41. 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

42. 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/

43. ASTR 103: Relativity - General Theory general relativity. Space and Time as Creations of the Universe. From the preceding reality. Inertia and Weight in general relativity. In 1916 http://www.physics.gmu.edu/classinfo/astr103/CourseNotes/Text/Lec06/Lec06_pt2_tx

ASTR 103 - Text Supplement General Theory of Relativity Latest Modification: November 11, 1998 Table of Contents General Relativity Space and Time as Creations of the Universe Inertia and Weight in General Relativity Curved Space-Time in General Relativity ... Gravitational Radiation General Relativity Space and Time as Creations of the Universe From the preceding discussion, what can we infer about space and time for the Universe as a whole? Newton's concept of an absolute space and time envisions a material Universe inserted into preexisting space and time. But in Einstein's concept, space and time are in the Universe; that is, the Universe creates space and time in both a local sense and a global sense: Einsteinian Space and Time: There is no space beyond the Universe, and there is neither time before nor after the Universe. Space and time and their local features are properties of the Universe. The concepts of relativity theory seem at first contemplation to be contrary to ordinary experience and to so violate common sense that can not be of any consequence. This is far from the case, for relativity theory has replaced old ideas of space and time with a unified theory that does indeed encompass common experience and at the same time leads us to new and unsuspected revelations about physical reality. Inertia and Weight in General Relativity In 1916, Einstein advanced his theory of relativity greatly by making it apply to observers (reference frames) moving nonuniformly (accelerating) relative to each other. Nature's fundamental laws, he reasoned, remain invariant throughout the Universe in all frames of reference, whether the observers are accelerated or not.

44. Kluwer Academic Publishers - Celestial Mechanics And Dynamical Astronomy An international journal concerned with the broadest range of dynamical astronomy and its applications, as well as with peripheral fields. The papers published include treatments of the mathematical, physical and computational aspects of planetory theory, lunar theory, general and special perturbation theory, ephemerides, resonance theory, geodesy of the Earth and the planets, dynamics, the 3body problem, the N-body problem, space mechanics, ring systems, galactic dynamics, reference frames, time, relativity, nongravitational forces, computer methods, computer languages for analytical developments, and database management. http://www.wkap.nl/journalhome.htm/0923-2958

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45. Unit 57 UNIT 57. THE general THEORY OF relativity. Written Only in the last few years has the experimental side of general relativity blossomed. We http://astro.physics.sc.edu/selfpacedunits/Unit57.html

UNIT 57 THE GENERAL THEORY OF RELATIVITY Written for students in the USC Self-paced Astronomy courses NOTE: This Unit assumes you have studied Unit 56. The Learning Objectives and references are in the Self-Paced Study Guide Essay on the General Theory of Relativity by John L. Safko A. General Principle of Covariance (or Only the Tides are Real) Consider yourself in an elevator. You cannot see outside, so you must determine the nature of the surrounding universe by local experiments. You let go of a coin and it falls to the bottom of the elevator. Aha!, you say, I am at rest on Earth. But, you could be in a spaceship that is accelerating and far from any other object. This is shown in Fig. 57-1. Fig. 57-1: Locally being at rest on the Earth's surface is equivalent to being in a uniformly accelerated spaceship. Consider the opposite case. You float from the floor and the coin does not fall when you release it. Aha!, you say again, I am in space far from any other body. But, you could be freely falling towards the Earth as shown in Fig. 57-2. Fig. 57-2:

46. ASTR 103: Relativity - General Theory ASTR 103 Astronomy. relativity - general Theory. Circumference of circle 2(pi)r; Area of circle (pi)r 2. general relativity - Basics. http://www.physics.gmu.edu/classinfo/astr103/CourseNotes/Html/Lec06/Lec06_pt2_re

ASTR 103 - Astronomy Relativity - General Theory Latest Modification: November 30, 1998 Newtonian Gravity - Problems Newtonian cosmology failed to develop a grand (encompassing) theory of gravity Serious defect in that gravity acted instantaneously everywhere Example - When apple falls to ground every place in universe receives information simultaneously Newtonian gravity ignores fact that speed of light is finite and information does not travel with infinite speed, i.e., inconsistent with special relativity Newtonian gravity overturns law of causality and allows effects to precede causes because of infinite speed of light Newtonian Space-Time Euclidean geometry, reasonable assumptions about nature of space Parallel postulate Given straight line and point not on straight line, one and only one straight line equidistant from given straight line may be drawn through given point Experience suggests that these two lines remain equidistant (parallel) across all space even though we can not verify it Plane triangle: sum of angles = 180 o Pythagorean theorem: c = a + b Space is absolute and time is absolute; both are unchanging

47. Being And Becoming In Modern Physics Discusses implications of general relativity for the philosophy of time; by Steven Savitt. http://plato.stanford.edu/entries/spacetime-bebecome/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z This document uses XHTML-1/Unicode to format the display. Older browsers and/or operating systems may not display the formatting correctly. last substantive content change JUL Being and Becoming in Modern Physics Does time flow or lapse or pass? Are the future or the past as real as the present? These metaphysical questions have been debated for more than two millennia, with no resolution in sight. Modern physics provides us, however, with tools that enable us to sharpen these old questions and generate new arguments. Does the special theory of relativity, for example, show that there is no passage or that the future is as real as the present? The focus of this entry will be these new questions and arguments. 1. Introduction 2. Newtonian Spacetime 2.1 Presentism, Possibilism, Eternalism 2.2 McTaggart's Argument ... Related Entries 1. Introduction Around 500 B. C. Heraclitus wrote the following: Everything flows and nothing abides; everything gives way and nothing stays fixed. You cannot step twice into the same river, for other waters and yet others, go flowing on.

48. Jorge Pullin Quantizing general relativity brings knot theory into quantum gravity. The Jones polynomial is shown to give rise to physical states of quantum gravity. Links to research papers by the author. http://www.phys.lsu.edu/faculty/pullin

Jorge Pullin Horace Hearne Chair in theoretical Physics, Louisiana State University Adjunct Professor of Physics, University of Utah Adjunct Professor of Physics, PennState Ph.D., Instituto Balseiro Honors and awards Phone/Fax: (225)578-0464 pullin@phys.lsu.edu Horace Hearne Institute for Theoretical Physics Want to hear those pipes? Research. ... Background. Research My research interests cover many aspects of gravitational physics, both classical and quantum mechanical. I am currently focusing on two topics: quantum gravity and black hole collisions . You can also get my complete publication list , but if you want to get the latest, go to the Hearne Institute page and click on publications. The explanations that follow are a bit longish, feel free to skip to the next topic if you get bored! Quantum gravity I collaborate with Rodolfo Gambini, of the University of the Republic in Montevideo, Uruguay, our collaboration has been going on since 1990. We coauthored a book "Loops, knots, gauge theories and quantum gravity" in 1996 and have published many papers together. We study the quantization of general relativity using canonical methods. There is a small community pursuing this kind of research, which is complementary to the mainstream approach to quantum gravity: string theory. String theorists believe that one cannot quantize general relativity because it is not a fundamental theory and one has to replace it with string theory in order to quantize it. General relativity will be an "effective" "low energy" theory.

49. MSN Encarta - Related Items - Einstein, Albert quotations. radiation, theories and research. relativity, general theory of. overview. relativity. application to astronomy. concept of mass. http://encarta.msn.com/related_761562147_19/relativity_general_theory_of.html

var fSendSelectEvents = true; var fSendExpandCollapseEvents = true; var fCallDisplayUAText = false; MSN Home My MSN Hotmail Shopping ... Money Web Search: logoImg('http://sc.msn.com'); Encarta Subscriber Sign In Help Home ... Upgrade to Encarta Premium Search Encarta Related Items from Encarta Einstein, Albert Theory of Relativity, formulated by Einstein E=mc², mass-energy equation E=mc², source of energy in nuclear weapons E=mc², source of energy in the Sun ... Feedback

50. Center For Gravitational Wave Physics One of 2 general relativity Centers at Penn State University. This center is active with the LIGO Project. http://cgwp.gravity.psu.edu/

51. MSN Encarta - Related Items - Einstein, Albert quotations. radiation, theories and research. relativity, general theory of. relativity, special theory of. role in development of nuclear weapons. subject of art. http://encarta.msn.com/related_761562147/Einstein_Albert.html

var fSendSelectEvents = true; var fSendExpandCollapseEvents = true; var fCallDisplayUAText = false; MSN Home My MSN Hotmail Shopping ... Money Web Search: logoImg('http://sc.msn.com'); Encarta Subscriber Sign In Help Home ... Upgrade to Encarta Premium Search Encarta Related Items from Encarta Einstein, Albert Theory of Relativity, formulated by Einstein E=mc², mass-energy equation E=mc², source of energy in nuclear weapons E=mc², source of energy in the Sun ... , theory, developed in the early 20th century, which originally attempted to account for certain anomalies in the concept of relative motion,... View article Try MSN Internet Software for FREE! MSN Home My MSN Hotmail ... Feedback

52. [gr-qc/9512024] Introduction To The Effective Field Theory Description Of Gravit This is a pedagogical introduction to the treatment of general relativity as a quantum effective field theory. http://arxiv.org/abs/gr-qc/9512024

General Relativity and Quantum Cosmology, abstract gr-qc/9512024 From: "John F. Donoghue" [ view email ] Date: Mon, 11 Dec 1995 15:28:08 -0500 (EST) (19kb) Introduction to the Effective Field Theory Description of Gravity Author: John F. Donoghue (Univ. of Massachusetts, Amherst) Comments: 26 pages, Latex, no figures, Lectures presented at the Advanced School on Effective Field Theories (Almunecar, Spain, June 1995), to be published in the proceedings Report-no: UMHEP-424 This is a pedagogical introduction to the treatment of general relativity as a quantum effective field theory. Gravity fits nicely into the effective field theory description and forms a good quantum theory at ordinary energies. Full-text: PostScript PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted) Which authors of this paper are endorsers? Links to: arXiv gr-qc find abs

53. Interactive Experiments In Gravity contains documents and interactive Java applets which explore aspects of both Newton s theory of universal gravitation and Einstein s general relativity. http://www.fourmilab.ch/gravitation/

Interactive Experiments in Gravity This directory contains documents and interactive Java applets which explore aspects of both Newton's theory of universal gravitation and Einstein's general relativity. The first two installments in the series are now available. Bending Spacetime in the Basement We live our entire lives within the Earth's gravitational field, yet rarely if ever do we experience the universality of gravitation: that every object in the universe attracts and is attracted by every other. This page presents a "basement science" experiment which reveals the gravitational attraction between objects less than a kilogram in mass. Knowledge in antiquity suggesting gravitation was universal is discussed, and the feasibility of an experimental test using only materials and techniques of the era is explored. Orbits in Strongly Curved Spacetime Close-in orbits around compact massive objects such as neutron stars and black holes trace out paths drastically different from the ellipses of Kepler's Laws. Since the velocity of an orbiting object cannot attain or exceed the speed of light, Einstein's general relativity predicts a different energy curve, resulting in precession absent in Newton's theory. This page includes an interactive applet that lets you explore such orbits and explains the theory behind them. by John Walker

54. Virtual Trips To Black Holes And Neutron Stars Page s and MPEG movies that take you on exciting trips. These movies are scientifically accurate computer animations made with strict adherence to Einstein's general Theory of relativity. The descriptions are written to be understandable on a variety of levels from the casually curious to the professionally inquisitive.(a NASA supported site)...... http://antwrp.gsfc.nasa.gov/htmltest/rjn_bht.html

Virtual Trips to Black Holes and Neutron Stars by Robert Nemiroff ( Michigan Technological University Ever wonder what it would look like to travel to a black hole? A neutron star? If so, you might find this page interesting. Here you will find descriptions and MPEG movies that take you on such exciting trips. These movies are scientifically accurate computer animations made with strict adherence to Einstein's General Theory of Relativity. The descriptions are written to be understandable on a variety of levels - from the casually curious to the professionally inquisitive. It is hoped that students from grade school to graduate school will find these virtual trips educational. "A stimulating, relativistically accurate trip!" - Kip Thorne The Feynman Professor of Theoretical Physics, California Institute of Technology, Author of "Black Holes and Time Warps - Einstein's Outrageous Legacy" Earth if compressed to ultracompact density and viewed from the photon sphere. Written Description of Visible Distortion Effects Below is a published paper understandable to undergraduates: "Visual Distortions Near a Black Hole and Neutron Star," Nemiroff, R. J. 1993, American Journal of Physics, 61, 619

55. Orbits In Strongly Curved Spacetime collapsed objects like neutron stars and black holes, Newton s theory is inaccurate; calculations must be done using Einstein s theory of general relativity. http://www.fourmilab.ch/gravitation/orbits/

Orbits in Strongly Curved Spacetime Sorryit appears your browser doesn't understand Java applets. Introduction The display above shows, from three different physical perspectives, the orbit of a low-mass test particle , the small red circle, around a non-rotating black hole (represented by a grey circle in the panel at the right, where the radius of the circle is the black hole's gravitational radius , or event horizon . Kepler's laws of planetary motion, grounded in Newton's theory of gravity, state that the orbit of a test particle around a massive object is an ellipse with one focus at the centre of the massive object. But when gravitational fields are strong, as is the case for collapsed objects like neutron stars and black holes, Newton's theory is inaccurate; calculations must be done using Einstein's theory of General Relativity. In Newtonian gravitation, an orbit is always an ellipse. As the gravitating body becomes more massive and the test particle orbits it more closely, the speed of the particle in its orbit increases without bound, always balancing the gravitational force. For a black hole, Newton's theory predicts orbital velocities greater than the speed of light, but according to Einstein's Special Theory of Relativity, no material object can achieve or exceed the speed of light. In strong gravitational fields, General Relativity predicts orbits drastically different from the ellipses of Kepler's laws. This page allows you to explore them. The Orbit Plot The panel at the right of the applet shows the test mass orbiting the black hole, viewed perpendicular to the plane of its orbit. The path of the orbit is traced by the green line. After a large number of orbits the display will get cluttered and may start to flash; just click the mouse anywhere in the right panel to erase the path and start over. When the test mass reaches its greatest distance from the black hole, a yellow line is plotted from the centre of the black hole to that point, the

56. Gravitation And The General Theory Of Relativity general relativity. The general Theory of relativity Tests of the Theory of general relativity. general relativity and Newton s gravitational http://csep10.phys.utk.edu/astr162/lect/cosmology/gravity.html

Gravitation and the General Theory of Relativity As we have discussed in an earlier section , the theoretical physicist Albert Einstein introduced his Special Theory of Relativity in 1905 and his General Theory of Relativity in 1915. The first showed that Newton's Three Laws of Motion were only approximately correct, breaking down when velocities approached that of light. The second showed that Newton's Law of Gravitation was also only approximately correct, breaking down when gravitation becames very strong. Special Relativity Einstein's Special Theory of Relativity is valid for systems that are not accelerating. Since from Newton's second law an acceleration implies a force, special relativity is valid only when no forces act. Thus, it cannot be used generally when there is a gravitational field present (as we shall see below in conjunction with the Principle of Equivalence, it can be used over a sufficiently localized region of spacetime). We have already discussed some of the important implications of the Special Theory of Relativity. For example, the most famous is probably the relationship between mass and energy . Other striking consequences are associated with the dependence of space and time on velocity: at speeds near that of light, space itself becomes contracted in the direction of motion and the passage of time slows. Although these seem bizarre ideas (because our everyday experience typically does not include speeds near that of light), many experiments indicate that the Special Theory of Relativity is correct and our "common sense" (and Newton's laws) are incorrect near the speed of light.

57. Dr. Mendel Sachs On compatibility of the quantum theory and theory of general relativity by Dr. Mendel Sachs http://www.compukol.com/mendel/

The Future of Physics? My name is Mendel Sachs. My subject is theoretical physics. I have recently become aware of this excellent means of communicating ideas to my fellow physicists. I would like to ask your indulgence in some of my thoughts about physics today. I have discovered during my professional career that in order to increase our comprehension of the material world, it is necessary to ask significant questions and then try to answer them, as completely and rigorously as possible no matter how hard this may seem to be at the outset. A "significant question" to me is one whose answer could possibly increase our understanding. Of course, there is no guarantee at the outset that the question would turn out to be significant in the final analysis. On the other hand, it is often clear when a question (that a great deal of attention may be given to) is not significant! Let me start out, then, with some questions that I believe are significant, and then try to answer them, in my view. 1) What do we presently believe are the most fundamental assertions of the laws of nature? My answer is: The bases of the quantum theory and the theory of relativity. I am not referring here to mathematical expressions of these theories; I refer to the basic concepts that underlie these expressions. If you do not agree with this answer, or those to the questions below, please respond with your own views.

58. Albert Einstein And The Theory Of Relativity For a more comprehensive introduction to both Special and general relativity, see the links at relativity on the WWW, and The Light Cone (An Illuminating http://csep10.phys.utk.edu/astr161/lect/history/einstein.html

Albert Einstein and the Theory of Relativity Albert Einstein Newton's theory of gravitation was soon accepted without question, and it remained unquestioned until the beginning of this century. Then Albert Einstein shook the foundations of physics with the introduction of his Special Theory of Relativity in 1905, and his General Theory of Relativity in 1915 (Here is an example of a thought experiment in special relativity ). The first showed that Newton's Three Laws of Motion were only approximately correct, breaking down when velocities approached that of light. The second showed that Newton's Law of Gravitation was also only approximately correct, breaking down in the presence of very strong gravitational fields. Newton vs. Einstein: Albert's Turn to Kick Butt We shall consider Relativity in more detail later . Here, we only summarize the differences between Newton's theory of gravitation and the theory of gravitation implied by the General Theory of Relativity. They make essentially identical predictions as long as the strength of the gravitational field is weak, which is our usual experience. However, there are three crucial predictions where the two theories diverge, and thus can be tested with careful experiments. The orientation of Mercury's orbit is found to precess in space over time, as indicated in the adjacent figure (the magnitude of the effect is greatly exaggerated in this figure). This is commonly called the "precession of the perihelion", because it causes the position of the perihelion to move. Only part of this can be accounted for by perturbations in Newton's theory. There is an extra 43 seconds of arc per century in this precession that is predicted by the Theory of General Relativity and observed to occur (a second of arc is 1/3600 of an angular degree). This effect is extremely small, but the measurements are very precise and can detect such small effects very well.

59. General Relativity Notes By Kristen Wecht general relativity Tutorials. by Kristen Wecht. I designed the following general relativity tutorials for beginning graduate students in 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

60. General Relativity Introduction to general relativity. Problems with Newtonian Gravity. Newton Thus was born the general theory of relativity. Einstein s http://www.physics.fsu.edu/Courses/Spring98/AST3033/Relativity/GeneralRelativity

Introduction to General Relativity Problems with Newtonian Gravity Newton was fully aware of the conceptual difficulties of his action-at-a-distance theory of gravity. In a letter to Richard Bentley Newton wrote: It is inconceivable, that inanimate brute matter should, without the mediation of something else, which is not material, operate upon, and affect other matter without mutual contact; as it must do, if gravitation, ...., be essential and inherent in it. And this is one reason, why I desired you would not ascribe innate gravity to me. That gravity should be innate, inherent, and essential to matter, so that one body may act upon another, at a distance through vacuum, without the mediation of anything else, by and through their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it." So, clearly, Newton believed that something had to convey gravitational influence from one body to another. When later it became clear that influences travel at finite speeds it was reasonable to suppose this true of gravity also. But Newton's law of gravity did not incorporate the finite travel time of gravitational influences. If right now the sun were to be destroyed by a passing black hole we would not feel the gravitational effects until about 8 minutes had elapsed. Because Newton's law did not include such retardation effects, and permitted violations of special relativity, it was clear that Newton's law had to be an approximation to the correct law of gravity.

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