Introduction to Special Relativity

Introduction to Special Relativity tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn về tất cả các lĩ...

Int. J. Med. Sci. 2009, 6 http://www.medsci.org 116IInntteerrnnaattiioonnaall JJoouurrnnaall ooff MMeeddiiccaall SScciieenncceess 2009; 6(3):116-117 © Ivyspring International Publisher. All rights reserved Editorial Introduction to special issue on Eye and Zoonosis – from the guest editors Jelka G. ORSONI and Paolo MORA  Inflammatory and Autoimmune Ocular Diseases Service - Institute of Ophthalmology - University of Parma - Italy  Correspondence to: Dr. Paolo MORA, Inflammatory and Autoimmune Ocular Diseases Service - Institute of Ophthal-mology - University of Parma – Italy. E-mail: paolo.mora@unipr.it Published: 2009.03.19 Abstract Papers of this special issue are based on the presentations given in the Congress “Eye and Zoonosis” - October 10-11th 2008, Parma (Italy). This issue aims to provide researchers with timely update on a number of important topics on Zoonosis in Ophthalmology. On the occasion of the first International Con-gress on Ocular Zoonoses held in Lausanne, Switzer-land in 2006, we were asked by the promoter, Dr. Yan Guex-Crosier, to organize the second Congress in Parma, Italy. It was a great pleasure for us to accept this invitation. We do believe that every ophthalmologist cop-ing with inflammatory eye diseases, either because specifically working on inflammation or because in-flammation has been observed by chance during an ocular examination performed for other purposes, must be aware of zoonotic diseases that affect the eye. This Congress held in Parma during two half-day sessions could not cover all zoonoses; con-sequently, only those most frequently observed in the European/Mediterranean area were dealt with. Zoonoses may be imported by immigrants, who represent a relatively recent phenomenon in Italy; but also travellers coming back from endemic areas are transmitting diseases hitherto unknown or forgotten in our own countries. Moreover, it must be remem-bered that our domestic animals can also be trans-mitters of zoonoses. If our pets, such as dogs and cats, are correctly cared for, they will not represent a res-ervoir for ticks, fleas and other potential vectors. Ocular zoonoses can no longer be ignored; every ophthalmologist, working on his own or in a public institution must remember that a red eye or a vitriitis or retinitis without any current explanation might be due to a disease transmitted by arthropod vectors from foreign countries or by animals. Correct information on this subject will prove extremely useful to our patients, avoiding severe consequences of ocular function. Contents of this special issue are based on the presentations given in the Congress “Eye and Zoono-sis” - October 10-11th 2008, Parma (Italy). They in-clude: • Incidence of ocular Zoonoses referred to the In-flammatory and Autoimmune Ocular Diseases Service of the University of Parma (Italy) • Introduction into Pathology of Ocular Zoonoses • Local epidemiology and clinical manifestations of Lyme disease • Ocular manifestations of Lyme borreliosis in Europe • Ocular manifestations of Rickttesiosis: 1. Medi-terranean Spotted Fever: laboratory analysis and case reports • Ocular manifestations of Rickttesiosis: 2. Retinal involvement and treatment • Ocular Toxocariasis • Ocular Bartonellosis • Human toxoplasmosis and the role of veterinary clinicians • Laboratory diagnosis of Toxoplasma gondii in-fection • Congenital and acquired Toxoplasmosis (The content of Dr Brezin's presentation has been published in the December 2008 issue of the Introduction to Special Relativity Introduction to Special Relativity Bởi: OpenStaxCollege Special relativity explains why traveling to other star systems, such as these in the Orion Nebula, is unreasonable using our current level of technology (credit: s58y, Flickr) Have you ever looked up at the night sky and dreamed of traveling to other planets in faraway star systems? Would there be other life forms? What would other worlds look like? You might imagine that such an amazing trip would be possible if we could just travel fast enough, but you will read in this chapter why this is not true In 1905 Albert Einstein developed the theory of special relativity This theory explains the limit on an object’s speed and describes the consequences Relativity The word relativity might conjure an image of Einstein, but the idea did not begin with him People have been exploring relativity for many centuries Relativity 1/2 Introduction to Special Relativity is the study of how different observers measure the same event Galileo and Newton developed the first correct version of classical relativity Einstein developed the modern theory of relativity Modern relativity is divided into two parts Special relativity deals with observers who are moving at constant velocity General relativity deals with observers who are undergoing acceleration Einstein is famous because his theories of relativity made revolutionary predictions Most importantly, his theories have been verified to great precision in a vast range of experiments, altering forever our concept of space and time Many people think that Albert Einstein (1879–1955) was the greatest physicist of the 20th century Not only did he develop modern relativity, thus revolutionizing our concept of the universe, he also made fundamental contributions to the foundations of quantum mechanics (credit: The Library of Congress) It is important to note that although classical mechanic, in general, and classical relativity, in particular, are limited, they are extremely good approximations for large, slow-moving objects Otherwise, we could not use classical physics to launch satellites or build bridges In the classical limit (objects larger than submicroscopic and moving slower than about 1% of the speed of light), relativistic mechanics becomes the same as classical mechanics This fact will be noted at appropriate places throughout this chapter 2/2 INTRODUCTION TO GENERAL RELATIVITY G. ’t Hooft CAPUTCOLLEGE 1998 Institute for Theoretical Physics Utrecht University, Princetonplein 5, 3584 CC Utrecht, the Netherlands version 30/1/98 PROLOGUE General relativity is a beautiful scheme for describing the gravitational field and the equations it obeys. Nowadays this theory is often used as a prototype for other, more intricate constructions to describe forces between elementary particles or other branches of fundamental physics. This is why in an introduction to general relativity it is of importance to separate as clearly as possible the various ingredients that together give shape to this paradigm. After explaining the physical motivations we first introduce curved coordinates, then add to this the notion of an affine connection field and only as a later step add to that the metric field. One then sees clearly how space and time get more and more structure, until finally all we have to do is deduce Einstein’s field equations. As for applications of the theory, the usual ones such as the gravitational red shift, the Schwarzschild metric, the perihelion shift and light deflection are pretty standard. They can be found in the cited literature if one wants any further details. I do pay some extra attention to an application that may well become important in the near future: gravitational radiation. The derivations given are often tedious, but they can be produced rather elegantly using standard Lagrangian methods from field theory, which is what will be demonstrated in these notes. LITERATURE C.W. Misner, K.S. Thorne and J.A. Wheeler, “Gravitation”, W.H. Freeman and Comp., San Francisco 1973, ISBN 0-7167-0344-0. R. Adler, M. Bazin, M. Schiffer, “Introduction to General Relativity”, Mc.Graw-Hill 1965. R. M. Wald, “General Relativity”, Univ. of Chicago Press 1984. P.A.M. Dirac, “General Theory of Relativity”, Wiley Interscience 1975. S. Weinberg, “Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity”, J. Wiley & Sons. year ??? S.W. Hawking, G.F.R. Ellis, “The large scale structure of space-time”, Cambridge Univ. Press 1973. S. Chandrasekhar, “The Mathematical Theory of Black Holes”, Clarendon Press, Oxford Univ. Press, 1983 Dr. A.D. Fokker, “Relativiteitstheorie”, P. Noordhoff, Groningen, 1929. 1 J.A. Wheeler, “A Journey into Gravity and Spacetime, Scientific American Library, New York, 1990, distr. by W.H. Freeman & Co, New York. CONTENTS Prologue 1 literature 1 1. Summary of the theory of Special Relativity. Notations. 3 2. The E¨otv¨os experiments and the equaivalence principle. 7 3. The constantly accelerated elevator. Rindler space. 9 4. Curved coordinates. 13 5. The affine connection. Riemann curvature. 19 6. The metric tensor. 25 7. The perturbative expansion and Einstein’s law of gravity. 30 8. The action principle. 35 9. Spacial coordinates. 39 10. Electromagnetism. 43 11. The Schwarzschild solution. 45 12. Mercury and light rays in the Schwarzschild metric. 50 13. Generalizations of the Schwarzschild solution. 55 14. The Robertson-Walker metric. 58 15. Gravitational radiation. 62 2 1. SUMMARY OF THE THEORY OF SPECIAL RELATIVITY. NOTATIONS. Special Relativity is the theory claiming that space and time exhibit a particular symmetry pattern. This statement contains two ingredients which we further explain: (i) There is a transformation law, and these transformations form a group. (ii) Consider a system in which a set of physical variables is described as being a correct solution to the laws of physics. Then if all these physical variables are transformed appropriately according to the given transformation law, one obtains a new solution to the laws of physics. A “point-event” is a point in space, given by its three coordinates x =(x, y, z), at a given instant t in time. For short, we will call this a “point” in [...]... 2002 Number-Flux Vector and Stress-Energy Tensor c 2000, 2002 Edmund Bertschinger 1 Introduction These notes supplement Section 3 of the 8.962 notes Introduction to Tensor Calculus for General Relativity. ” Having worked through the formal treatment of vectors, one-forms and tensors, we are ready to evaluate two particularly useful and important examples, the number-flux four-vector and the stress-energy... Spring 2002 Tensor Calculus, Part 2 c 2000, 2002 Edmund Bertschinger 1 Introduction The first set of 8.962 notes, Introduction to Tensor Calculus for General Relativity, discussed tensors, gradients, and elementary integration The current notes continue the discussion of tensor calculus with orthonormal bases and commutators (§2), parallel transport and geodesics (§3), and the Riemann curvature tensor (§4)... a vector is called a unit vector if A A = 1 and similarly for a one-form The four-velocity of a massive particle is a timelike unit vector Now that we have introduced basis vectors and one-forms, we can de ne the contraction of a tensor Contraction pairs two arguments of a rank (m n) tensor: one vector and one one-form The arguments are replaced by basis vectors and one-forms and summed over For example,... ingredients of tensor algebra that we will need in general relativity Before moving on to more advanced concepts, let us re ect on our treatment of vectors, one-forms and tensors The mathematics and notation, while straightforward, are complicated Can we simplify the notation without sacri cing rigor? One way to modify our notation would be to abandon ths basis vectors and one-forms and to work only... )=g ~ ( ): e (43) e e We will refer to ~ as a dual basis vector to contrast it from both the basis vector ~ and the basis one-form e The dots are present in equation (43) to remind us that a ~ one-form may be ✡ ✡ ✡ ✪ ✪ ✪    ✱ ✱ ✱ ✱ ✑ ✑ ✑ ✟ ✟ ❡ ❡ ❡ ❅ ❅ ❅ ❧ ❧ ❧ ◗ ◗ ◗ ❍ ❍    ❳ ❳ ❳ ❤ ❤ ❤ ❤ ✭ ✭ ✭ ✭ ✏ ✏ ✟ IFT Instituto de F´ısica Te´orica Universidade Estadual Paulista An Introduction to GENERAL RELATIVITY R. Aldrovandi and J. G. Pereira March-April/2004 A Preliminary Note These notes are intended for a two-month, graduate-level course. Ad- dressed to future researchers in a Centre mainly devoted to Field Theory, they avoid the ex cathedra style frequently assumed by teachers of the sub- ject. Mainly, General Relativity is not presented as a finished theory. Emphasis is laid on the basic tenets and on comparison of gravitation with the other fundamental interactions of Nature. Thus, a little more space than would be expected in such a short text is devoted to the equivalence principle. The equivalence principle leads to universality, a distinguishing feature of the gravitational field. The other fundamental interactions of Nature—the electromagnetic, the weak and the strong interactions, which are described in terms of gauge theories—are not universal. These notes, are intended as a short guide to the main aspects of the subject. The reader is urged to refer to the basic texts we have used, each one excellent in its own approach: • L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Perg- amon, Oxford, 1971) • C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation (Freeman, New York, 1973) • S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972) • R. M. Wald, General Relativity (The University of Chicago Press, Chicago, 1984) • J. L. Synge, Relativity: The General Theory (North-Holland, Amster- dam, 1960) i Contents 1Introduction 1 1.1 General Concepts . 1 1.2 Some Basic Notions 2 1.3 The Equivalence Principle 3 1.3.1 Inertial Forces . . . 5 1.3.2 The Wake of Non-Trivial Metric . . 10 1.3.3 Towards Geometry 13 2 Geometry 18 2.1 Differential Geometry . . . 18 2.1.1 Spaces . . . 20 2.1.2 Vector and Tensor Fields . . 29 2.1.3 Differential Forms . 35 2.1.4 Metrics . . 40 2.2 Pseudo-Riemannian Metric 44 2.3 The Notion of Connection 46 2.4 The Levi–Civita Connection 50 2.5 Curvature Tensor . 53 2.6 Bianchi Identities . 55 2.6.1 Examples . 57 3 Dynamics 63 3.1 Geodesics . 63 3.2 The Minimal Coupling Prescription 71 3.3 Einstein’s Field Equations 76 3.4 Action of the Gravitational Field . 79 3.5 Non-Relativistic Limit . . 82 3.6 About Time, and Space . 85 3.6.1 Time Recovered . . 85 3.6.2 Space . . . 87 ii 3.7 Equivalence, Once Again . 90 3.8 More About Curves 92 3.8.1 Geodesic Deviation 92 3.8.2 General Observers 93 3.8.3 Transversality . . . 95 3.8.4 Fundamental Observers . . . 96 3.9 An Aside: Hamilton-Jacobi 99 4 Solutions 107 4.1 Transformations . . 107 4.2 Small Scale Solutions . . . 111 4.2.1 The Schwarzschild Solution 111 4.3 Large Scale Solutions . . . 128 4.3.1 The Friedmann Solutions . . 128 4.3.2 de Sitter Solutions 135 5Tetrad Fields 141 5.1 Tetrads . . 141 5.2 Linear Connections 146 5.2.1 Linear Transformations . . . 146 5.2.2 Orthogonal Transformations 148 5.2.3 Connections, Revisited . . . 150 5.2.4 Back to Equivalence 154 5.2.5 Two Gates into Gravitation 159 6 Gravitational Interaction of the Fundamental Fields 161 6.1 Minimal Coupling Prescription . . 161 6.2 General Relativity Spin Connection 162 6.3 Application to the Fundamental Fields . . 164 6.3.1 Scalar Field 164 6.3.2 Dirac Spinor Field 165 6.3.3 Electromagnetic Field . . . 166 7 General Relativity with Matter Fields 170 7.1 Global Noether Theorem . 170 7.2 Energy–Momentum as Source of Curvature 171 7.3 Energy–Momentum Conservation . 173 7.4 Examples . 175 7.4.1 Scalar Field 175 7.4.2 Dirac Spinor Field 176 iii 7.4.3 Electromagnetic Field . . . 177 8 Closing Remarks 179 Bibliography 180 iv Chapter 1 Introduction 1.1 General Concepts Instructor’s Resource Manual and Test Bank for Exceptional Children An Introduction to Special Education Tenth Edition William L.Heward The Ohio State University Prepared by Blanche Jackson Glimps Tennessee University Karen Coughenour Francis Marion University Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo i Copyright © 2013, 2009, 2006, 2003, 2000 by Pearson Education, Inc All rights reserved Manufactured in the United States of America This publication is protected by Copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise To obtain permission(s) to use material from this work, please submit a written request to Pearson Education, Inc., Permissions Department, One Lake Street, Upper Saddle River, New Jersey 07458, or you may fax your request to 201-236-3290 Instructors of classes using Heward’s Exceptional Children: An Introduction to Special Education, 10e, may reproduce material from the resource manual and test bank for classroom use 10 ISBN-10: 0-13-278247-2 ISBN-13: 978-0-13-278247-0 www.pearsonhighered.com i TABLE OF CONTENTS Message to Instructors iv Suggested Speakers, Field Experiences, Student Presentations, and Projects iv Alternative Assessments vi CHAPTER GUIDES Chapter 1: The Purpose and Promise of Special Education Chapter 2: Planning and Providing Special Education Services Chapter 3: Collaborating with Parents and Families in a Culturally and Linguistically Diverse Society 12 Chapter 4: Intellectual Disabilities 18 Chapter 5: Learning Disabilities 24 Chapter 6: Emotional or Behavioral Disorders 29 Chapter 7: Autism Spectrum Disorders 34 Chapter 8: Communication Disorders 39 Chapter 9: Deafness and Hearing Loss 43 Chapter 10: Blindness and Low Vision 48 Chapter 11: Physical Disabilities, Health Impairments, and ADHD 52 Chapter 12: Low-Incidence Disabilities: Severe/Multiple Disabilities, Deaf-Blindness, and Traumatic Brain Injury 57 Chapter 13: Gifted and Talented 61 Chapter 14: Early Childhood Special Education 67 Chapter 15: Transitioning to Adulthood 71 ii TEST BANK Chapter 1: The Purpose and Promise of Special Education 75 Chapter 2: Planning and Providing Special Education Services 83 Chapter 3: Collaborating with Parents and Families in a Culturally and Linguistically Diverse Society 91 Chapter 4: Intellectual Disabilities 99 Chapter 5: Learning Disabilities 102 Chapter 6: Emotional or Behavioral Disorders 114 Chapter 7: Autism Spectrum Disorders 122 Chapter 8: Communication Disorders 130 Chapter 9: Deafness and Hearing Loss 138 Chapter 10: Blindness and Low Vision 146 Chapter 11: Physical Disabilities, Health Impairments, and ADHD 153 Chapter 12: Low-Incidence Disabilities: Severe/Multiple Disabilities, Deaf-Blindness, and Traumatic Brain Injury 161 Chapter 13: Gifted and Talented 169 Chapter 14: Early Childhood Special Education 177 Chapter 15: Transitioning to Adulthood 185 ANSWER KEY 193 iii MESSAGE TO INSTRUCTORS Dear Instructor, Welcome to the instructor’s manual for the 10th edition of the textbook Exceptional Children: An Introduction to Special Education, written by William Heward I have the special and exciting privilege of updating this resource I have used the textbook for many years and continue to be impressed about the quality of the content Although this book is tagged as an “intro” book, it makes for an excellent reference book for any course in special education You will find an impressive amount of supplemental resources and information that can further enhance the course that you are teaching Heward’s book, and this instructor’s manual, will make your students’ learning an enjoyable and .. .Introduction to Special Relativity is the study of how different observers measure the same event Galileo and Newton developed the first correct version of classical relativity Einstein... developed the modern theory of relativity Modern relativity is divided into two parts Special relativity deals with observers who are moving at constant velocity General relativity deals with observers... acceleration Einstein is famous because his theories of relativity made revolutionary predictions Most importantly, his theories have been verified to great precision in a vast range of experiments,