physics of the computer concerned.

Abstract:
The logic--linguistic structure of quantum physics is analysed. The role of formal systems and interpretations in the representation of nature is investigated. The problems of decidability, completeness, and consistency can affect quantum physics in different ways. Bohr's complementarity is of great interest,because it is a contradictory proposition. We shall see that the flowing of time prevents the birth of contradictions in nature, because it makes a cut between two different, but complementary aspects of the reality.

Abstract:
In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a "cobordism". Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this expository paper, we make some of these analogies precise using the concept of "closed symmetric monoidal category". We assume no prior knowledge of category theory, proof theory or computer science.

Abstract:
The question of the origins of logic as a formal discipline is of special interest to the historian of physics since it represents a turning inward to examine the very nature of reasoning and the relationship between thought and reality. In the West, Aristotle (384-322 BCE) is generally credited with the formalization of the tradition of logic and also with the development of early physics. In India, the Rigveda itself in the hymn 10.129 suggests the beginnings of the representation of reality in terms of various logical divisions that were later represented formally as the four circles of: "A", "not A", ":A and not A", and "not A and not not A''. According to Puranic accounts, Medhatithi Gautama and Aksapada Gautama (or Gotama), which are perhaps two variant names for the author of the early formal text on Indian logic, belonged to about 550 BCE. The Greek and the Indian traditions seem to provide the earliest formal representations of logic, and in this article we ask if they influenced each other. We are also interested in the scope of early logic, since this gives an idea to us of the way early thinkers thought about nature and change. We will show that Greek and Indian logical traditions have much that is distinctive and unique and that they must have emerged independently.

Abstract:
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and ensembles, clarifies the logical relations and operations for them, and shows how they give rise to dynamics and probabilities. States are identified with maximal consistent sets of weak equalities in the algebra of observables (instead of, as usual, with the rays in a Hilbert space). This leads to a concise foundation of quantum mechanics, free of undefined terms, separating in a clear way the deterministic and the stochastic features of quantum physics. The traditional postulates of quantum mechanics are derived from well-motivated axiomatic assumptions. No special quantum logic is needed to handle the peculiarities of quantum mechanics. Foundational problems associated with the measurement process, such as the reduction of the state vector, disappear. The new interpretation of quantum mechanics contains `elements of physical reality' without the need to introduce a classical framework with hidden variables. In particular, one may talk about the state of the universe without the need of an external observer and without the need to assume the existence of multiple universes.

Abstract:
This volume contains the proceedings of the ninth workshop on Quantum Physics and Logic (QPL2012) which took place in Brussels from the 10th to the 12th of October 2012. QPL2012 brought together researchers working on mathematical foundations of quantum physics, quantum computing, and spatio-temporal causal structures. The particular focus was on the use of logical tools, ordered algebraic and category-theoretic structures, formal languages, semantical techniques, and other computer science methods for the study of physical behaviour in general.