Two-dimensional approach to relativistic positioning systems

A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in the two-dimensional case. This simplified approach allows to explain and to analyze the properties and interest of these new systems. The positioning system defined by geodesic emitters in flat metric is developed in detail. The information that the data generated by a relativistic positioning system give on the space-time metric interval is analyzed, and the interest of these results in gravimetry is pointed out.Comment: 11 pages, 5 figures. v2: a brief description of the principal bibliography has been adde

Relativistic Positioning Systems: The Emission Coordinates

This paper introduces some general properties of the gravitational metric and the natural basis of vectors and covectors in 4-dimensional emission coordinates. Emission coordinates are a class of space-time coordinates defined and generated by 4 emitters (satellites) broadcasting their proper time by means of electromagnetic signals. They are a constitutive ingredient of the simplest conceivable relativistic positioning systems. Their study is aimed to develop a theory of these positioning systems, based on the framework and concepts of general relativity, as opposed to introducing `relativistic effects' in a classical framework. In particular, we characterize the causal character of the coordinate vectors, covectors and 2-planes, which are of an unusual type. We obtain the inequality conditions for the contravariant metric to be Lorentzian, and the non-trivial and unexpected identities satisfied by the angles formed by each pair of natural vectors. We also prove that the metric can be naturally split in such a way that there appear 2 parameters (scalar functions) dependent exclusively on the trajectory of the emitters, hence independent of the time broadcast, and 4 parameters, one for each emitter, scaling linearly with the time broadcast by the corresponding satellite, hence independent of the others.Comment: 13 pages, 3 figures. Only format changed for a new submission. Submitted to Class. Quantum Gra

Relativistic Positioning Systems

The theory of relativistic {\em location systems} is sketched. An interesting class of these systems is that of relativistic {\em positioning systems,} which consists in sets of four clocks broadcasting their proper time. Among them, the more important ones are the {\em auto-located positioning systems,} in which every clock broadcasts not only its proper time but the proper times that it receives from the other three. At this level, no reference to any exterior system (the Earth surface, for example) and no synchronization are needed. Some properties are presented. In the SYPOR project, such a structure is proposed, eventually anchored to a classical reference system on the Earth surface, as the best relativistic structure for Global Navigation Satellite Systems.Comment: 8 pages; 1 figure; to appear in Proc. Spanish Relativity Meeting ERE-2005, Oviedo (Spain); v2: minor formal change

Student teachers' perception of their role and responsibilities as Catholic educators

This article is concerned with 26 primary and secondary student teachers' early perception of themselves as Catholic educators in Scotland. It analyses their perspectives on what it means to be a Catholic teacher, what is expected of them by the Church and what motivated them to chose this particular career path. Discussion of these issues reveals an astute awareness of their role in the Catholic sector but a deep apprehension about their ability to succeed in fulfilling this. Their religious biographies and identities highlight much about the Scottish context of which they are a part, yet their responses to faith indicate differing levels of confidence in teaching, particularly with regard to the content of the Religious Education curriculum which they are expected to implement. The challenge these students present to the major stakeholders in Scottish education is to provide them with adequate support in developing their own faith - and knowledge and understanding of it - in order to enable them to carry out their role as Catholic teachers effectively within the state funded system

High energy factorization predictions for the charm structure function F2^c at HERA

High energy factorization predictions for F2^c are derived using BFKL descriptions of the proton structure function F2 at HERA. The model parameters are fixed by a fit of F2 at small x. Two different approaches of the non perturbative proton input are shown to correspond to the factorization at the gluon or quark level, respectively. The predictions for F2^c are in agreement with the data within the present error bars. However, the photon wave-function formulation (factorization at quark level) predicts significantly higher F2^c than both gluon factorization and a next-leading order DGLAP model.Comment: latex file + 6 encapsulated figures, 28 page

Do we expect too much? Reflection on chemistry content in higher education

Education research in the 1970s, like other related areas, was dominated by quantitative work¹ during an era for which social sciences sought to draw upon the successful scientific approach typically used in the physical sciences (in particular) to investigate teaching and learning.¹’² So if we felt a cohort of students did not understand some con¬cept, we tried to find out whether or not a different teach¬ing approach could fix their misconceptions.³ But how to do this? Well, drawing on a scientific approach, we would divide the class or classes up, teach one cohort the same way we always had, and the other cohort in our new way, and evaluate any differences in conceptual understanding using, e.g. a standardized topic test. Differences would be examined for statistical significance of evidence that our new approach to teaching had worked. And this is the way much research was done at the time. Control of variables, randomized sampling, and so on, were all embedded in such an approach to educational research