Showing papers on "Special relativity (alternative formulations) published in 2012"

Exact Space-Times in Einstein's General Relativity, by Jerry B. Griffiths and Jiří Podolský. Scope: reference. Level: postgraduate

Abstract: Optical sensors find various applications in all fields of scientific research, instrumentation and practical applications. Optical techniques are widely used in physics, chemistry, biology and medicine. They also have a great impact on today’s technological advances in telecommunications, photolithography on semiconductor chips, particle detection or object tracking to name a few. A book that would provide a summary of all optical sensors and their practical applications would be attractive to many readers across the board. The author’s intent to give an overview on this topic is well suited to meet this goal. This book serves as a good introduction to optical sensors. It covers the basics of light sources, detectors, various optical elements, and goes through some concepts about optical sensors and techniques. Optical sensors may refer to devices for light detection, e.g. CCD or CMOS cameras or PIN photodiodes. The author expands this concept and defines an optical sensor as a system consisting of a light source, a photodetector and optical elements for light delivery. He then describes the basic properties of incoherent and coherent light followed by numerous examples of optical sensors and their applications. Rigorous mathematical treatment, details about experimental arrangements and device architecture are beyond the scope of the book. However, the author provides an extended list of references on any given topic. Some of the references may be unfamiliar to the English speaking audiences. A comprehensive description of many modern optical sensor concepts is provided. The reader will find general coverage on how the humans and insects differ in their vision. The material touches upon the Purkinje effect on the shift of human eye’s spectral sensitivity. The reader will also find an extensive coverage about switches, rain sensors, displacement, velocity and distance measurement concepts, and laser vibrometers. A good discussion on optical techniques for temperature measurement is given. The reader will find examples about pyrometers and microbolometers as well as other thermal sensors used in different wavelength ranges. Microscopy and holography techniques are also discussed among the others. Various interferometric techniques and their applications are provided along with interesting examples. The reader will also find the basic concept of fluorescence detection and its applications. The reader will not find discussion on the state-of-the-art ultrafast techniques, e.g. laser induced fluorescence or four-wavemixing-based methods and their wide range of applications in science and technologies. Concepts and applications in the deep and extreme ultraviolet range, important for the photolithography, are not discussed either. The next editions of the book will hopefully include these important topics. The book is a good start for beginners who want to learn about optical sensors. An experimentalist may use this book as a reference. Engineering undergraduate students may find the material useful to jump start their projects and can use the references provided therein for more in-depth studies. A reader interested in biological applications of optical sensors, e.g. photodynamic therapy or fibre-optic based diagnostic techniques, will not find relevant material in this book. Teachers and general readers may find the material useful in preparing for classroom presentations and for general understanding of the optical sensor principles.

Topics in the Foundations of General Relativity and Newtonian Gravitation Theory

Abstract: In "Topics in the Foundations of General Relativity and Newtonian Gravitation Theory", David B. Malament presents the basic logical-mathematical structure of general relativity and considers a number of special topics concerning the foundations of general relativity and its relation to Newtonian gravitation theory. These special topics include the geometrized formulation of Newtonian theory (also known as Newton-Cartan theory), the concept of rotation in general relativity, and Godel spacetime. One of the highlights of the book is a no-go theorem that can be understood to show that there is no criterion of orbital rotation in general relativity that fully answers to our classical intuitions. "Topics" is intended for both students and researchers in mathematical physics and philosophy of science.

Einstein's special relativity beyond the speed of light

Abstract: We propose here two new transformations between inertial frames that apply for relative velocities greater than the speed of light, and that are complementary to the Lorentz transformation, giving ...

A logic road from special relativity to general relativity

Abstract: We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we “derive” an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.

The Poincare algebra in the context of ageing systems: Lie structure, representations, Appell systems and coherent states

Abstract: By introducing an unconventional realization of the Poincare algebra of special relativity as conformal transformations, we show how it may occur as a dynamical symmetry algebra for ageing systems in non-equilibrium statistical physics and give some applications, such as the computation of two-time correlators. We also discuss infinite-dimensional extensions of in this setting. Finally, we construct canonical Appell systems, coherent states and Leibniz function for as a tool for bosonic quantization.

Relativistic kinematics beyond special relativity

Abstract: In the context of departures from special relativity written as a momentum power expansion in the inverse of an ultraviolet energy scale M, we derive the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) composition law, dispersion relation, and transformation laws, at first order in the power expansion. In particular, we find that at that order the consistency of a modification of the energy-momentum composition law fixes the modification in the dispersion relation. We therefore obtain the most generic modification of special relativity which is rotational invariant and that preserves the relativity principle at leading order in 1/M. © 2012 American Physical Society.

Singularity Theorems in General Relativity: Achievements and Open Questions

Abstract: In this short note, written by a theoretical physicist, not a historian, I would like to present a brief overview of the acclaimed singularity theorems, which are often quoted as one of the greatest theoretical accomplishments in general relativity and mathematical physics

Thermodynamics of ideal gas in doubly special relativity

Abstract: We study thermodynamics of an ideal gas in doubly special relativity. A new type of special functions (which we call ``incomplete modified Bessel functions'') emerge. We obtain a series solution for the partition function and derive thermodynamic quantities. We observe that doubly special relativity thermodynamics is nonperturbative in the special relativity and massless limits. A stiffer equation of state is found.

Ways to resolve Selleri's paradox

Abstract: Selleri's paradox, based on an analysis of rotating frames, appears to show that the speed of light in an inertial system is not normally isotropic. This in turn seems at odds with the second postulate of special relativity requiring a universal light speed in inertial systems. First, it is demonstrated how to circumvent Selleri's argument using Einstein synchronization in rotating frames. Then the nature of Selleri's result is exposed: it simply corresponds to the adoption of a synchronization procedure different from Einstein's. In this scheme, anisotropic one-way speeds of light by no means contradict special relativity.

Prospective Teachers' Comprehension Levels of Special Relativity Theory and the Effect of Writing for Learning on Achievement

Abstract: In the present study, the comprehension levels of special relativity theory in prospective teachers who take the Introduction to Modern Physics lesson in the faculty of education science teaching department and the effect of writing for learning on their achievement is researched. In the research, a control group pre-test post-test quasiexperimental research model was used. Research data were obtained by using open-ended questions prepared by the researcher. The lesson was conducted in the beginning by using the verbal-written explanation method. Then each student in the experimental group wrote a summary which clearly explains the special relativity theory for a high school student within the framework of the writing for learning activity. By contrast, the control group students solved the problems related to the subject in the course book. A total of 73 students (51 female and 22 male) studying at the second grade in the 2011-2012 academic year participated in the study. The research findings showed that the comprehension levels of special relativity theory in prospective teachers were low; the result obtained by the qualitative and quantitative comparison of the post-test results of the experimental and control groups and their achievement percentage in the exam were in favor of the experimental group. Furthermore, 87.2% of the students who wrote down their opinions about the activity of writing for learning understood the special relativity theory; and the activity of writing for learning was effective in learning the special relativity theory.

Observable Equivalence between General Relativity and Shape Dynamics

Abstract: In this conceptual paper we construct a local version of Shape Dynamics that is equivalent to General Relativity in the sense that the algebras of Dirac observables weakly coincide. This allows us to identify Shape Dynamics observables with General Relativity observables, whose observables can now be interpreted as particular representative functions of observables of a conformal theory at fixed York time. An application of the observable equivalence of General Relativity and Shape Dynamics is to define the quantization of General Relativity through quantizing Shape Dynamics and using observable equivalence. We investigate this proposal explicitly for gravity in 2+1 dimensions.

Henri Poincaré and the principle of relativity

Abstract: Often considered as the last ‘encyclopedist’, Henri Poincare died one hundred years ago. If he was a prominent man in 1900 French Society, his heritage is not so clearly recognised, particularly in France. Among his too often misunderstood works is his contribution to the theory of relativity, mainly because it is almost never presented within Poincare's general approach to science, including his philosophical writings. Our aim is therefore to provide an historical account of the main steps (experimental as well as theoretical) which led Poincare to contribute to the theory of relativity. Starting from the optical experiments which led to the inconsistency of the classical (Galilean) composition law for velocities to explain light propagation, we introduce the FitzGerald and Lorentz contraction which was viewed as the ‘sole hypothesis’ to explain the Michelson and Morley experiment. We then show that Poincare's contribution starts with a discussion of the principles governing the mechanics and was built s...

How Einstein Created Relativity out of Physics and Astronomy

Abstract: Part I: Genesis: Riding a Beam of Light.- Part II: Special Relativity.- Part III: General Relativity.- Part IV: Cosmology.- Part V: Exodus: Quest for a Unified Field Theory.

Symmetry Doubling: Doubly General Relativity

Abstract: We show that the equivalence of General Relativity and Shape Dynamics can be extended to a theory, that respects the BRST-symmetries of General Relativity as well as the ones of an extended version of Shape Dynamics. This version of Shape Dynamics implements local spatial conformal transformations as well as a local an abstract analogue of special conformal transformations. Standard effective field theory arguments suggest that the definition of a gravity theory should implement this duality between General Relativity and Shape Dynamics, thus the name “Doubly General Relativity.” We briefly discuss several consequences: bulk/bulk- duality in classical gravity, experimental falsification of Doubly General Relativity and possible implications for the renormalization of quantum gravity in the effective field theory framework.

Superluminal neutrinos from special relativity with de sitter spacetime symmetry

Abstract: We explore the recent OPERA experiment of superluminal neutrinos in the framework of special relativity with de Sitter spacetime symmetry (dS-SR). According to Einstein, a photon is treated as a massless particle in the framework of special relativity. In special relativity (SR) we have the universal parameter c, the photon velocity cphoton and the phase velocity of a light wave in vacuum cwave = λν. Due to the null experiments of Michelson–Morley we have c = cwave. The parameter cphoton is determined by the Noether charges corresponding to the spacetime symmetries of SR. In Einstein's special relativity (E-SR) we have c = cphoton. In dS-SR, i.e. the special relativity with SO(4, 1) de Sitter spacetime symmetry, we have cphoton > c. In this paper, the OPERA datum are examined in the framework of dS-SR. We show that OPERA anomaly is in agreement with the prediction of dS-SR with R≃1.95×1012 l.y. Based on the p-E relation of dS-SR, we also prove that the Cohen and Glashow's argument of possible superluminal neutrino's Cherenkov-like radiation is forbidden. We conclude that OPERA and ICARUS results are consistent and they are explained in the dS-SR framework.

Special Relativity over the Field of Rational Numbers

Abstract: We investigate the question: what structures of numbers (as physical quantities) are suitable to be used in special relativity? The answer to this question depends strongly on the auxiliary assumptions we add to the basic assumptions of special relativity. We show that there is a natural axiom system of special relativity which can be modeled even over the field of rational numbers.

On special relativity teaching using modern experimental data

Abstract: A new methodological approach to the study of relativistic space-time properties is proposed based on the 20th century's vast experimental research on relativistic accelerator and cosmic ray particles. This approach vividly demonstrates that relativistic effects are the manifestation of fundamental space-time properties and refutes the false notion that relativity is only of relevance to light phenomena.

Theories of Gravitation in the Twilight of Classical Physics

Abstract: More than is the case for any other theory of modern physics, general relativity is usually seen as the work of one man, Albert Einstein. In taking this point of view, however, one tends to overlook the fact that gravitation has been the subject of controversial discussion since the time of Newton. That Newton’s theory of gravitation assumes action at a distance, i.e., action without an intervening mechanism or medium, was perceived from its earliest days as being problematical. Around the turn of the last century, in the twilight of classical physics, the problems of Newtonian gravitation theory had become more acute, also due to the rise of field theory suggesting alternative perspectives. Consequently, there was a proliferation of alternative theories of gravitation which were quickly forgotten after the triumph of general relativity. Yet in order to understand this triumph, it is necessary to compare general relativity to its contemporary competitors. General relativity owes much to this competition. The proliferation of theories of gravitation provides an exemplary case for studying the role of alternative pathways in the history of science. Thus, from this perspective, the emergence of general relativity constitutes an ideal topic for addressing longstanding questions in the philosophy of science on the basis of detailed historical evidence.

De Sitter Relativity: a Natural Scenario for an Evolving Λ

Abstract: In de Sitter special relativity, spacetime translations are replaced by a combination of translations and proper conformal transformations. As a consequence, the energy-momentum current is replaced by a combination of ordinary energy-momentum and proper conformal currents. Whereas the ordinary energy-momentumtensor remains to be a dynamic source of the spacetime curvature, the proper conformal current appears as a kinematic source of Λ. The de Sitter special relativity, therefore, allows for a new interpretation of dark energy as an entity encoded in the kinematic group of spacetime. Furthermore, since ordinary energy is allowed to transform into dark energy and vice versa, it provides a natural scenario for an evolving cosmological term. A qualitative discussion on how a Λ-evolving universe would behave is presented.

Symmetry, causal structure and superluminality in Finsler spacetime

Abstract: The superluminal behaviors of neutrinos were reported by the OPERA collaboration recently. It was also noticed by Cohen and Glashow that, in standard quantum field theory, the superluminal neutrinos would lose their energy via the Cherenkov-like process rapidly. Finslerian special relativity may provide a framework to cooperate with the OPERA neutrino superluminality without Cherenkov-like process. We present clearly the symmetry, causal structure and superluminality in Finsler spacetime. The principle of relativity and the causal law are preserved. The energy and momentum are well defined and conserved in Finslerian special relativity. The Cherenkov-like process is proved to be forbidden kinematically and the superluminal neutrinos would not lose energy in their distant propagations from CERN to the Gran Sasso Laboratory. The energy dependence of neutrino superluminality is studied based on the reported data of the OPERA collaboration as well as other groups.

A note on "Einstein's special relativity beyond the speed of light by James M. Hill and Barry J. Cox"

Abstract: We show that the transformations J. M. Hill and B. J. Cox introduce between inertial observers moving faster than light with respect to each other are consistent with Einstein's principle of relativity only if the spacetime is 2 dimensional.

Existence of faster than light signals implies hypercomputation already in special relativity

Abstract: Within an axiomatic framework, we investigate the possibility of hypercomputation in special relativity via faster than light signals. We formally show that hypercomputation is theoretically possible in special relativity if and only if there are faster than light signals.

On singular lagrangians and Dirac's method

Abstract: We show some instances of singular lagrangians from the classical mechanics of particles and apply Dirac’s method for building the canonical equations. We find then the reason for the singularity, and therefore, we get the Hamilton equations with the familiar procedure, that is without the need of Dirac’s procedure. Known cases of singular lagrangians in special relativity are also presented, and their non-singular alternatives.

The Boltzmann equation in special and general relativity

Abstract: Relativistic field equations for a gas in special and general relativity are determined from the Boltzmann equation The constitutive equations are obtained from the Chapman-Enskog methodology applied to a relativistic model equation proposed by Anderson and Witting Two applications in general relativity are considered: one refers to a gas in a homogeneous and isotropic Universe where irreversible processes are present during its evolution; in the other it is analyzed a gas under the influence of a spherically symmetrical non-rotating and uncharged source of the gravitational field

Gravity, a Geometrical Course: Volume 1: Development of the Theory and Basic Physical Applications

Abstract: Acknowledgement -- Preface -- Special Relativity: setting the stage.- Manifolds and fibre bundles -- Connections and Metrics -- Motion in the Schwarzschild Field -- Einstein versus Yang Mills Field Equations -- Stellar Equilibrium -- Gravitational Waves and the Binary Pulsars -- Conclusion of volume 1 -- Appendix A: Spinors and Gamma Matrix Algebra -- Appendix B: Mathematica Packages -- Index.

Cherenkov radiation versus X-shaped localized waves: reply

Abstract: Our aim in this paper is a reply to Seshadri’s comments [J. Opt. Soc. Am. A29, 2532 (2012)] on a previous article of ours, titled “Cherenkov radiation versus X-shaped localized waves” [J. Opt. Soc. Am. A27, 928 (2010)], as well as to his more extended criticism of the extended special relativity theory, called by him nonrestricted relativity, and in particular of the extended Maxwell equations.

Designing learning scenarios for a 3D virtual environment: The case of special relativity

Abstract: Special Relativity, as introduced by Einstein, is regarded as one of the most important revolutions in the history of physics. Nevertheless, the observation of direct outcomes of this theory on mundane objects is impossible because they can only be witnessed when travelling at relative speeds approaching the light velocity c. These effects are so counterintuitive and contradicting with our daily understanding of space and time that physics students find it hard to learn special relativity beyond mathematical equations and to understand the deep implications of the theory. Although we cannot travel at the speed of light, Virtual Reality (VR) makes it possible to experiment the effects of relativity in a 3D immersive environment (a CAVE: Cave Automatic Virtual Environment). The use of the immersive environment is underpinned by the development of dedicated learning scenarios created through a dialectic between VR-related computational constraints and cognitive constraints that include students' difficulties. Investigating student's understanding of relativistic situations (that involve relative speeds close to c) led to the typifying of a cognitive profile that governed the situations to be implemented into the CAVE and the associated learning scenarios.

Understanding Information and Computation: From Einstein to Web Science

Abstract: Contents: Foreword, Yorick Wilks Foreword. L.J. Rich Preface Introduction Dot-to-dots point the way Hitler, Turing and quantum mechanics A different perspective on numbers, straight lines and other such mathematical curiosities Twists, turns and nature's preference for curves Curves of curves To process or not? Information and computation as a field Why are conic sections important? The gifts that Newton gave, Turing opened and which no chapter one has really appreciated yet Einstein's torch bearers Special relativity General relativity Beyond the fourth dimension Time to reformulate with a little help from information retrieval research Supporting evidence Where does this get us? References Index.

Translating cosmological special relativity into geometric algebra

Abstract: Geometric algebra and Clifford algebra are important tools to describe and analyze the physics of the world we live in. Although there is enormous empirical evidence that we are living in four dimensional spacetime, mathematical worlds of higher dimensions can be used to present the physical laws of our world in an aesthetical and didactical more appealing way. In physics and mathematics education we are therefore confronted with the question how these high dimensional spaces should be taught. But as an immediate confrontation of students with high dimensional compactified spacetimes would expect too much from them at the beginning of their university studies, it seems reasonable to approach the mathematics and physics of higher dimensions step by step. The first step naturally is the step from four dimensional spacetime of special relativity to a five dimensional spacetime world. As a toy model for this artificial world cosmological special relativity, invented by Moshe Carmeli, can be used. This five dimensional non-compactified approach describes a spacetime which consists not only of one time dimension and three space dimensions. In addition velocity is regarded as a fifth dimension. This model very probably will not represent physics correctly. But it can be used to discuss and analyze the consequences of an additional dimension in a clear and simple way. Unfortunately Carmeli has formulated cosmological special relativity in standard vector notation. Therefore a translation of cosmological special relativity into the mathematical language of Grassmann and Clifford (Geometric algebra) is given and the physics of cosmological special relativity is discussed.