101. Relativity This will be a book on the foundations of special relativity from a The geometry of the visual effects in special relativity (apparent shape and, http://www.ime.usp.br/~bianconi/rel.html

Special Relativity and Geometry C. E. Harle, R. Bianconi Einstein's synchronization principle: light rays are red , observers are blue and magenta (these work as a sort of mirrors This will be a book on the foundations of Special Relativity from a synthetic viewpoint. This means that we start from a few postulates on how to represent light rays and the principle of inertia and using Einstein's idea of light clocks we define the notion of measure of time and distance (and simultaneity) and introduce coordinates a posteriori The book has a strong visual appeal, modelling with affine geometry. As a subproduct we develop several geometric algorithms which allow us to write programs to visualize relativistic motions. Download a preliminary version (The two and three dimensional spacetimes) in gzipped postscript format. NEW (May, 2001: Beware of the typographic (and, I am afraid, other) errors. Sorry, not yet fully proofread ;-) Things to come: Some odds and ends in the three dimensional model (hyperboloid of synchronization, etc). The four dimensional model: how to do four dimensional descriptive geometry!

102. Relativistic Optics At The ANU High resolution DVDs (PAL format only) of Visualizing special relativity and Seeing relativity and other relativistic movies may be purchased by visiting http://www.anu.edu.au/Physics/Searle/

Seeing Relativity Please visit the Through Einstein's Eyes site to find out about our latest multimedia work on relativistic visualisation. If the speed of light could be reduced from over a billion kilometers per hour to just a few meters per second, the world would look very different. The Australian National University relativistic visualization project has used supercomputers to simulate what we might see in a world where the effects of Einstein's theory of special relativity are everyday experiences. View selected stills in the gallery download the complete movies (17 minutes / 22 megabytes) and explanatory commentary or purchase complete VHS copies. A paper is available explaining the physics of relativistic optics. Doppler-Shifted Highway At 76% the speed of light straight lines appear distorted, clouds bunch at the horizon, and a red desert is Doppler-shifted into a rainbow of different colours. Antony.Searle@anu.edu.au

103. 1: Special Relativity Fortunately, many problems in special relativity involve only one dimension of To avoid this kind of complication, special relativity deals only with http://gregegan.customer.netspace.net.au/FOUNDATIONS/01/found01.html

Foundations Special Relativity From Special to General Black Holes Quantum Mechanics Foundations ... Framed Site Map 1: Special Relativity Spacetime Rotations in Space Spacetime Geometry Rotations in Spacetime ... Doppler Shift and Aberration A nyone who reads science fiction will be familiar with some of the remarkable predictions of twentieth-century physics. Time dilation, black holes, and the uncertainty principle have all been part of the SF lexicon for decades. In this series of articles I'm going to describe in detail how these phenomena arise, and along the way I hope to shed some light on the theories that underpin them: special relativity, general relativity, and quantum mechanics. The foundations of modern physics. Spacetime T he idea that we inhabit a four-dimensional spacetime is a very natural and intuitive one. It's only because we take the duration of objects so much for granted that we tend to gloss over it and refer to them as three-dimensional. Since most of the Earth's landscape changes slowly, factoring out time from our mental models and paper maps is a very pragmatic thing to do, but it's this unchanging space that we imagine for convenience that's the abstract mental construct, not spacetime. Spacetime is simply what we live in, all four dimensions of it. Drawing a diagram of spacetime comes almost as naturally as making any other kind of map; every historical timeline is halfway there, and placing a timeline for Germany next to one for France, then sketching in the movement of armies between the two, is as good a spacetime diagram as anything you'll find in particle physics. Of course, a spacetime diagram in ink on paper has only two useful dimensions, so it generally only shows time plus one dimension of space (though one more can be added, using the standard techniques for drawing three-dimensional objects). Fortunately, many problems in special relativity involve only one dimension of space; for example, a spacecraft flying from here to Sirius would almost certainly travel along a straight line.

104. Reflections On Relativity Comprehensive presentation of the special and general theories of relativity. http://www.mathpages.com/rr/rrtoc.htm

Reflections on Relativity Contents Preface 1. First Principles Experience and Spacetime Systems of Reference Inertia and Relativity The Dilemma of Light ... Null Coordinates 2. A Complex of Phenomena The Spacetime Interval Force Laws and Maxwell's Equations The Inertia of Energy Doppler Shift for Sound and Light ... Thomas Precession 3. Several Valuable Suggestions Postulates and Principles Natural and Violent Motions De Mora Luminis Stationary Paths ... Constructing the Principles 4. Weighty Arguments Immovable Spacetime Inertial and Gravitational Separations Free-Fall Equations Force, Curvature, and Uncertainty ... The Breakdown of Simultaneity 5. Extending the Principle Absorbing Acceleration Tensors, Contravariant and Covariant Curvature, Intrinsic and Extrinsic Relatively Straight ... The Field Equations 6. Ist Das Wirklich So? An Exact Solution Anomalous Precession Bending Light Radial Paths in a Spherically Symmetrical Field ... Sources in Motion 7. Cosmology Is the Universe Closed? The Formation and Growth of Black Holes Falling Into and Hovering Near A Black Hole Curled-Up Dimensions ... Global Interpretations of Local Experience 8. The Secret Confidence of Nature Kepler, Napier, and the Third Law

105. Tensors In Special Relativity Tensors and relativity Chapter 3. Tensors in special relativity although the concepts will apply to curved spacetime and General relativity. http://vishnu.mth.uct.ac.za/omei/gr/chap3/frame3.html

Next: Metrics and forms Tensors and Relativity: Chapter 3 Tensors in Special Relativity We need to express the equations of physics in a frame independent way. This can be done for some equations by using four- vectors [ e.g. Newton's Laws ] but what about the rest of physics!!? We now extend this idea by introducing more general coordinate independent quantities called Tensors . In this section we will confine our discussion to Minkowski spacetime , although the concepts will apply to curved spacetime and General Relativity. Metrics and forms One- forms Gradients The metric as a mapping of vectors onto one- forms ... course welcome page. Peter Dunsby Sat Jun 8 15:29:35 ADT 1996

106. A Primer On Special Relativity When people first hear about special relativity they often wonder if it s One major shortcoming with the way in which special relativity is usually http://www.mathpages.com/home/kmath307/kmath307.htm

A Primer on Special Relativity An inertial coordinate system is a system of space and time coordinates with respect to which inertia is homogeneous and isotropic.  Homogeneity implies that every material body free of external influence moves at constant speed in a straight line, and isotropy implies that if two identical material objects initially adjacent and at rest act to repel each other, they acquire equal speeds in opposite directions.  Given one inertial coordinate system we can construct infinitely many others by means of arbitrary fixed translations and spatial rotations, which leave the speed of every object unchanged.  Such an equivalence class of inertial coordinate systems is called an inertial reference frame .  It's important to recognize that the definition of an inertial reference frame not only identifies inertial motion with straight paths of constant speed, it also establishes an operational definition of simultaneity (i.e., the synchronization of times at spatially separate events), because inertial isotropy implies that we can use identical physical objects acting against each other to synchronize clocks equidistant from their center of mass. Given this definition of inertial reference frames, the

107. [gr-qc/0409105] Synchronization Gauges And The Principles Of Special Relativity The principles of special relativity Theory (SRT) allow for a wide range of ‘theories’ that differ from the standard SRT only for the difference in the http://arxiv.org/abs/gr-qc/0409105

General Relativity and Quantum Cosmology, abstract gr-qc/0409105 From: Matteo Luca Ruggiero [ view email ] Date ( ): Tue, 28 Sep 2004 10:25:49 GMT (128kb) Date (revised v2): Mon, 18 Oct 2004 12:31:56 GMT (129kb) Synchronization Gauges and the Principles of Special Relativity Authors: Guido Rizzi Matteo Luca Ruggiero Alessio Serafini Categories: gr-qc Comments: 56 pages, 3 eps figures, invited paper; to appear in Foundations of Physics (Special Issue to honor Prof. Franco Selleri on his 70th birthday) Journal-ref: Found.Phys. 34 (2005) 1835-1887 DOI: Full-text: PostScript PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv gr-qc find abs

108. University Lectures On Special Relativity Lecture notes on special relativity, prepared by J. D. Cresser, Department of Physics, Macquarie University. 44 pages. http://www.physics.mq.edu.au/~jcresser/Phys378/LectureNotes/SpecialRelativityNot

109. Special Relativity This is chapter two of Christoph Schiller's 1000 page walk through the whole of physics, from classical mechanics to relativity, electrodynamics, thermodynamics, quantum theory, nuclear physics and unification. 61 pages. http://www.motionmountain.net/C-2-CLSC.pdf

110. RELATIVITY: Bookmarks Rob Salgado's bookmarks http://physics.syr.edu/research/relativity/RELATIVITY.html

RELATIVITY: bookmarks RELATIVITY This is a collection of MUCH TOO MANY bookmarks that I don't really have time to update or maintain. Many links are probably dead. I do not necessarily endorse the content of any of these bookmarked sites. (new) Relativity Einstein Archives Online FJE Enterprises Home Page Modern Physics (Wijekumar - IUP) Fields and Spacetime (Schumacher - Kenyon) ... Hisaaki Shinkai's Links United States NSF Gravitational Physics NRC Committee on Gravitational Physics Grand Challenge Alliance Directory (via NCSA) A-R Austin College Boston U. (Einstein Papers Project) Brandeis U. Caltech TAPIR (Theoretical Astrophysics and Relativity) ... Saint Louis U. (Math) S-Z Syracuse U. Syracuse U. / NPAC Texas AM (Math-Phy) Truman State U. (Math) ... Washington U. - St. Louis Canada U. Alberta - CIAR Cosmology U. British Columbia U. Calgary (Hobill) U. Guelph ... U. Windsor Mexico Autonomous University of Puebla (BUAP - Mexico) UNAM-ICN (Mexico) CINVESTAV (Mexico) SOUTH AMERICA U. Nacional de Cordoba UERJ (Rio de Janeiro, Brazil) U. Buenos Aires (Quantum Theory and Gravitation) Instituto de Fisica (Montevideo, Uruguay) EUROPE / United Kingdom Austria U. Vienna

111. Lecture Notes On General Relativity Lecture notes for a onesemester course in General relativity. http://pancake.uchicago.edu/~carroll/notes/

Lecture Notes on General Relativity Sean M. Carroll (gravitational waves disturbing a black hole, from NCSA This set of lecture notes on general relativity has been expanded into a textbook, Spacetime and Geometry: An Introduction to General Relativity , available for purchase online or at finer bookstores everywhere. About 50% of the book is completely new; I've also polished and improved many of the explanations, and made the organization more flexible and user-friendly. The notes as they are will always be here for free. These lecture notes are a lightly edited version of the ones I handed out while teaching Physics 8.962, the graduate course in General Relativity at MIT , during Spring 1996. Each of the chapters is available here as uncompressed postscript, but see next paragraph. (Need a postscript previewer ?) Constructive comments and general flattery may be sent to me via the address below. Dates refer to the last nontrivial modification of the corresponding file (fixing typos doesn't count). The notes as a whole are available as gr-qc/9712019 Other formats: if you don't like postscript, the notes are

112. General Relativity Simulation Contest The purpose of this Contest is to prove General relativity using a (simple) algorithm. http://users.pandora.be/nicvroom/contest.htm

General Relativity Simulation Contest Description of Contest The purpose of this Contest is to prove General Relativity. The Contest consist of the following task: Write one general purpose program (any programming language will do) which simulates the movement of n objects over a certain period of time. The simulation method used (algorithms), should be based on the Rules of General Relativity. The program should be able to simulate and demonstrate the following examples: Forward movement (perihelion shift) of the planet Mercury (43 arc sec angle) around the Sun. The bending of light around the Sun (1.75 sec). The movement of a binary star system. The stars should spiral together. A clock in a space ship around the Earth. Twin paradox (SR). i.e. at least two clocks should be included. The behaviour of black holes. The results of the simulation should match actual observations. For the rules of General Relativity see the following: General Relativity with John Baez For the most elaborate list of links for General Relativity see: Relativity on the World Wide Web by Chris Hillman , maintained by John Baez For a technical discussion about the problems with numerical simulations regarding General Relativity see: Numerical Relativity If you want more about celestial mechanics simulations informal newsletter

113. Theory Of Universal Relativity - Shrinking Theory Shrinking Theory of the universe and Consequences of the relativity of the speed of light, speed, distance, size, mass, and time. http://www.crownedanarchist.com/Shrinking.htm

The C rowned Anarchist Sci-Fi Helper Universal ... The Crowned Anarchist Literature Sci-Fi Helper Star Trek and Science Photos Forum ... Relativité Universelle I lost my mind the second I was born! - RMT THE SH RIN KI N G T HEORY THE UNIVERSAL THEORY OF RELATIVITY (Universal Relativity) By Roland Michel Tremblay Maintenant en Français! The Relative Universe (Science Fiction novel based on these theories) SCI-FI HELPER - Inspiration for Sci-fi Writers and Scientific Advisers Note: If you are new to the concepts of relativity, super strings and quantum mechanics, please bear in mind that these are my own theories, they do not reflect what is said today in science. This is a work in progress, some points are wrong. Only with your comments and questions can I develop this further: rm@crownedanarchist.com . My Shrinking Theory is practically stated in the book The Elegant Universe by Brian Greene, page 249 (Two Interrelated Notions of Distance in String Theory). Note that none of my ideas need String Theories, I do not talk about many different dimensions or strings. The most important part to be read on this page is called (Consequences of the Shrinking Theory and the Universal Relativity) and it comes after the following 8 points and the three images that follow.

114. [gr-qc/9911051] Complex Geometry Of Nature And General Relativity A paper by Giampiero Esposito attempting to give a selfcontained introduction to holomorphic ideas in general relativity. The main topics are complex manifolds, spinor and twistor methods, heaven spaces. http://arxiv.org/abs/gr-qc/9911051

General Relativity and Quantum Cosmology, abstract gr-qc/9911051 From: Esposito Giampiero [ view email ] Date: Mon, 15 Nov 1999 11:06:50 GMT (124kb) Complex Geometry of Nature and General Relativity Authors: Giampiero Esposito Categories: gr-qc Comments: 229 pages, plain Tex Report-no: DSF preprint 99/38 An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, spinor and twistor methods, heaven spaces. Full-text: PostScript PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv gr-qc find abs

115. Spacetime Wrinkles Major advances in computation are only now enabling scientists to simulate how black holes form, evolve, and interact. Learn about relativity and its predictions through text and video files at this site. http://archive.ncsa.uiuc.edu/Cyberia/NumRel/NumRelHome.html

SPACETIME WRINKLES In 1905, Albert Einstein published his famous Special Theory of Relativity and overthrew commonsense assumptions about space and time. Relative to the observer, both are altered near the speed of light: distances appear to stretch; clocks tick more slowly. A decade and a year later, Einstein further challenged conventional wisdom by describing gravity as the warping of spacetime, not a force acting at a distance. Since then, Einstein's revolutionary insights have largely stood the test of time. One by one, his predictions have been borne out by experiment and observation. But it wasn't until much later that scientists accepted one of the most dramatic ramifications of Einstein's theory of gravitation: the existence of black holes from whose extreme gravity nothing, not even light, can escape. Major advances in computation are only now enabling scientists to simulate how black holes form, evolve, and interact. They're betting on powerful instruments now under construction to confirm that these exotic objects actually exist. You might like to take a two-minute video tour of this exhibit's contents. However, the Quicktime movie is rather large (12.3 MB!), so be patient when downloading. It could take several minutes. (Further information on downloading movies can be obtained from the

116. A Quantum Leap For Cosmology (November 2001) - Physics World - PhysicsWeb A theory that unites quantum mechanics and general relativity claims that there was no first moment in time, but it still agrees with the predictions of classical cosmology. http://physicsweb.org/article/world/14/11/3

Advanced site search physics world sample issue Request a sample issue browse the archive January February March April May June July August September October November December Latest issue Subscribe to Physics World Media Information ... Editorial Staff quick search Search Physics World Physics World November 2001 A quantum leap for cosmology Physics in Action: November 2001 A theory that unites quantum mechanics and general relativity claims that there was no first moment in time, but it still agrees with the predictions of classical cosmology. It's in the stars One of the most challenging problems in modern physics is the application of quantum theory to the universe as a whole. Progress in this area has been plagued by two types of problem: conceptual and technical. The conceptual problems arise from the old difficulties of interpreting quantum theory. The standard interpretations require that the measuring instruments and observers are outside the quantum system described by the wavefunction. In the late 1950s, however, Hugh Everett proposed an interpretation of quantum theory that might apply to systems that include the observers and measuring instruments, but the adequacy of such interpretations has remained controversial to this day. The technical problems are no less severe or fundamental. Ever since the pioneering work of Bryce DeWitt, Charles Misner and others in the 1960s, quantum cosmology has basically been studied by applying quantum theory to simple models of the universe. These models typically assume that the universe is completely homogeneous. As a result they only have a few degrees of freedom - the radius of the universe and the value of one or more matter fields. One then makes a quantum-cosmological model by quantizing these simple descriptions of the universe.

117. GEOMETRY AND PHYSICS OF BRANES The SIGRAV Graduate School in Contemporary relativity and Gravitational Physics is held annually at the Centre for Scientific Culture Alessandro Volta , Villa Olmo, Como. It is primarily addressed to PhD students and young researchers in Physics and Mathematics who are interested in general relativity, astrophysics, experimental gravity and the quantum theories of gravitation. http://www.sissa.it/~bruzzo/sagp2001/sagp2001.html

4th SIGRAV GRADUATE SCHOOL ON CONTEMPORARY RELATIVITY AND GRAVITATIONAL PHYSICS and 2001 SCHOOL ON ALGEBRAIC GEOMETRY AND PHYSICS (SAGP2001) VILLA OLMO (COMO), 7-11 MAY 2001 GEOMETRY AND PHYSICS OF BRANES Supported by: SIGRAV (Italian Society for Gravitational Physics), National Research Project "Singularities, Integrability, Symmetries", SISSA (Trieste), University of Insubria (Como-Varese), Departmente of Chemistry, Physics and Mathematics of the University of Insubria at Como, Physics Department of the University of Milan, Physics Department of the University of Turin, Physics Department of the University of Rome "La Sapienza", Physics Department of the University of Rome "Tor Vergata", Physics Department of the University of Pavia. Download the first circular (Latex file) See the programme (PDF) The SIGRAV Graduate School in Contemporary Relativity and Gravitational Physics is held annually at the Centre for Scientific Culture "Alessandro Volta", Villa Olmo, Como. It is primarily addressed to PhD students and young researchers in Physics and Mathematics who are interested in general relativity, astrophysics, experimental gravity and the quantum theories of gravitation. In 2001 the School will be a joint venture with the School on Algebraic Geometry and Physics organized by the Mathematical Physics Group of the International School for Advanced Studies (SISSA) in Trieste. The School on Algebraic Geometry and Physics is part of a series of events that SISSA is organizing since 1996 aiming at fostering the interaction between mathematicians working in pure algebraic geometry and researchers who are interested in applications of algebraic geometry to physics, especially string theory and integrable systems. Information on the "Algebraic Geometry and Physics'' series is available from the web page

118. Scale Relativity Fractal relativity. Spacetime is nondifferentiable. http://www.chez.com/etlefevre/rechell/ukrechel.htm

Scale Relativity Warning: these HTML pages have been developped from a first version achieved by . For more detail, refer either to the book (1993), or to a more recent (1996) review paper , more generally to the bibliography published on the subject, or to the author at the following e-mail address: Laurent.Nottale@obspm.fr The author: This theory is proposed by Laurent Nottale , researcher at observatoire de Paris-Meudon . He worked for a long time in parallel on gravitational lenses , but is now devoting most of his activity to the development of the theory of Scale Relativity DAEC department. The origin In this chapter, we first present the origin of the Scale Relativity (or ScR) theory: we will briefly evoke the reasons that led to its development. The fundamental principle of ScR: It is an extension of Einstein's principle of relativity. It can be stated as follows: The laws of nature must be valid in every coordinate systems, whatever their state of motion and of scale. The results obtained show once again the extraordinary efficiency of this principle at constraining the laws of physics. The method: The formalism developed by L. Nottale for ScR is already sufficiently settled to be used "as is" to deal with a particular problem in many situations. The procedure is outlined in this chapter. The most general version of the theory is still under construction.

119. Lanczos Collection Site announces the availability of the Cornelius Lanczos Collected Published Papers with commentaries. Lanczos (18931974) was one of the twentieth century's most versatile and innovative physicists and mathematicians. His papers cover an array of disciplines including general relativity, quantum mechanics, scientific computation, applied mathematics and numerical analysis. http://www.physics.ncsu.edu/lanczos

Announcing the CORNELIUS LANCZOS COLLECTED PUBLISHED PAPERS WITH COMMENTARIES Published by North Carolina State University College of Physical and Mathematical Sciences and Department of Physics Raleigh, North Carolina 27695-8202 USA [1998] Library of Congress Catalog Card Number: 98-67928 ISBN (for the Collection of Volumes I-VI): 0-929493-01-X [See Web: www.physics.ncsu.edu/lanczos (View the Order Form Ordering Instructions Collection 24 September 2002) (All orders are now being shipped from Raleigh, North Carolina) Cornelius Lanczos (1893-1974) was a physicist and mathematician who had a profound impact on the foundations of twentieth century science. His papers cover a vast array of disciplines, including general relativity, quantum mechanics, scientific computation, applied mathematics and numerical analysis. This Collection provides documentation (a) that Lanczos was indeed one of the twentieth century's most versatile and innovative scientific minds, and (b) that many of Lanczos's ideas are still of interest to present-day research in physics and applied mathematics. This Collection will be of special interest to theoretical physicists, numerical analysts and science historians. The Cornelius Lanczos Collected Published Papers with Commentaries (Lanczos Collection or CLCPPC herein-after referred to as the Collection) represents the second phase of a two-part celebration of the life and work of Cornelius Lanczos. The first phase of this celebration occurred in December 1993 when North Carolina State University's College of Physical and Mathematical Sciences hosted the Cornelius Lanczos International Centenary Conference. [See the

120. Accueil The principle of the relativity of energy applied to unit systems, to electrostatics and magnetism, will give us a unified vision of the electromagnetic fields. http://perso.wanadoo.fr/j.p.serodino/Anglais/welcome.htm

Cette présentation comporte : An english version. Un résumé donnant un bref aperçu de la totalité des chapitres de notre travail. Un résumé de chacun des chapitres permettant d'obtenir une idée plus précise de notre théorie. Une étude détaillée des principaux points développés dans notre théorie. Cette page utilise des cadres, mais votre navigateur ne les prend pas en charge.

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