Folk Theorems on the Correspondence between State-Based and Event-Based Systems

Kripke Structures and Labelled Transition Systems are the two most prominent semantic models used in concurrency theory. Both models are commonly believed to be equi-expressive. One can find many ad-hoc embeddings of one of these models into the other. We build upon the seminal work of De Nicola and Vaandrager that firmly established the correspondence between stuttering equivalence in Kripke Structures and divergence-sensitive branching bisimulation in Labelled Transition Systems. We show that their embeddings can also be used for a range of other equivalences of interest, such as strong bisimilarity, simulation equivalence, and trace equivalence. Furthermore, we extend the results by De Nicola and Vaandrager by showing that there are additional translations that allow one to use minimisation techniques in one semantic domain to obtain minimal representatives in the other semantic domain for these equivalences.Comment: Full version of SOFSEM 2011 pape

Introduction to Loop Quantum Gravity

This article is based on the opening lecture at the third quantum geometry and quantum gravity school sponsored by the European Science Foundation and held at Zakopane, Poland in March 2011. The goal of the lecture was to present a broad perspective on loop quantum gravity for young researchers. The first part is addressed to beginning students and the second to young researchers who are already working in quantum gravity.Comment: 30 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:gr-qc/041005

A simple axiomatics of dynamic play in repeated games

This paper proposes an axiomatic approach to study two-player infinitely repeated games. A solution is a correspondence that maps the set of stage games into the set of infinite sequences of action profiles. We suggest that a solution should satisfy two simple axioms: individual rationality and collective intelligence. The paper has three main results. First, we provide a classification of all repeated games into families, based on the strength of the requirement imposed by the axiom of collective intelligence. Second, we characterize our solution as well as the solution payoffs in all repeated games. We illustrate our characterizations on several games for which we compare our solution payoffs to the equilibrium payoff set of Abreu and Rubinstein (1988). At last, we develop two models of players' behavior that satisfy our axioms. The first model is a refinement of subgame-perfection, known as renegotiation proofness, and the second is an aspiration-based learning model.Axiomatic approach, repeated games, classification of games, learning, renegotiation

Consciousness, cognition, and the hierarchy of context: extending the global neuronal workspace model

We adapt an information theory analysis of interacting cognitive biological and social modules to the problem of the global neuronal workspace, the new standard neuroscience paradigm for consciousness. Tunable punctuation emerges in a natural way, suggesting the possibility of fitting appropriate phase transition power law, and away from transition, generalized Onsager relation expressions, to observational data on conscious reaction. The development can be extended in a straightforward manner to include psychosocial stress, culture, or other cognitive modules which constitute a structured, embedding hierarchy of contextual constraints acting at a slower rate than neuronal function itself. This produces a 'biopsychosociocultural' model of individual consciousness that, while otherwise quite close to the standard treatment, meets compelling philosophical and other objections to brain-only descriptions

On the Argument from Physics and General Relativity

I argue that the best interpretation of the general theory of relativity has need of a causal entity, and causal structure that is not reducible to light cone structure. I suggest that this causal interpretation of GTR helps defeat a key premise in one of the most popular arguments for causal reductionism, viz., the argument from physics

Skyrmion black hole hair: Conservation of baryon number by black holes and observable manifestations

We show that the existence of black holes with classical skyrmion hair invalidates standard proofs that global charges, such as the baryon number, cannot be conserved by a black hole. By carefully analyzing the standard arguments based on a Gedankenexperiment in which a black hole is seemingly-unable to return the baryon number that it swallowed, we identify inconsistencies in this reasoning, which does not take into the account neither the existence of skyrmion black holes nor the baryon/skyrmion correspondence. We then perform a refined Gedankenexperiment by incorporating the new knowledge and show that no contradiction with conservation of baryon number takes place at any stage of black hole evolution. Our analysis also indicates no conflict between semi-classical black holes and the existence of baryonic gauge interaction arbitrarily-weaker than gravity. Next, we study classical cross sections of a minimally-coupled massless probe scalar field scattered by a skyrmion black hole. We investigate how the skyrmion hair manifests itself by comparing this cross section with the analogous cross section caused by a Schwarzschild black hole which has the same ADM mass as the skyrmion black hole. Here we find an order-one difference in the positions of the characteristic peaks in the cross sections. The peaks are shifted to smaller scattering angles when the skyrmion hair is present. This comes from the fact that the skyrmion hair changes the near horizon geometry of the black hole when compared to a Schwarzschild black hole with same ADM mass. We keep the study of this second aspect general so that the qualitative results which we obtain can also be applied to black holes with classical hair of different kind. (C) 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license

Topological aspects of classical and quantum black hole hair

The study of black holes, that are objects with escape velocity larger than the speed of light which can be formed in gravitational collapse and in high energy particle collisions, is a fascinating research topic in particle physics, astrophysics and cosmology. From the observational point of view a lot of progress has been achieved within the last decades. In particular, many (candidates for) astrophysical black holes have been discovered in our universe and recently the detection of gravitational waves from a black hole merger has been celebrated. In theoretical black hole physics, which we will focus on in this thesis, conjectures have been stated and theorems have been proven which tell us a lot about black hole formation and black hole properties. According to the famous Cosmic Censorship conjecture, black holes are formed in every gravitational collapse which leads to a spacetime with a singularity. According to the no-hair conjecture stationary black holes can be uniquely characterized by parameters associated to a classical Gauss law. Semi-classically, black holes are known to be thermal objects which carry entropy and emit thermal “Hawking” radiation. Black hole hairs, that are parameters which characterize a black hole but are not associated to a classical Gauss law, do, in agreement with the no-hair conjecture, not exist in many concrete models, a fact which has been proven (under certain assumptions) in so-called uniqueness and no-hair theorems. Today, we know however that in general there are counterexamples to the no-hair conjecture, there are models in which black hole solutions with hair do exist! These hairy black holes are black holes with classical hair on the one hand and black holes with quantum hair (that are black hole parameters not measurable classically but only quantum mechanically) on the other hand. Some of these known hairy black holes are not very relevant in the sense that they are dynamically unstable and are therefore not expected to be formed in any realistic physical process. There are however also hairy black holes which are known to be dynamically stable or which at least show symptoms of dynamical stability, that is they are known to be stable against linear perturbations. Many of these hairy black holes which seem to be dynamically stable are known to be tightly related to the concept of topology: On the one hand, the asymptotically flat and spherically symmetric black holes with classical hair which are known to be stable against perturbations all have in common that they are obtained as solutions of the Einstein field equations in a theory with a matter Lagrangian coupled to gravity which allows for topological solitons as solutions. On the other hand, many black hole quantum hairs can be related to a non-vanishing Aharonov-Bohm phase shift. In this thesis we study several topological aspects of hairy black holes and beyond. First, we argue that, for given asymptotic characteristics, one can distinguish a black hole with classical hair with these asymptotic characteristics from a black hole without classical hair with the same asymptotic characteristics via classical scattering of waves. We demonstrate the viability of this proposal by calculating differential scattering cross sections for many concrete examples of hairy and non-hairy black holes numerically. Second, we study the particular case of skyrmion black hole hair. We show that on top of the known black holes with classical skyrmion hair also black holes with quantum Aharonov-Bohm-type skyrmion hair do exist. The connection of these black holes with classical skyrmion hair on the one hand and with quantum skyrmion hair on the other hand has many interesting physical consequences which we discuss in detail. Most importantly, we point out a loophole in the black hole folk theorems argument which allows for a self-consistent possibility of baryon number conservation by semi-classical black holes. Third, we discuss several aspects of cosmic strings in spacetimes with boundary, in particular we argue from a boundary point of view under which conditions these cosmic strings can obey fractional anyon-type statistics and point out how such anyonic cosmic strings appear in situations of black holes with discrete quantum ZN Aharonov-Bohm-type hair.Das Studium Schwarzer Löcher - das sind Objekte mit einer Fluchtgeschwindigkeit größer als die Lichtgeschwindigkeit, die in Folge eines Gravitationskollapses oder in hochenergetischen Teilchenkollisionen entstehen können - ist ein faszinierendes Forschungsfeld in der Astrophysik, in der Teilchenphysik und in der Kosmologie. Aus Sicht der beobachtenden Astrophysik wurden in den letzten Jahrzehnten große Fortschritte erzielt. Insbesondere wurden viele (Kandidaten für) astrophysikalische Schwarze Löcher in unserem Universum entdeckt und kürzlich wurde die Detektion von Gravitationswellen verschmelzender Schwarzer Löcher gefeiert. In der theoretischen Physik Schwarzer Löcher, auf die wir uns in dieser Arbeit beschränken, wurden Hypothesen formuliert und Theoreme bewiesen, die viel darüber aussagen wie Schwarze Löcher entstehen und was für Eigenschaften sie haben. Die berühmte Cosmic Censorship Hypothese besagt, dass Schwarze Löcher in jedem Gravitationskollaps, der zu einer Raumzeitsingularität führt, entstehen. Die No-Hair Hypothese besagt, dass man stationäre Schwarze Löcher eindeutig durch Parameter, die einem klassischen Gaußschen Gesetz folgen, charakterisieren kann. Semiklassisch ist bekannt, dass Schwarze Löcher Objekte sind, denen eine Entropie zugeordnet werden kann und die thermische Hawkingstrahlung emittieren. Haare Schwarzer Löcher, das sind Parameter, die Schwarze Löcher charakterisieren, aber keinem klassischen Gaußschen Gesetz folgen, existieren in Übereinstimmung mit der No-Hair Hypothese in vielen konkreten Modellen nicht - ein Faktum, das in sogenannten Eindeutigkeits- und No-Hair Theoremen (unter bestimmten Voraussetzungen) bewiesen wurde. Heutzutage wissen wir jedoch, dass im Allgemeinen Gegenbeispiele zur No-Hair Hypothese existieren - es gibt Modelle, in denen haarige Schwarze Löcher als Lösungen existieren. Das sind auf der einen Seite Schwarze Löcher mit klassischen Haaren und auf der anderen Seite Schwarze Löcher mit quantenmechanischen Haaren (letzteres sind Parameter, die nicht klassisch, sondern nur quantenmechanisch gemessen werden können). Einiger dieser bekannten Schwarzen Löcher mit Haaren sind nicht relevant in dem Sinne dass sie dynamisch instabil sind und man deshalb nicht erwartet, dass sie in einem realistischen physikalischen Prozess auftreten. Es gibt allerdings auch Schwarze Löcher mit Haaren, von denen wir wissen, dass sie dynamisch stabil sind oder die zumindest Stabilitätssymptome zeigen, die stabil gegen lineare Störungen sind. Viele dieser Schwarzen Löcher mit Haaren, die dynamisch stabil zu sein scheinen, stehen eng in Verbindung mit dem Konzept der Topologie: Auf der einen Seite haben diejenigen asymptotisch flachen und sphärisch symmetrischen Schwarzen Löcher mit klassischen Haaren, von denen wir wissen, dass sie dynamisch stabil gegen lineare Störungen sind, es alle gemeinsam, dass sie Lösungen der Einsteinschen Feldgleichungen in einer Theorie mit an die Gravitation gekoppelter Lagrangefunktion, welche topologische Solitonen als Lösungen hat, sind. Auf der anderen Seite können viele Schwarze Löcher mit quantenmechanischen Haaren in Beziehung zu einer nicht verschwindenden Aharonov-Bohm-Phase gebracht werden. In dieser Arbeit untersuchen wir verschiedene topologische Aspekte von Schwarzen Löchern mit Haaren und darüber hinaus. Erstens argumentieren wir für vorgegebene asymptotische Parameter, dass man ein Schwarzes Loch ohne klassische Haare mit diesen Parametern von einem Schwarzen Loch mit klassischen Haaren und mit denselben Parametern durch die Streuung von Wellen unterscheiden kann. Wir demonstrieren dies, indem wir die differenziellen Wirkungsquerschnitte für viele konkrete Beispiele von Schwarzen Löchern mit und ohne Haare numerisch bestimmen. Zweitens studieren wir das konkrete Beispiel von skyrmionischen Haaren Schwarzer Löcher. Wir zeigen, dass es neben den bekannten Schwarzen Löchern mit klassischen skyrmionischen Haaren auch Schwarze Löcher mit quantenmechanischen skyrmionischen Haaren vom Aharonov-Bohmschen Typ gibt. Die Kombination der Schwarzen Löcher mit klassischen skyrmionischen Haaren und derjenigen mit quantenmechanischen skyrmionischen Haaren hat viele interessante physikalische Konsequenzen, die wir im Detail untersuchen; vor allem weisen wir auf eine Lücke in dem Beweis der sogenannten Folk Theoreme hin, die es erlaubt, ein selbstkonsistentes Szenario zu formulieren, in dem Schwarze Löcher Baryonenzahl nicht verletzen. Drittens diskutieren wir verschiedene Aspekte von kosmischen Strings in berandeten Raumzeiten, insbesondere argumentieren wir aus Sicht des Randes unter welchen Bedingungen diese kosmischen Strings fraktionale Statistik haben können und stellen heraus wie solche kosmische Strings in Situationen mit Schwarzen Löchern mit Aharonov-Bohm ZN Haaren auftreten

Some Aspects of Modality in Analytical Mechanics

This paper discusses some of the modal involvements of analytical mechanics. I first review the elementary aspects of the Lagrangian, Hamiltonian and Hamilton-Jacobi approaches. I then discuss two modal involvements; both are related to David Lewis' work on modality, especially on counterfactuals. The first is the way Hamilton-Jacobi theory uses ensembles, i.e. sets of possible initial conditions. The structure of this set of ensembles remains to be explored by philosophers. The second is the way the Lagrangian and Hamiltonian approaches' variational principles state the law of motion by mentioning contralegal dynamical evolutions. This threatens to contravene the principle that any actual truth, in particular an actual law, is made true by actual facts. Though this threat can be avoided, at least for simple mechanical systems, it repays scrutiny; not least because it leads to some open questions.Comment: 36 pages, no figures. Delivered at a Philosophy of Science Association Symposium in memory of the distinguished philosopher David Lewis, Milwaukee, November 2002. This version includes significant additions to Section 5.1. This version is forthcoming in `Formal Teleology and Causality', ed. M. Stoeltzner, P. Weingartner, Paderborn, Germany: Mentis. A precis of the first half of the paper is forthcoming in the journal Philosophy of Scienc