81. Mathematical Physics Mathematical Physics in the Department of Physics and Mathematical Physics. Research areas quantum field theory, string theory, statistical mechanics, theoretical condensed matter. physics, general relativity, quantum gravity and cosmology http://www.physics.adelaide.edu.au/mathphysics/

The University of Adelaide Home Departments Search ... Publications Department of Physics THE UNIVERSITY OF ADELAIDE ADELAIDE, SA 5005 AUSTRALIA Telephone: Facsimile: Mathematical Physics Group We are the Mathematical Physics Group in the Department of Physics and Mathematical Physics of the University of Adelaide We work in diverse areas such as quantum field theory, string theory, statistical mechanics, theoretical condensed matter physics, general relativity, quantum gravity and cosmology, and are involved with the National Institute for Theoretical Physics , the Special Research Centre for the Subatomic Structure of Matter and the Institute for Geometry and its Applications , all based at the University of Adelaide. NEWS: © 2004 The University of Adelaide Last Modified 16/12/2004 Web Master Privacy

82. Early Philosophical Interpretations Of General Relativity These are the principles of equivalence, of general relativity, of general It cannot be denied that general relativity proved a considerable stimulus http://plato.stanford.edu/entries/genrel-early/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A ... Z This document uses XHTML/Unicode to format the display. If you think special symbols are not displaying correctly, see our guide Displaying Special Characters last substantive content change NOV The Encyclopedia Now Needs Your Support Please Read How You Can Help Keep the Encyclopedia Free Early Philosophical Interpretations of General Relativity 1. The Search for Philosophical Novelty 2. Machian Positivism 3. Kantian and Neo-Kantian Interpretations 4. Logical Empiricism ... Related Entries 1. The Search for Philosophical Novelty Extraordinary public clamor greeted an announcement of the joint meeting of the Royal Society of London and the Royal Astronomical Society on the 6th of November, 1919. To within acceptable margin of error, astronomical observations during the solar eclipse the previous May 29 th revealed the displacement of starlight passing near the surface of the sun predicted by Einstein's gravitational theory of curved spacetime. By dint of having "overthrown" such a permanent fixture of the cognitive landscape as Newtonian gravitational theory, the general theory of relativity at once became a principal focus of philosophical interest and inquiry. Although some physicists and philosophers initially opposed it, mostly on non-physical grounds, surveyed here are the principal philosophical interpretations of the theory accepting it as a definite advance in physical knowledge. Even so, these include positions ill-informed as to the mathematics and physics of the theory. Further lack of clarity stemmed from the scientific

83. Ricci: A Mathematica Package For Doing Tensor Calculations In Differential Geome A Mathematica package for doing tensor calculations in differential geometry and general relativity. http://www.math.washington.edu/~lee/Ricci/

Ricci A Mathematica package for doing tensor calculations in differential geometry Version 1.51 Last Updated June 28, 2004 Ricci is a Mathematica package for doing symbolic tensor computations that arise in differential geometry. It has the following features and capabilities: Manipulation of tensor expressions with and without indices Implicit use of the Einstein summation convention Correct manipulation of dummy indices Display of results in mathematical notation, with upper and lower indices Automatic calculation of covariant derivatives Automatic application of tensor symmetries Riemannian metrics and curvatures Differential forms Any number of vector bundles with user-defined characteristics Names of indices indicate which bundles they refer to Complex bundles and tensors Conjugation indicated by barred indices Connections with and without torsion Limitations: Ricci currently does not support computation of explicit values for tensor components in coordinates, or derivatives of tensors depending on parameters (as in geometric evolution equations or calculus of variations), although support for these is planned for a future release. Ricci also has no explicit support for general relativity, or for other mathematical physics or engineering applications, and none is planned. If you are interested in such support, I recommend that you consider the commercial package MathTensor, which is far more extensive than Ricci, and provides all these capabilities and more. MathTensor is available from

84. Einstein, Albert. 1920. Relativity: The Special And General Theory Einstein, Albert. 1920. relativity The Special and general Theory. http://www.bartleby.com/173/

Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia Cultural Literacy World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations Respectfully Quoted English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Nonfiction Albert Einstein Who would imagine that this simple law [constancy of the velocity of light] has plunged the conscientiously thoughtful physicist into the greatest intellectual difficulties? Chap. VII

85. General Relativity One way of stating this fundamental principle of general relativity is to say general relativity predicts an additional 43 seconds of arc and was one of http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/grel.html

Principle of Equivalence Experiments performed in a uniformly accelerating reference frame with acceleration a are indistinguishable from the same experiments performed in a non-accelerating reference frame which is situated in a gravitational field where the acceleration of gravity = g = -a = intensity of gravity field. One way of stating this fundamental principle of general relativity is to say that gravitational mass is identical to inertial mass. One of the implications of the principle of equivalence is that since photons have momentum and therefore must be attributed an inertial mass, they must also have a gravitational mass. Thus photons should be deflected by gravity . They should also be impeded in their escape from a gravity field, leading to the gravitational red shift and the concept of a black hole . It also leads to gravitational lens effects. Index General relativity ideas HyperPhysics Relativity R Nave Go Back Advance of Mercury's Perihelion The perihelion of the orbit of the planet Mercury advances 2 degrees per century. 80 seconds of that advance was accounted for by perturbations from the other planets, etc., but the last 40 seconds of arc were unaccounted for. General relativity predicts an additional 43 seconds of arc and was one of the first triumphs of Einstein's theory.

86. General Relativity Notes By Kristen Wecht Detailed steps on how to Linearize Einstein's field equations of general relativity. http://www.lehigh.edu/~kdw5/project/

General Relativity Tutorials Designed by a Graduate Student for Graduate Students by Kristen Wecht I designed the following general relativity tutorials for beginning graduate students in general relativity. My goal here is to fill in the missing steps between the equations in popular text books on the subject. How to Linearize Einstein's Field Equations (PDF format) How to Construct a Coordinate System That Simplifies the Linearized Field Equations (Work in progress) How to Make Physical Predictions Using the Simplified Linearized Field Equations (Work in progress) Questions or comments? email: Kristen Wecht

87. GrayAlbert A two part overview of the Shapiro radar bounce test of general relativity. (The two parts consist of a section for normal people, and one for nerds) http://world.std.com/~sweetser/PopScience/timeDelay/timeDelay.html

The time delay of radar reflections off of Mercury installation 1995 For Folks It takes a few minutes for light to get to Mercury from Earth, but it takes a little longer due to the Sun. Radar signals from the Haystack Observatory in Westford Massachusetts were sent out into space to bounce off Mercury. The time the radar signals spent flying between the two planets was carefully measured. As the radar's path in space moved closer to the Sun, a small time delay grew in the radar reflections which is given by equations in the big, black book (Gravitation, by Misner, Thorne and Wheeler). Written in chalk is the artist's method to calculate the time delay. The tools used come directly from quantum mechanics which is not supposed to be an aid for such a calculation. Yet the results are the same (equation 40.13). For Nerds Irwin I. Shapiro measured the time delay of radar reflections off Mercury caused by the gravitational field of the Sun. The logarithmic dependence on the impact parameter confirmed general relativity's prediction. The Lorentz group will be employed for a similar end. The gravitational fields for a bound test mass are characterized by a member of the Lorentz group in the following manner: take the Newtonian orbital velocity

88. Concepts Of Special Relativity Conceptual Framework relativity. Index relativity concepts Solvay Conference, 1911 Go Back. Conceptual Framework general relativity. Index http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/conrel.html

Conceptual Framework: Relativity Index Relativity concepts Solvay Conference, 1911 HyperPhysics ... Relativity R Nave Go Back Conceptual Framework: General Relativity Index HyperPhysics Relativity R Nave Go Back

89. Southampton GR Explorer Home Page An introduction to Einstein's theory of general relativity and related topics. These pages include informative text, pictures and movies. http://www.maths.soton.ac.uk/relativity/GRExplorer/

Welcome to the Southampton GR Explorer. On these pages you will find an overview of Einstein's theory of General Relativity and related topics. We focus on subjects that are close to the research interests of the Southampton group. A more technical description of our various ongoing research projects can be found here This site is best viewed with frames, which are not supported by your browser. You can either: or Internet Explorer alternatively Turn the frames off

90. Relativity: The Special And General Theory A Few Inferences from the general Principle of relativity The Structure of Space According to the general Theory of relativity. Appendices http://www.marxists.org/reference/archive/einstein/works/1910s/relative/

Albert Einstein Reference Archive Relativity The Special and General Theory Written: Source: Publisher: First Published: December, 1916 Translated: Robert W. Lawson (Authorised translation) Transcription/Markup: Brian Basgen Copyleft: Einstein Reference Archive (marxists.org) 1999, 2002. Permission is granted to copy and/or distribute this document under the terms of the GNU Free Documentation License Download HTML Download PDF Preface Part I: The Special Theory of Relativity Physical Meaning of Geometrical Propositions The System of Co-ordinates Space and Time in Classical Mechanics The Galileian System of Co-ordinates ... Minkowski's Four-dimensial Space Part II: The General Theory of Relativity Special and General Principle of Relativity The Gravitational Field The Equality of Inertial and Gravitational Mass as an Argument for the General Postulate of Relativity In What Respects are the Foundations of Classical Mechanics and of the Special Theory of Relativity Unsatisfactory? ... The Solution of the Problem of Gravitation on the Basis of the General Principle of Relativity Part III: Considerations on the Universe as a Whole Cosmological Difficulties of Newton's Theory The Possibility of a "Finite" and yet "Unbounded" Universe The Structure of Space According to the General Theory of Relativity Appendices: Simple Derivation of the Lorentz Transformation (sup. ch. 11)

91. Gravity Probe B Gravity Probe B is the relativity gyroscope experiment being developed by NASA and Stanford University to test two extraordinary, unverified predictions of Albert Einstein's general theory of relativity. http://einstein.stanford.edu/

92. General Relativity & Black Holes Gene Smith s Astronomy Tutorial general relativity Black Holes. http://cassfos02.ucsd.edu/public/tutorial/GR.html

University of California, San Diego Gene Smith's Astronomy Tutorial Einstein's General Theory of Relativity The General Theory of Relativity is an expansion of the Special Theory to include gravity as a property of space. Start with this Gravity Tutorial The Equivalence Principle The Theory of Special Relativity has as its basic premise that light moves at a uniform speed, c = 300,000 km/s , in all frames of reference. This results in setting the speed of light as the absolute speed limit in the Universe and also produced the famous relationship between mass and energy, E = mc . The foundation of Einstein's General Theory is the Equivalence Principle which states the equivalence between inertial mass and gravitational mass Inertial Mass is the quantity that determines how difficult it is to alter the motion of an object. It is the mass in Newton's Second Law: F = ma Gravitational mass is the mass which determines how strongly two objects attract each other by gravity, e.g. the attraction of the earth: It is the apparent equivalence of these two types of mass which results in the uniformity of gravitational acceleration Galileo's result that all objects fall at the same rate independent of mass: Galileo and Newton accepted this as a happy coincidence, but Einstein turned it into a fundamental principle. Another way of stating the equivalence principle is that gravitational acceleration is indistinguishable from other forms of acceleration. According to this view a student in a closed room could not tell the difference between experiencing the gravitational pull of the earth at the earth's surface and being in a rocketship in space accelerating with a = 9.8 m/s

93. Index Of /~wesson We are a group of physicists and astronomers working on a 5dimensional version of general relativity. http://astro.uwaterloo.ca/~wesson/#PUB

Index of /~wesson Name Last modified Size Description ... Parent Directory 07-Mar-2004 16:12 - 19-Feb-2003 16:15 - 19-Feb-2003 16:15 - 19-Feb-2003 16:15 - 19-Feb-2003 16:15 - 19-Feb-2003 16:15 - 19-Feb-2003 16:15 - home.html 11-Jul-2003 19:47 5k images/ 19-Feb-2003 16:15 - intro.htm 23-Jul-2003 19:43 7k people.htm 04-Oct-2003 17:00 20k publications.htm 12-Jul-2003 00:17 10k publications/ 12-Apr-2004 00:20 - Apache/1.3.27 Server at astro.uwaterloo.ca Port 80

94. Cassiopaea Glossary These were treated in his general Theory Of relativity which Einstein From the point of view of general relativity, space becomes curved in the presence http://glossary.cassiopaea.com/glossary.php?id=955&lsel=R

95. General Relativity In The Global Positioning System In general relativity (GR), coordinate time, such as is expressed approximately by a slowmotion, weak-field metric, covers the solar system. http://www.phys.lsu.edu/mog/mog9/node9.html

General relativity in the global positioning system Neil Ashby University of Colorado n_ashby@mobek.colorado.edu The Global Position System (GPS) consists of 24 earth-orbiting satellites, each carrying accurate, stable atomic clocks. Four satellites are in each of six different orbital planes, of inclination 55 degrees with respect to earth's equator. Orbital periods are 12 hours (sidereal), so that the apparent position of a satellite against the background of stars repeats in 12 hours. Clock-driven transmitters send out synchronous time signals, tagged with the position and time of the transmission event, so that a receiver near the earth can determine its position and time by decoding navigation messages from four satellites to find the transmission event coordinates, and then solving four simultaneous one-way signal propagation equations. Conversely, gamma-ray detectors on the satellites could determine the space-time coordinates of a nuclear event by measuring signal arrival times and solving four one-way propagation delay equations. Apart possibly from high-energy accelerators, there are no other engineering systems in existence today in which both special and general relativity have so many applications. The system is based on the principle of the constancy of c in a local inertial frame: the Earth-Centered Inertial or ECI frame. Time dilation of moving clocks is significant for clocks in the satellites as well as clocks at rest on earth. The weak principle of equivalence finds expression in the presence of several sources of large gravitational frequency shifts. Also, because the earth and its satellites are in free fall, gravitational frequency shifts arising from the tidal potentials of the moon and sun are only a few parts in

96. [physics/9908041] Gravitational Waves: An Introduction This paper presents an elementary introduction to the theory of gravitational waves. This article is meant for students who have had an exposure to general relativity, but results from general relativity have been derived in the appendices. http://arxiv.org/abs/physics/9908041

Physics, abstract physics/9908041 From: Indrajit Chakrabarty [ view email ] Date: Sat, 21 Aug 1999 12:54:07 GMT (19kb) Gravitational Waves: An Introduction Authors: Indrajit Chakrabarty Categories: physics.ed-ph physics.pop-ph Comments: Lecture notes presenting an elementary introduction to the theory of gravitational waves. To be submitted to Resonance, Journal of Science Education with a lesser mathematical content. For later revisions, see this http URL Subj-class: Physics Education; Popular Physics In this article, I present an elementary introduction to the theory of gravitational waves. This article is meant for students who have had an exposure to general relativity, but, results from general relativity used in the main discussion have been derived and discussed in the appendices. The weak gravitational field approximation is first considered and the linearized Einstein's equations are obtained. We discuss the plane wave solutions to these equations and consider the transverse-traceless (TT) gauge. We then discuss the motion of test particles in the presence of a gravitational wave and their polarization. The method of Green's functions is applied to obtain the solutions to the linearized field equations in presence of a nonrelativistic, isolated source. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers?

97. Lecture 24: General Relativity The Principal of Equivalence; Consequences of general relativity. slowing of clocks; curvature of space This is the foundation of general relativity. http://instruct1.cit.cornell.edu/courses/astro101/lec24.htm

Lecture 24: General Relativity Astronomy 101/103 Terry Herter, Cornell University Course Home Page Index to Lectures Lecture Topics The Principal of Equivalence Consequences of General Relativity slowing of clocks curvature of space-time Tests of GR Escape Velocity General Relativity A Theory of Gravity Albert Einstein Incorporates accelerated motions into Special Relativity Principle of Equivalence Principle of Equivalence Gravity and acceleration due to a force are indistinguishable. In a small local environment (Must be a small enough "box") This is the foundation of General Relativity.

98. The Cosmological Constant An overview of why Einstein added an extra term in general relativity, and why it is still examined. http://pancake.uchicago.edu/~carroll/encyc/

The Cosmological Constant Sean M. Carroll University of Chicago This is a short article I wrote for the Encyclopedia of Astronomy and Astrophysics (Institute of Physics). See also The Preposterous Universe , or related reviews, lectures, and talks Here is the postscript version , and the pdf version Cosmological Constant The cosmological constant, conventionally denoted by the Greek letter , is a parameter describing the energy density of the vacuum (empty space), and a potentially important contributor to the dynamical history of the universe. Unlike ordinary matter, which can clump together or disperse as it evolves, the energy density in a cosmological constant is a property of spacetime itself, and under ordinary circumstances is the same everywhere. A sufficiently large cosmological constant will cause galaxies to appear to accelerate away from us, in contrast to the tendency of ordinary forms of energy to slow down the recession of distant objects. The value of in our present universe is not known, and may be zero, although there is some evidence for a nonzero value; a precise determination of this number will be one of the primary goals of observational cosmology in the near future. The Cosmological Constant and Vacuum Energy We live in an expanding universe: distant galaxies are moving away from us, such that the more distant ones are receding faster. Cosmologists describe this expansion by defining a

99. General Relativity And Black Holes general relativity and Black Holes. How is the geometry around a Black Hole? A Black Hole is one of the most fascinating objects in the universe, http://www.astro.ku.dk/~cramer/RelViz/text/exhib1/exhib1.html

General relativity and Black Holes. How is the geometry around a Black Hole? A Black Hole is one of the most fascinating objects in the universe, and it can be understood on basis of Einstein's general theory of relativity. In the following pages, you will get an impression of how the curvature changes near a Black Hole, what happens when the hole rotates, and what special effects the Black Hole has on particles and light moving close to the Black Hole. I will not go in much detail with the formulas, because the aim of this World Wide Web Exhibition is presentation and graphics. You can, if you want, read all the relevant details about metric tensors of Black Holes in this hypertext about "Geometry Around Black Holes". Instead, I will use some of the fundamental results to get a view of the geometry around a Black Hole. I will concentrate on curvature and the trajectories of relativistic particles. In flat (euclidian) space, bodies move in a background of space and time. Newton called it absolute space and absolute time. Einstein changed this view radically in 1915 when he completed his general theory of relativity which resulted in a unified 4-dimensional space-time . All distances along a world line are called separations , and they are measured by the metric: This metric defines flat Minkowski space-time , and is much like Newtons absolute space plus a time dimension (note the sign of the time is negative).

100. General Relativity In general relativity Einstein links the curvature of spacetime with the way One of the weirdest predictions of general relativity involves the idea of http://scholar.uwinnipeg.ca/courses/38/4500.6-001/Cosmology/general_relativity.h

Click here to download a PRINTABLE pdf version of this page. In 1916 Albert Einstein put forward his theory of gravity called General Relativity . In this theory Einstein assumes that the effects of gravity can be described in terms of the curvature of space and time together. This hybrid 4-D space, upon which Einstein formulated his theory, is called spacetime . There are three dimensions of space in the four-dimensional spacetime combined with one dimension of time. In General Relativity Einstein links the curvature of spacetime with the way matter and energy are distributed in the universe. One can summarize the coupled arrangement between matter and spacetime curvature in Einstein's gravity theory by the following statements: Mass (the source of the gravitational field) tells spacetime how to curve. Spacetime tells matter (any massive body besides the source mass) how to move. Before Einstein's radical proposal about spacetime, space was thought of as an unchanging stage upon which all the motions and interactions of matter were played out. Space was like a tabletop upon which transactions occurred independently of the structure and layout of the table. Einstein's ideas however implied that space was highly changeable. It was like a flexible material that accommodated every massive object by curving appropriately in the local vicinity of the object, much like a stretched sheet of elastic material would accommodate itself to a heavy ball placed on its center area.

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