61. Chapter 8: General Relativity Chapter 8 general relativity. general relativity attacks this problemand in so doing, discovers that gravity is related to geometry. http://astsun.astro.virginia.edu/~jh8h/Foundations/chapter8.html

Foundations of Modern Cosmology Previous Chapter Table of Contents Next Chapter Chapter 8: General Relativity Chapter Summary Tidal forces prevent a perfect equivalence of freefall and gravity. If the gravitational field diverges over the size of an object, the various parts of the object will be pulled by different amounts or in different directions. These differential effects are known as tidal forces. The equivalence principle requires only that the size of the inertial frame be sufficiently small that tidal forces are negligible. General Relativity predicts the bending of light by gravity, gravitational time dilation and length contraction, gravitational redshifts and blueshifts, the precession of Mercury's orbit, and the existence of gravitational radiation. All these effects have been measured, although gravitational radiation has been observed only indirectly via the decay of the orbits of binary pulsars. The LIGO project is an attempt to build a giant Michelson-Morley type of interferometer to detect gravitational radiation directly. Two interferometers will be built, each one with perpendicular light-carrying vacuum pipes 5 kilometers long. Figure 8.11

62. Physics 7 Page undergraduate course notes include both special relativity (e.g., spacetime, Lorentz invariance, various paradoxes ) and general relativity (e.g., equivalence principle, black holes, gravitational waves, experimental tests of gtr). Apparently a survey course for nonmajors, with little math but some very nice graphics. http://phyun5.ucr.edu/~wudka/physics7.html

The Physics 7 Page Poll results Syllabus Course Info Course Notes ... Final grades Send e-mail to Jose Wudka. UCR Class Schedule utility This page has been accessed times.

63. Riemannian Geometry And General Relativity Riemannian Geometry and general relativity. (Differential Geometry2, MTH 3412, Winter1997 ). Professor M.Shubin. 2. General Theory of Relativity, by PAM.Dirac. http://mystic.math.neu.edu/courses/diffgeom/intro.htm

Riemannian Geometry and General Relativity (Differential Geometry-2, MTH 3412, Winter 1997 ) Professor M.Shubin Course Description: Riemannian geometry is designed to describe the universe of creatures who live on a curved surface or in a curved space and do not know about the world of higher dimensions or do not have any access to it. One of the main notions of the Riemannian geometry is the notion of connection, which is, in fact, the key notion of the entire geometry, though it is not always explicitly formulated. The connection (or parallel transport) allows to compare what is happening at two distant points of a curved space, in spite of the fact that there is no direct and immediate way to communicate between these points. Recently connections appeared in the theory of gauge fields which is considered a basis of the modern physics of elementary particles. Earlier, in the 1910's, A.Einstein discovered that the Riemannian geometry can be successfully used to describe General Relativity which is in fact a classical theory of gravitation. (Here the word ``classical" stands as opposite to ``quantum", but the quantum theory of gravitation is still terra incognita!) By its intrinsic beauty, as well as by wealth of applications the Riemannian geometry lies at the core of modern mathematics.

64. Spacetime 101 some basic background covering how mathematical models of space and time have evolved since ancient times, from the Pythagorean Rule to Newtonian mechanics, Special Relativity and general relativity. http://www.theory.caltech.edu/people/patricia/st101.html

Here's some basic background covering how mathematical models of space and time have evolved since ancient times, from the Pythagorean Rule to Newtonian mechanics, Special Relativity and General Relativity. What is spacetime? Why was Einstein's Special Theory of Relativity needed? How does Einstein's Special Theory of Relativity work? What is "causality" and what does it have to do with time travel? ... Go back to Time Travel in Flatland.

65. MIT Physics Department -- General Relativity And Cosmology general relativity and Cosmology. CTP physicists have also been asking whetherit is possible to use general relativity to build time machines. http://web.mit.edu/physics/research/general_relativity_cosmology.htm

Physics Research at MIT Astrophysics Atomic, Molecular, and Optical Physics Biological and Medical Physics ... Elementary Particle Physics Experimental: Collider Experiments Particle Physics and Astrophysics Theory: Field Theory String Theory and Gravitation General Relativity and Cosmology Quantum Statistical Mechanics ... Research Centers and Facilities General Relativity and Cosmology CTP physicists have been using general relativity to ask fundamental questions about cosmology and the structure of space-time. One question recently addressed is: "Is it possible to build a universe in the laboratory?" The present view of the observable universe holds that it started as a very tiny (and very dense) region of space with a total mass of just a few kilograms. It is possible to imagine engineering a region of space-time so that it inflates into a large region much like our present universe; however, it appears that this cannot actually be done, at least in the context of classical general relativity. If quantum mechanical effects are included, though, the answer is not certain and still bears investigating. CTP physicists have also been asking whether it is possible to use general relativity to build time machines. The impetus for this work is that cosmic string solutions do exist for Einstein's equations that include time machines. The physical question is whether these solutions represent machines that actually can be assembled and used for time travel. The answer is no, but the investigation has shed a great deal of light on the workings of general relativity.

66. Einstein An introduction to general relativity http://math.ucr.edu/home/baez/einstein/einstein.html

Next: Introduction The Meaning of Einstein's Equation John C. Baez Department of Mathematics, University of California Riverside, California 92521 USA email: baez@math.ucr.edu March 10, 2001 Also available in Postscript. Abstract: This is a brief introduction to general relativity, designed for both students and teachers of the subject. While there are many excellent expositions of general relativity, few adequately explain the geometrical meaning of the basic equation of the theory: Einstein's equation. Here we give a simple formulation of this equation in terms of the motion of freely falling test particles. We also sketch some of its consequences, and explain how the formulation given here is equivalent to the usual one in terms of tensors. Finally, we include an annotated bibliography of books, articles and websites suitable for the student of relativity. Introduction Preliminaries Einstein's Equation Some Consequences ... home

67. The Net Advance Of Physics The Net Advance of Physics general relativity. general relativity GeneralDefinitions Weisstein 98/06;; General Introductory Baez 96/02; Léon 98;; http://web.mit.edu/redingtn/www/netadv/Xgenerrela.html

The Net Advance of Physics: GENERAL RELATIVITY GENERAL RELATIVITY: General: Definitions: Weisstein 98/06; General: Introductory: Baez 96/02; General: Textbooks: Modern Relativity Page; Brown no date; Carroll 97/12; Siegel 99/12; General: Brown (homepage); Bicak 2000/04; Baez 2001/03; General: ALGEBRAIC COMPUTING: Lake 98/03; Toussaint 2001/05; General: EXPERIMENTAL/OBSERVATIONAL: Will 98/11; Damour 99/04; General: EXPERIMENTAL/OBSERVATIONAL: BLACK HOLES; GRAVITATIONAL RADIATION; General: EXPERIMENTAL/OBSERVATIONAL: Re: NEUTRINOS: Leung 2000/02; General: EXPERIMENTAL/OBSERVATIONAL: Re: PULSARS: Damour 97/11; General: ANALOGUES: Visser 2001/11; General: FIELD EQUATIONS: Chrusciel 98/03; Frank 2002/03; General: FIELD EQUATIONS: EXISTENCE THEOREMS: Rendall 98/01; General: FIELD EQUATIONS: HYPERBOLIC METHODS: Reula 98/01; General: INTEGRATION: DeBenedictis 98/02; General: NUMERICAL RELATIVITY: Anninos et al. 95; Anninos 98/01; Winicour 98/03; Seidel 98/06; ... Lehner 2001/06; General: NUMERICAL RELATIVITY: Re: BLACK HOLES: Masso 94/12;

68. Ingenta Select Similar pages Analog models of general relativityWebsite for the Workshop on Analog Models for general relativity, contains linksto articles related to the talks, transparencies from the talks, information http://www.catchword.com/titles/00017701.htm

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69. Jean-Luc's General Relativity Glossary general relativity Glossary JeanLuc's general relativity Glossary. AAcceleration. B BaryonMass; BrillWaves. C Constraints. D E F 3+1-Formalism.G http://jean-luc.aei-potsdam.mpg.de/Glossary/

General Relativity Glossary Jean-Luc's General Relativity Glossary A Acceleration B BaryonMass ... Z

70. Wald, Robert M.: General Relativity Wald, Robert M. general relativity, university press books, shopping cart, newrelease notification. Wald, Robert M. general relativity. xiv, 492 p. 1984. http://www.press.uchicago.edu/cgi-bin/hfs.cgi/00/2499.ctl

Go to ... Full text search Excerpts Subject catalogs Subject index ... Shopping cart contents or Print an order form Wald, Robert M. General Relativity . xiv, 492 p. 1984 LC: 83017969 Class: QC173.6 Paper $37.00tx 0-226-87033-2 "Wald's book is clearly the first textbook on general relativity with a totally modern point of view; and it succeeds very well where others are only partially successful. The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."S. Chandrasekhar "A tour de force : lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."L. P. Hughston, Times Higher Education Supplement "Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."James W. York, Physics Today Subjects: Physical Sciences: Theoretical Physics Physical Sciences: Astronomy and Astrophysics The University of Chicago Press You may purchase this title at these fine bookstores . Outside the USA, consult our

71. General Relativity General Theory of Relativity. Just as moving clocks run slow, GeneralRelativity predicts that clocks in gravitational fields run slow. http://www.upscale.utoronto.ca/GeneralInterest/Harrison/GenRel/GenRel.html

General Theory of Relativity Click here to go to the UPSCALE home page. Click here to go to the JPU200Y home page. Click here to go to the Physics Virtual Bookshelf. Einstein's Special Theory of Relativity of 1905 concerns itself with observers who are in uniform relative motion. His General Theory of Relativity of 1916 considers observers in any state of relative motion including acceleration. It will turn out that this will also be a theory of gravitation. This document introduces the General Theory of Relativity. Three "Easy" Pieces Einstein used three different pieces to built the General Theory of Relativity, which we describe here. Piece 1 - Geometry is Physics Consider the figure to the right, which shows a distant star, the Sun, and the Earth. Clearly the figure is not drawn to scale. There is a straight dotted line connecting the star and the Earth. Imagine a light ray that leaves the star along the dotted line: it is headed directly for the Earth. However, we know that E = m c . And since the light that left the star has energy, we now know that it also has a mass. And

72. General Relativity general relativity. Einstein provided the resolution around 1915 with a newtheory of gravitation, which he called the general theory of relativity. http://www.theory.caltech.edu/people/jhs/strings/str113.html

General Relativity Einstein was not content with the special theory of relativity, because it was in contradiction with Newton's theory of gravitation. Newtonian gravitation was a very successful theory. In particular, it accounted for the motion of the planets to high precision. However, it has a peculiar property that had even bothered Newton. It implies instantaneous transmission of the gravitation force between two objects across great distances. Einstein knew this had to be wrong, because special relativity implies that no signal can be transmitted faster than the speed of light. Einstein provided the resolution around 1915 with a new theory of gravitation, which he called the general theory of relativity. It agrees with the Newtonian theory for low speeds and weak gravitational fields, but differs from it at high speeds and strong fields. The theory had several immediate observational successes. First it implied a small correction to the orbit of the planet Mercury that accounted for a small discrepancy between the orbit implied by the Newtonian theory and the observed orbit. (The effect is too small to be observed for the other planets.) Second, it predicted that light from a distant star passing near to the limb of sun would be bent by a small but measurable angle. The measurement was made by Eddington during a solar eclipse.

73. Smaller Programs Tests Of General Relativity Smaller Programs Optical Companions and Bow Shocks. Smaller ProgramsTests of general relativity. Spiral in of double neutron stars 10 http://www.jb.man.ac.uk/~pulsar/research/jodsum/node13.html

74. Quantum Mechanics Versus General Relativity Quantum Mechanics versus general relativity. The classical hypothesis of Einsteinwas general relativity is more fundamental than Quantum theory. http://www.berlinet.de/schmelzer/PG/QMvsGR.html

Quantum Mechanics versus General Relativity Which of these two theories is the more fundamental theory? The classical hypothesis of Einstein was: General Relativity is more fundamental than Quantum theory The majority of attempts to create a quantum gravity has been based on this assumption. In our concept for the quantization of gravity we propose here the reverse principle: Principle of the Priority of Quantum Mechanics The principle of the Priority of Quantum Mechanics is: Quantum theory is more fundamental than General Relativity. Our scheme of quantization may be described as a natural consequence of the application of this principle. Argumentation There are a lot of arguments for this point of view. Until now, we have already had some contradictions between the principles of GR and QM where the question was solved by experiment or theoretical considerations. In every case the winner of the competition seems to be QM: The general question if quantization of gravity is necessary Bell's theorem Superluminal tunneling speed After Einstein, the basic principles of QM have been better understood. Remember only Path integral formulations.

75. Time In General Relativity Time in general relativity. In the ideology of special and general relativity,only time measurement by clocks will be considered Time Measurement. http://www.berlinet.de/schmelzer/PG/timeGR.html

Time in General Relativity Let's consider now relativistic theory. In the ideology of special and general relativity, only time measurement by clocks will be considered: Time Measurement The path-dependent time of GR defined by has the following properties: It depends on the physical state (the gravitational field). Already for the case of quantum theory on a fixed background metric it becomes uncertain, because the path of a quantum particle is uncertain. Thus, it is obviously the realization of the concept of time measurement Present Time The present time is not considered in standard general relativity. But does this mean that there cannot be a present time? I think not. The notion of present time is simply outside the theory. It will be considered as something like God, life or conciousness. The formal reason not to consider present time is that there is no measurement procedure to detect absolute contemporaneity of events. But this reason fails, because measurability is not a property of the concept of present time. There are two concepts in GR which may be considered as a realization of present time in GR: Families of space-like surfaces.

76. New Observations Of Black Holes Confirm General Relativity Sir Isaac Newton (right) could never have dreamed of the beauty and complexityof general relativity developed by Einstein (left), much less our ability to http://science.msfc.nasa.gov/newhome/headlines/ast06nov97_1.htm

Einstein was right...again!!! Satellite observations of Black Holes confirm frame-dragging effect 80 years after prediction November 6, 1997: T he next time you feel like you're barely dragging along, blame relativity. You'll be stretching the point, but it appears that Einstein was right: space and time get pulled out of shape near a rotating body. Einstein predicted the effect, called ``frame dragging,'' 80 years ago. Like many other aspects of Einstein's famous theories of relativity, it's so subtle that no conventional method could measure it. Using recent observations by X-ray astronomy satellites, including NASA's Rossi X-ray Timing Explorer , a team of astronomers is announcing that they see evidence of frame dragging in disks of gas swirling around a black hole. The discovery will be announced today at a meeting of the High Energy Astrophysics Division of the American Astronomical Society in Estes Park, Colo., by Dr. Wei Cui of the Massachusetts Institute of Technology, and his colleagues, Dr. Nan Zhang

77. General Relativity Around The World general relativity around the world. Relativity Servers. NCSA Relativity Group;Gravitational Physics Relativity Aristotle University of Thessaloniki. http://www.astro.auth.gr/Science-Subjects/Gravity/Gravity_Links1.html

General Relativity around the world Relativity Servers NCSA Relativity Group Aristotle University of Thessaloniki. HyperSpace at QMW Malcolm MacCallum's Server Center for Relativity at Austin, Texas. Center for Gravitational Physics and Geometry , Penn State University. Pittsburgh Relativity Group University of Pittsburgh. Cardiff Relativity Group University of Wales, College of Cardiff. Hyperspace at UBC University of British Columbia. Mathematical Relativity Australian National University Southhampton Relativity Gopher University of Southhampton. LIGO California and Massachusetts Institutes of Technology Balearic Islands University. SIGRAV CIAR Cosmology Program Canadian Institute of Advanced Research Tufts Institute of Cosmology Syracuse University Relativity Group University of New Brunswick Relativity Montana State University Physics Department University of Maryland Physics Department Imperial College of Science, Technology and Medicine University of British Columbia Hyperspace at UBC Pisa-VIRGO Interferometer Home Page Wake Forest University Univeristy of Newcastle Relativity and Quantum Fields Relativistic Movies (Tuebingen) LSU Gravity Wave Experiment Home Page GR : Hyperspace Form interface to search MacCallum's lists.

78. Remarks On General Relativity Remarks on general relativity. Michael Fowler University of Virginia. GeneralRelativity and the Global Positioning System. Despite http://www.phys.virginia.edu/CLASSES/252/general_relativity.html

Remarks on General Relativity Michael Fowler University of Virginia Physics 252 Home Page Link to Previous Lecture Relativity: the Special and the General Theory , he introduces general relativity with a parable. He imagines going into deep space, far away from gravitational fields, where any body moving at steady speed in a straight line will continue in that state for a very long time. Einstein points out that there will be no gravity, the observer will tend to float around inside the room. How does all this look to the man in the room? If he releases anything, it accelerates towards the floor, and in fact all bodies accelerate at the same rate. Just then he would discover the hook and rope, and conclude that the room was suspended by the rope. Einstein asks: should we just smile at this misguided soul? In other words, being inside the (from an outside perspective) uniformly accelerating room is physically equivalent to being in a uniform gravitational field This is the basic postulate of general relativity. Special relativity said that all inertial frames were equivalent.

79. Tests Of General Relativity. Tests of general relativity. Since 1916 there have been many measurements whichagree with the General Theory of Relativity to the available accuracy. http://phyun5.ucr.edu/~wudka/Physics7/Notes_www/node97.html

Next: Precession of the perihelion Up: The General Theory of Previous: Summary. Tests of general relativity. After Einstein first published the General Theory of Relativity there was a very strong drive to test its consequences; Einstein himself used his equations to explained a tiny discrepancy in the motion of Mercury. Yet he most dramatic effect was the shifting of the positions of the stars (see below). Since 1916 there have been many measurements which agree with the General Theory of Relativity to the available accuracy. Here I will concentrate on the ``classical'' tests of the thoery. Precession of the perihelion of Mercury Gravitational red-shift. Light bending The double pulsar Jose Wudka

80. International Society On General  Relativity GR16, International Society on general relativity Gravitation. 16th InternationalConference 15 21 July 2001, Durban, South Africa http//www.gr16.nu.ac.za. http://www.gr16.nu.ac.za/

International Society on General Relativity 16th International Conference 15 - 21 July 2001, Durban, South Africa http://www.gr16.nu.ac.za First Circular Second Circular Programme Update Registration ... Transportation The Sixteenth meeting of the International Society on General Relativity and Gravitation (GR16) will be held from 15 - 21 July, 2001 at the International Convention Centre, Durban, South Africa. The main purpose of the triennal GR meetings is to provide a platform to relativists, cosmologists, astrophysicists and mathematicians for exchange of ideas, review of recent developments, planning of future projects and for fostering international interactions in the area of general relativity and gravitation. We wish to bring to your attention that the Amaldi Conference on Gravitional Waves takes place from 8 - 13 July 2001 in Perth, Australia. So it is possible to attend both the GR16 Conference and the Amaldi Conference. Information regarding the Amaldi Conference can be found at: http://www.gravity.uwa.edu.au/amaldi/amaldi.htm

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