Diffraction-limited performance and focusing of high harmonics from relativistic plasmas

When a pulse of light reflects from a mirror that is travelling close to the speed of light, Einstein's theory of relativity predicts that it will be up-shifted to a substantially higher frequency and compressed to a much shorter duration. This scenario is realized by the relativistically oscillating plasma surface generated by an ultraintense laser focused onto a solid target. Until now, it has been unclear whether the conditions necessary to exploit such phenomena can survive such an extreme interaction with increasing laser intensity. Here, we provide the first quantitative evidence to suggest that they can. We show that the occurrence of surface smoothing on the scale of the wavelength of the generated harmonics, and plasma denting of the irradiated surface, enables the production of high-quality X-ray beams focused down to the diffraction limit. These results improve the outlook for generating extreme X-ray fields, which could in principle extend to the Schwinger limit.

Events: Temporal and Eternal (in preparation)

This monograph develops a theory of events which provides the foundation for a plausible and coherent account of God’s relation to time, and which has independent appeal (independent, that is, of theological considerations). The book is divided into three parts. The first part involves an investigation of those fundamental aspects of time which have important implications for the nature of events, such as whether time is substantival or relational, and whether time is continuous, dense, or discrete. This part also includes a chapter on how these issues relate to different interpretations of the special theory of relativity. The second part involves a defense of the fundamentality of events, and the development of a theory of events in time. The third part considers ways in which we might plausibly conceive of events as eternal entities. This involves an investigation of different ways of characterizing divine eternity, and then an analysis of the possible relations these ways bear to the antecedently developed theory of temporal events. The thought here is that there are certain characteristics of temporal events which can be assimilated to eternity, and that by evaluating the extent to which different theories of divine eternity allow for this assimilation, we will be able to determine which of those theories is most plausible, and therefore which conception of God’s relation to time is most plausible. The basis of this evaluation will be the theory’s ability to coherently account for God’s knowledge of, and interaction with, the created temporal world. One specific issue here is how to account for God’s knowledge of the future free actions of humans (an issue that I address in 'Eternity, Knowledge, and Freedom'), but there are many other difficulties associated with God’s relation to time, such as God’s creation of contingent time, God’s knowledge of what is happening now, God’s dialogue with humans, and God’s causally interacting with the temporal world in general. A successful theory of eternal events, and, in particular, divine events, will provide a framework for dealing with these difficulties.

I have not yet sough a publisher for this work, but intend to do so in 2013, with a target publication date of 2014.

Relativistic electron mirrors from nanoscale foils for coherent frequency upshift to the extreme ultraviolet

Reflecting light from a mirror moving close to the speed of light has been envisioned as a route towards producing bright X-ray pulses since Einstein's seminal work on special relativity. For an ideal relativistic mirror, the peak power of the reflected radiation can substantially exceed that of the incident radiation due to the increase in photon energy and accompanying temporal compression. Here we demonstrate for the first time that dense relativistic electron mirrors can be created from the interaction of a high-intensity laser pulse with a freestanding, nanometre-scale thin foil. The mirror structures are shown to shift the frequency of a counter-propagating laser pulse coherently from the infrared to the extreme ultraviolet with an efficiency >10 4 times higher than in the case of incoherent scattering. Our results elucidate the reflection process of laser-generated electron mirrors and give clear guidance for future developments of a relativistic mirror structure. 

Possession Taken by Theft and the Original Acquisition of Personal Property Rights

This paper queries the soundness of the view that wrongful possession (eg a thief’s possession of goods he has stolen) should be protected by the standard actions for interference with goods. It uses close historical analysis of the development of the relevant concepts through the cases to argue that this is not a proposition that is compelled on the authorities, nor one demanded as a matter of principle. It then abstracts to consider the implications of this argument at a theoretical level, exposing great need for development in the common law’s basic principles of possessory protection. It argues innovatively that the objects of the law might be better served by the creation of a more limited form of possessory protection, achieved through the possessor’s acquisition of a personal right, and correlatively that the values that underpin and justify our basic rules of possessory protection entail a more nuanced response to matters of property acquisition.

Nonlinear hydrodynamic Langmuir waves in fully degenerate relativistic plasma

The combined effect of special relativity and electron degeneracy on Langmuir waves is analyzed by utilizing a rigorous fully relativistic hydrodynamic model. Assuming a traveling wave solution form, a set of conservation laws is identified, together with a pseudo-potential function depending on the relativistic parameter p<inf>F</inf>/(m c) (where p<inf>F</inf> is the Fermi momentum, m is the mass of the charge carriers and c the speed of light), as well as on the amplitude of the electrostatic energy perturbation.

The Extra-territorial Obligations of European States regarding Human Rights in the Context of Terrorism

This chapter focuses on the growing tendency of international human rights law to require states to protect the rights of non-nationals who are in the state unlawfully and of nationals and non-nationals who are outside the state, especially when any of these people are involved in terrorist or counter-terrorist activity. It reviews these additional obligations within a European context, focusing on EU law and the law of the European Convention on Human Rights and drawing on the case law of UK courts. Part 1 considers when a European state must grant asylum to alleged terrorists on the basis that otherwise they would suffer human rights abuses in the state from which they are fleeing. Part 2 examines whether, outside of asylum claims, a European state must not deport or extradite an alleged terrorist because he or she might suffer an abuse of human rights in the receiving state. Part 3 looks at whether a European state whose security forces are engaged in counter-terrorism activities abroad is obliged to protect the human rights of the individuals serving in those forces and/or the human rights of the alleged terrorists they are confronting. While welcoming the extension of state responsibility, the chapter notes that it is occurring in a way which introduces three aspects of relativity into the protection of human rights. First, European law protects only some human rights extra-territorially. Second, it protects those rights only when there is ‘a real risk’ of their being violated. Third, sometimes it protects those rights only when there is a real risk of their being violated ‘flagrantly’.

Ecos do silêncio : para um estudo iconológico do fado

Tese de doutoramento, História (Arte Património e Restauro), Universidade de Lisboa, Faculdade de Letras, 2015

Relativistic time effects in financial dynamics

Financial time series have a complex dynamic nature. Many techniques were adopted having in mind standard paradigms of time flow. This paper explores an alternative route involving relativistic effects. It is observed that the measuring perspective influences the results and that we can have different time textures.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

La problématique du consentement à l'arbitrage multipartite au sein des groupements de sociétés

"Mémoire présenté à la Faculté des Études supérieures En vue de l'obtention du grade de Maîtrise en droit (LL.M.) option : Droit des affaires". Ce mémoire a été accepté à l'unanimité et classé parmi les 15% des mémoires de la discipline.

Towards a philosophical reconstruction of the dialogue between modern physics and Advaita Vedanta : an inquiry into the concepts of akasa, vacuum and reality

Vers la fin du 19ème siècle, le moine et réformateur hindou Swami Vivekananda affirma que la science moderne convergeait vers l'Advaita Vedanta, un important courant philosophique et religieux de l'hindouisme. Au cours des décennies suivantes, suite aux apports scientifiques révolutionnaires de la théorie de la relativité d'Einstein et de la physique quantique, un nombre croissant d'auteurs soutenaient que d'importants "parallèles" pouvaient être tracés entre l'Advaita Vedanta et la physique moderne. Encore aujourd'hui, de tels rapprochements sont faits, particulièrement en relation avec la physique quantique. Cette thèse examine de manière critique ces rapprochements à travers l'étude comparative détaillée de deux concepts: le concept d'akasa dans l'Advaita Vedanta et celui de vide en physique quantique. L'énoncé examiné est celui selon lequel ces deux concepts pointeraient vers une même réalité: un substratum omniprésent et subtil duquel émergent et auquel retournent ultimement les divers constituants de l'univers. Sur la base de cette étude comparative, la thèse argumente que des comparaisons de nature conceptuelle favorisent rarement la mise en place d'un véritable dialogue entre l'Advaita Vedanta et la physique moderne. Une autre voie d'approche serait de prendre en considération les limites épistémologiques respectivement rencontrées par ces disciplines dans leur approche du "réel-en-soi" ou de la "réalité ultime." Une attention particulière sera portée sur l'épistémologie et le problème de la nature de la réalité dans l'Advaita Vedanta, ainsi que sur le réalisme scientifique et les implications philosophiques de la non-séparabilité en physique quantique.

Structure et interactions de bulles d'espace-temps en relativité générale

Nous analysons des bulles d'espace-temps d'épaisseur finie en relativité générale. Les conditions d'énergie sont utilisées afin d'obtenir un ensemble de critères permettant de restreindre la structure du bord de la bulle. Dans le cas des bulles statiques et à symétrie sphérique, nous obtenons quatre inégalités différentielles équivalentes aux trois conditions d'énergie les plus communes. Nous montrons qu'elles sont équivalentes à un ensemble de deux inégalités différentielles simples lorsque le potentiel gravitationnel effectif a une forme particulière. Nous paramétrons alors l'espace-temps de manière à rendre la vérification de ces inégalités plus simple lorsqu'il sera question de bulles d'espace-temps. Nous traitons en particulier quatre formes de bulles, toutes caractérisées par un extérieur de type Schwarzschild de Sitter. Nous montrons que notre méthode donne les bons résultats lorsque la limite où l'épaisseur de la bulle tend vers zéro est prise. Nous terminons par un traitement succinct du problème d'une onde gravitationnelle se propageant dans un nuage de bulles d'espace-temps.

Sur la pertinence de la culture en pragmatique

Un débat perdure toujours entre les partisans du relativisme linguistique et ceux qui penchent plutôt pour l’universalisme. Depuis Whorf, plusieurs expériences ont été menées pour déterminer si la langue avait une influence sur l’esprit d’un individu, mais très peu ont porté sur la pragmatique. Je propose d’explorer le relativisme linguistique selon la perspective de la pragmatique du langage. Deux approches théoriques en pragmatique s’opposent sur la question du relativisme : l’ethnopragmatique et la théorie de la pertinence. En utilisant des modèles de l’interaction culturelle en anthropologie, en particulier les idées de Bourdieu et le concept d’assemblage, je démontre que la flexibilité de la théorie de la pertinence permettrait d’y intégrer une composante relativiste, et ce, sans avoir à la dénaturer. Pour illustrer cette possibilité, j’introduis l’Identité Cognitive qui agit comme composante relativiste tout en permettant une interaction avec la pertinence universaliste du modèle.

Complexité de la communication sur un canal avec délai

Nous introduisons un nouveau modèle de la communication à deux parties dans lequel nous nous intéressons au temps que prennent deux participants à effectuer une tâche à travers un canal avec délai d. Nous établissons quelques bornes supérieures et inférieures et comparons ce nouveau modèle aux modèles de communication classiques et quantiques étudiés dans la littérature. Nous montrons que la complexité de la communication d’une fonction sur un canal avec délai est bornée supérieurement par sa complexité de la communication modulo un facteur multiplicatif d/ lg d. Nous présentons ensuite quelques exemples de fonctions pour lesquelles une stratégie astucieuse se servant du temps mort confère un avantage sur une implémentation naïve d’un protocole de communication optimal en terme de complexité de la communication. Finalement, nous montrons qu’un canal avec délai permet de réaliser un échange de bit cryptographique, mais que, par lui-même, est insuffisant pour réaliser la primitive cryptographique de transfert équivoque.

Analysis of Fluctuations in the Early Universe Using Fokker-Planck Formalism

The thesis begins with a review of basic elements of general theory of relativity (GTR) which forms the basis for the theoretical interpretation of the observations in cosmology. The first chapter also discusses the standard model in cosmology, namely the Friedmann model, its predictions and problems. We have also made a brief discussion on fractals and inflation of the early universe in the first chapter. In the second chapter we discuss the formulation of a new approach to cosmology namely a stochastic approach. In this model, the dynam ics of the early universe is described by a set of non-deterministic, Langevin type equations and we derive the solutions using the Fokker—Planck formalism. Here we demonstrate how the problems with the standard model, can be eliminated by introducing the idea of stochastic fluctuations in the early universe. Many recent observations indicate that the present universe may be approximated by a many component fluid and we assume that only the total energy density is conserved. This, in turn, leads to energy transfer between different components of the cosmic fluid and fluctuations in such energy transfer can certainly induce fluctuations in the mean to factor in the equation of state p = wp, resulting in a fluctuating expansion rate for the universe. The third chapter discusses the stochastic evolution of the cosmological parameters in the early universe, using the new approach. The penultimate chapter is about the refinements to be made in the present model, by means of a new deterministic model The concluding chapter presents a discussion on other problems with the conventional cosmology, like fractal correlation of galactic distribution. The author attempts an explanation for this problem using the stochastic approach.