Causality and Superluminal Fields

The expression of causality depends on an underlying choice of chronology. Since a chronology is provided by any Lorentzian metric in relativistic theories, there are as many expressions of causality as there are non-conformally related metrics over spacetime. Although tempting, a definitive choice of a preferred metric to which one may refer to is not satisfying. It would indeed be in great conflict with the spirit of general covariance. Moreover, a theory which appear to be non causal with respect to (hereafter, w.r.t) this metric, may well be causal w.r.t another metric. In a theory involving fields that propagate at different speeds (e.g. due to some spontaneous breaking of Lorentz invariance), spacetime is endowed with such a finite set of non-conformally related metrics. In that case one must look for a new notion of causality, such that 1. no particular metric is favored and 2. there is an unique answer to the question : ``is the theory causal?''. This new causality is unique and defined w.r.t the metric drawing the wider cone in the tangent space of a given point of the manifold. Moreover, which metric defines the wider cone may depend on the location on spacetime. In that sense, superluminal fields are generically causal, provided that some other basic requirements are met.Comment: 3 pages, Prepared for the Proceedings of the Eleventh Marcel Grossmann Meeting on General Relativity, Berlin, Germany, 23-27 July 2006; document class change

On causality and superluminal behavior in classical field theories. Applications to k-essence theories and MOND-like theories of gravity

Field theories whose full action is Lorentz invariant (or diffeomorphism invariant) can exhibit superluminal behaviors through the breaking of local Lorentz invariance. Quantum induced superluminal velocities are well-known examples of this effect. The issue of the causal behavior of such propagations is somewhat controversial in the literature and we intend to clarify it. We provide a careful analysis of the meaning of causality in classical relativistic field theories, and we stress the role played by the Cauchy problem and the notions of chronology and time arrow. We show that superluminal behavior threaten causality only if a prior chronology on spacetime is chosen. In the case where superluminal propagations occur, however, there is at least two non conformally related metrics on spacetime and thus two available notions of chronology. These two chronologies are on equal footing and it would thus be misleading to choose \textit{ab initio} one of them to define causality. Rather, we provide a formulation of causality in which no prior chronology is assumed. We argue this is the only way to deal with the issue of causality in the case where some degrees of freedom propagate faster than others. We actually show that superluminal propagations do not threaten causality. As an illustration of these conceptual issues, we consider two field theories, namely k-essences scalar fields and bimetric theories of gravity, and we derive the conditions imposed by causality. We discuss various applications such as the dark energy problem, MOND-like theories of gravity and varying speed of light theories.Comment: 15 pages, 2 figures; minor changes, references added, submitted to Phys.Rev.

The two-body problem: analytical results in a toy-model of relativistic gravity

The two body problem in a scalar theory of gravity is investigated. We focus on the closest theory to General Relativity (GR), namely Nordstr\"om's theory of gravity (1913). The gravitational field can be exactly solved for any configuration of point-particles. We then derive the exact equations of motion of two inspiraling bodies including the exact self-forces terms. We prove that there is no innermost circular orbit (ICO) in the exact theory whereas we find (order-dependent) ICOs if post-Newtonian (PN) truncations are used. We construct a solution of the two body problem in an iterative (non-PN) way, which can be viewed as a series in powers of $(v/c)^{5}$. Besides this rapid convergence, each order also provides non-perturbative information. Starting from a circular Newtonian-like orbit, the first iteration already yields the 4.5 PN radiation reaction. These results not only shed light on some non-perturbative effects of relativistic gravity, but may also be useful to test numerical codes.Comment: 7 Figures, To appear in the proceedings of Albert Einstein's Century International Conference, Paris, France, 18-22 Jul

Field-theoretical formulations of MOND-like gravity

Modified Newtonian dynamics (MOND) is a possible way to explain the flat galaxy rotation curves without invoking the existence of dark matter. It is however quite difficult to predict such a phenomenology in a consistent field theory, free of instabilities and admitting a well-posed Cauchy problem. We examine critically various proposals of the literature, and underline their successes and failures both from the experimental and the field-theoretical viewpoints. We exhibit new difficulties in both cases, and point out the hidden fine tuning of some models. On the other hand, we show that several published no-go theorems are based on hypotheses which may be unnecessary, so that the space of possible models is a priori larger. We examine a new route to reproduce the MOND physics, in which the field equations are particularly simple outside matter. However, the analysis of the field equations within matter (a crucial point which is often forgotten in the literature) exhibits a deadly problem, namely that they do not remain always hyperbolic. Incidentally, we prove that the same theoretical framework provides a stable and well-posed model able to reproduce the Pioneer anomaly without spoiling any of the precision tests of general relativity. Our conclusion is that all MOND-like models proposed in the literature, including the new ones examined in this paper, present serious difficulties: Not only they are unnaturally fine tuned, but they also fail to reproduce some experimental facts or are unstable or inconsistent as field theories. However, some frameworks, notably the tensor-vector-scalar (TeVeS) one of Bekenstein and Sanders, seem more promising than others, and our discussion underlines in which directions one should try to improve them.Comment: 66 pages, 6 figures, RevTeX4 format, version reflecting the changes in the published pape

Béarnais émigrés en Amérique : des marges qui résistent?

Les Français qui émigrèrent vers les Amériques au xixe siècle furent très largement issus des marges géographiques de la France, le plus fort contingent étant fourni par les groupes basques, béarnais et bigourdans originaires des Pyrénées occidentales. Si des observateurs ont remarqué que des groupes de migrants conservaient, voire revivifiaient leurs traditions culturelles dans les pays d’arrivée, il ne semble pas en avoir été de même pour les Béarnais et les Bigourdans. (Nous laisserons de côté les Basques qui, par leur langue et statut spécifiques, ainsi que par le rôle de l’Église catholique, furent davantage amenés à maintenir, en l’organisant, leur identité.) Si l’on se base principalement sur les lettres de ces émigrés, il apparaît que l’identité béarnaise à la première génération se maintient dans un entre-soi à travers la perpétuation du parler béarnais, de la cuisine locale, de la pratique de certains jeux, et s’exprime et se renforce au travers d’un fort lobbying; en revanche, dès qu’il s’agit de présentation de soi dans la société environnante (par les vêtements notamment), on observe le souci de ne pas se singulariser; par ailleurs, quand les émigrés créent des sociétés d’entraide, c’est sous la bannière française qu’ils le font. On se demandera alors si la perpétuation de leurs traits culturels, plus que l’affirmation d’une identité, ne correspondait pas surtout à la nécessité de renforcement d’un groupe, tremplin et gage de l’intégration souhaitée. Cette hypothèse sera replacée dans la nature et l’époque de l’émigration pyrénéenne

The role of archaeological sources in the construction of management models of natural hazards in the Roman Empire: the example of flood risk

Cet article propose un essai de modélisation de la gestion des inondations par les sociétés urbaines de l’époque romaine, sur la base des sources archéologiques. L’objectif est de montrer comment ces dernières peuvent être utilisées pour comprendre les pratiques de gestion des risques naturels dans l’Antiquité. Sur le plan méthodologique, la construction de ces modèles est d’abord resituée dans l’histoire des recherches sur les relations sociétés / milieux naturels en archéologie antique. Le corpus d’étude est présenté dans une seconde partie. La démonstration repose sur la mise en série de cas de villes romaines exposées à l’inondation, essentiellement en Gaule. Les différentes étapes du raisonnement, depuis les observations de terrain jusqu’à l’interprétation historique, sont décrites puis synthétisées sous la forme de 5 schémas. Les résultats témoignent de la diversité des politiques de gestion des risques, évoluant en fonction des échelles de temps et d’espace auxquelles l’observateur se place.This paper presents a preliminary model about flooding management, based on archaeological data, by the urban Roman societies. The aim is to show why and how archaeology can be considered as a usefull source to understand the strategies of adaptation to natural hazards. The production of those models is first linked to the state of research adressing the relationships between societies and their natural environment in French archaeology. In a second part, we present the corpus of roman cities, mainly from Gaul, and how the archeological and palaeoenvironmental data are crossed. The model is summarized in 5 detailed diagrams presenting the different steps from the field data to historical interpretation. The outcome provides evidence of the diversity of flood hazard management in roman cities. However, techniques and policies change, and their efficiency can be assessed differentially according to the time and space scales used to study roman sites