41. 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 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 Want to hear those pipes? I recently joined the faculty at LSU, after being on the faculty at Penn State for eight years. This web page is in sort of transition between both places, with some links still pointing back to PSU. Research. Teaching. Service. Honors and awards. ... 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 . 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"

42. Modern Relativity Modernrelativity Special General Black Hole Mass Energy Einste For info on special relativity try our special relativity unit Unit I - Specialrelativity. general relativity Preface. Foundations For general relativity. http://www.geocities.com/zcphysicsms/

By David Waite Modern Relativity These units explain general relativity only. We assume that the reader already has a full understanding of special relativity . For info on special relativity try our special relativity unit - Unit I - Special Relativity General Relativity Preface Unit II Foundations For General Relativity Chapter 4 Starting GR 4.1 - The Conceptual Premises For GR 4.2 - Tensors in GR 4.3 - The Metric and Invariants of GR ... 6.3 - Stress Energy of Matter and Einstein's Field Equations Unit III Using General Relativity Chapter 7 Electromagnetism in GR 7.1 - Maxwell's Equations 7.2 - Larmor Radiation and the Abraham-Lorentz Formulae Chapter 8 Robertson-Walker and the Big Bang ... 9.2 - Newtonian Limit Vs Gravitomagnetism Unit IV Black Holes Chapter 10 The Schwarzschild Black Hole 10.1 - The Schwarzschild Solution 10.2 - Hovering over a Schwarzschild Black Hole 10.3 - "Apparently" Lighter With Speed ... 11.2 - Hawking Radiation Unit V Fringe Physics in General Relativity Chapter 12 The New Frontiers 12.1 - Metric Engineering 12.2 - Wormholes 12.3 - Time Travel ... Appendix A : Newtonian-Relativistic Comparisons Appendix B : Planck - SI Unit Conversion Index Misc Good Web Pages Email the author: WaiteDavid137@yahoo.com

43. 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

44. RELATIVITY: Bookmarks Rob Salgado's bookmarksCategory Science Physics relativity...... and Quanta (Brewer) MAGIC through two MILLENNIA Special relativity (U. Toronto)MAGIC throught two MILLENNIA - general relativity (U. Toronto) Homework 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 FJE Enterprises Home Page Modern Physics (Wijekumar - IUP) Fields and Spacetime (Schumacher - Kenyon) Alexander Levichev's homepage. ... 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

45. ASTR 103: Relativity - General Theory general relativity. Space and Time as Creations of the Universe. From thepreceding 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.

46. Modern Relativity Modernrelativity Special General Black Hole Mass Energy Einste Over 50 sections explaining derivations in general relativity. Has a special relativity subsection, Category Science Physics relativity Courses and Tutorials......modernrelativity special general relativity black hole mass energy Einsteinwormhole time travel Schwarzschild modern light Aclubierre warp. ã 2000. http://www.modernrelativity.com/

By David Waite voluntary contributions Modern Relativity These units explain general relativity only. We assume that the reader already has a full understanding of special relativity . For info on special relativity try our special relativity unit - Unit I - Special Relativity General Relativity Preface Unit II Foundations For General Relativity Chapter 4 Starting GR 4.1 - The Conceptual Premises For GR 4.2 - Tensors in GR 4.3 - The Metric and Invariants of GR ... 6.3 - Stress Energy of Matter and Einstein's Field Equations Unit III Using General Relativity Chapter 7 Electromagnetism in GR 7.1 - Maxwell's Equations 7.2 - Larmor Radiation and the Abraham-Lorentz Formulae Chapter 8 Robertson-Walker and the Big Bang ... 9.2 - Newtonian Limit Vs Gravitomagnetism Unit IV Black Holes Chapter 10 The Schwarzschild Black Hole 10.1 - The Schwarzschild Solution 10.2 - Hovering over a Schwarzschild Black Hole 10.3 - "Apparently" Lighter With Speed ... 11.2 - Hawking Radiation Unit V Fringe Physics in General Relativity Chapter 12 The New Frontiers 12.1 - Metric Engineering 12.2 - Wormholes 12.3 - Time Travel ... Appendix A : Newtonian-Relativistic Comparisons Appendix B : Planck - SI Unit Conversion Index Misc Good Web Pages Email the author: staff@modernrelativity.com

47. 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.

48. Australasian Society For General Relativity And Gravitation Includes a newsletter, information on events, and links to related research groups.Category Science Physics relativity Research Groups......Australasian Society for general relativity and Gravitation. generalrelativity, Gravitation and Cosmology WWW sites worldwide. Other http://www.physics.adelaide.edu.au/ASGRG/

Australasian Society for General Relativity and Gravitation Contents Membership information Newsletters Job vacancies Committee / contact information ... Other links worldwide The Australasian Society for General Relativity and Gravitation (ASGRG) was formed at a meeting of mathematicians and physicists in Canberra in September 1994. The Society aims to bring together researchers who work in a wide range of areas within mathematical, theoretical and experimental gravitation: exact solutions of general relativity, mathematical relativity, numerical relativity, quantum gravity, cosmology, estimation of the gravitational wave signals produced by astronomical sources, and development of techniques and technology for detecting these signals with earth- and satellite-based antennae. It was decided to form the society to facilitate discussion of mutual problems of interest and to provide greater cooperation to solve the outstanding problems in the various fields. We see our role as providing a regional forum in Australia and New Zealand similar to the recently formed Topical Interest Group in Gravitation of the American Physical Society, and the international GRG society. The official name and constitution of the Society were adopted at the first General Meeting, which was held during the

49. 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/rlt_genl.htm

ASTR 103 - Astronomy Relativity - General Theory Latest Modification: December 8, 1997 Geometry of Curved Spaces 1826, Karl Friedrich Gauss, German mathematician Mathematics of curved surfaces Showed that non-Euclidean spaces exist whose geometries do not conform to parallel postulate of Euclidean space Infinite number of lines can be drawn through given point parallel to given line 1854, Bernhard Riemann, German mathematician Showed than non-Euclidean spaces exist whose geometries also do not admit parallel postulate No lines can be drawn through given point parallel to given line Riemann foresaw intimate relationship between geometry and physics Albert Einstein "Only the genius of Riemann, solitary and uncomprehended, had won its way by the middle of the last century to a new concept of science." 1885, William Clifford, English mathematician Argued geometry and physics are interconnected "We may conceive our space to have everywhere a nearly uniform curvature, but that slight variations of curvature may occur from point to point, and themselves to vary with time. These variations of the curvature with time may produce effects which we not unnaturally attribute to physical causes independent of the geometry of our space. We might even go so far as to assign to this variation of the curvature of space 'what really happens to that phenomenon which we term the motion of matter." Predicted curvature waves (gravity waves) stating, "this property of being curved or distorted is continually being passed on from one region of space to another after the manner of a wave."

50. 8.033 > Relativity > General Information Special relativity French WW Norton Company, Inc. Exploring Black Holes, Introductionto general relativity Taylor Wheeler Addison Wesley Longman. http://web.mit.edu/8.033/info.html

Home General Info Handouts Problem Sets Quizzes Staff ... APOD General Information Lectures TR 2 pm Room 4-270 F 2 pm Room 6-120 Recitations MW 10 am Room 1-277 MW 11 am Room 1-375 MW 1 pm Room 1-277 Texts Basic Concepts in Relativity and Early Quantum Theory Macmillan Publishing Company Special Relativity French Exploring Black Holes, Introduction to General Relativity Addison Wesley Longman Grading (1) Weekly problem sets [20%] (2) Two one-hour quizzes [20% each] to be held on or about October 8 and November 12 (3) Three-hour final Exam [40%] to be held on Thursday, December 19, from 9 am to 12 pm in room 6-120 Syllabus postscript PDF

51. Physics Department, Tufts University Offers programs of graduate study leading to the Master of Science and the Doctor of Philosophy degrees. Current research programs are in the areas of High Energy Physics, Condensed Matter Physics, general relativity and Cosmology, Astronomy and Astrophysics, and Biophysics. http://ase.tufts.edu/physics/

Department of Physics and Astronomy : Tufts University : Robinson Hall : Medford, MA 02155 USA Tel. 617-627-3029 : Fax 617-627-3878 information about the images

52. 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.

53. Kevin Burton's Emacs Lisp Packages Offers Elisp packages in the following categories general, GNUS specific, CVS, JDE/Java related, XML/SGML related and Internet related. http://relativity.yi.org/emacs

home stack about bio ... XML GNU Emacs Software A collection of emacs stuff I have written. Since everything here is right from my CVS repository this code is at least stable but may be more recent than code I post to comp.emacs.sources. I also have some code which may not be released yet (or ever released) in WebCVS . This includes personal functions/commands which may not be fit for use elsewhere and small hack packages which may not work in all installations. Most of these packages can be installed by doing a (require 'package-name) within your .emacs file. You should read the commentary section for any specific instructions. Donations At this time I am requesting donations for all the Free Software I have written. This will allow me to spend more time focusing on Free Software in the future and maintaining the software and adding new user requested features. This also allows me to pay for the bandwidth and hardware resources necessary to support this website. I am hoping that voluntary donations could help me fund my work without having to resort to divide my time on projects which don't directly benefit the community. Total: Amount: burton@relativity.yi.org

54. Wired News: Putting Einstein To The Test A group of Stanford scientists, with the help of NASA and Lockheed Martin, are out to test Einstein's theory of general relativity. The US$550 million project uses spaceage gyroscopes, and an orbiting satellite. By Steven Brody. Wired News http://www.wired.com/news/technology/0,1282,14451,00.html

Welcome to Wired News. Skip directly to: Search Box Section Navigation Content Search: Wired News Animations Wired Magazine HotBot (the Web) Putting Einstein to the Test Page 1 of 1 04:00 AM Aug. 17, 1998 PT In the late '50s, a Stanford University physicist proposed an impossible experiment which would settle once and for all that Einstein was right and Newton was wrong. "No one has ever offered convincing experimental evidence of general relativity," said senior staff scientist John Mester, director of the Gravity Probe B , or GPB, project. "If our predictions are confirmed, this will be some of the strongest evidence yet that Einstein's theory of general relativity is an accurate model of the universe." Story Tools Today's Top 5 Stories Iraqi Currency Hot on EBay Reporters Flout Cuban Censorship IQ Test for Rebuilding Iraqi Net The Lab That Fell to Earth ... Unlocking Alzheimer's Mysteries The experiment will detect tiny changes in the direction of spin of four gyroscopes contained in the satellite orbiting at a 400-mile altitude directly over the poles. Since the gyroscopes are free from disturbance, they will provide an almost perfect space-time reference system, and will be able to measure how space and time are warped by the presence of the earth, the scientists claim. "It'll be great if the predictions are wrong," said Mester, with typical scientific enthusiasm. "That will mean that we have to take a good look at modifying the theory."

55. General Relativity general relativity. Einstein's 1916 paper on general relativity. In Thisis a basic postulate of the Theory of general relativity. It http://archive.ncsa.uiuc.edu/Cyberia/NumRel/GenRelativity.html

Forward Back Up Map ... Information General Relativity Einstein's 1916 paper on General Relativity In 1916 Einstein expanded his Special Theory to include the effect of gravitation on the shape of space and the flow of time. This theory, referred to as the General Theory of Relativity , proposed that matter causes space to curve. JPEG Image Embedding Diagrams Picture a bowling ball on a stretched rubber sheet. GIF Image The large ball will cause a deformation in the sheet's surface. A baseball dropped onto the sheet will roll toward the bowling ball. Einstein theorized that smaller masses travel toward larger masses not because they are "attracted" by a mysterious force, but because the smaller objects travel through space that is warped by the larger object. Physicists illustrate this idea using embedding diagrams Contrary to appearances, an embedding diagram does not depict the three-dimensional "space" of our everyday experience. Rather it shows how a 2D slice through familiar 3D space is curved downwards when embedded in flattened hyperspace. We cannot fully envision this hyperspace; it contains seven dimensions, including one for time! Flattening it to 3D allows us to represent the curvature. Embedding diagrams can help us visualize the implications of Einstein's General Theory of Relativity. The Flow of Spacetime Another way of thinking of the curvature of spacetime was elegantly described by Hans von Baeyer. In a prize-winning

56. Gen. Relativity Cosmology An online notes from the University of British Columbia featuring simple explanations of cosmological Category Science Physics relativity Courses and Tutorials......general relativity COSMOLOGY. As Elementary Particle Physicists directtheir attention ``down'' toward the indescribably tiny, so http://musr.physics.ubc.ca/~jess/p200/cosm/cosm.html

Next: Astronomy As Elementary Particle Physicists direct their attention ``down'' toward the indescribably tiny, so Cosmologists turn their gaze ``upward'' toward the unfathomably huge. Of course, these days both are increasingly likely to be incarnate in the same individual - I'll get to that later. As one who has never looked through a telescope larger than I could carry, I am certain to give short shrift to the magnificent observational science of astronomy , which provides cosmology (a theoretical discipline) with all its data. But a summary of the former without good colour plates of star fields and nebulae would be a terrible waste anyway, so I hope I have motivated the curious to go out and read a good Astronomy book on their own. Moreover, I am so ignorant of General Relativity and most of the fine points of Cosmology that I really have no business writing about either. Therefore I must content myself with a justification in terms of my ``unique point of view,'' whereby I excuse the following distortions. Astronomy Tricks of the Trade Parallax Spectroscopy ... Bang!

57. CONFERENCE On NONCOMPACT VARIATIONAL P Rutgers University, NJ, USA; 1418 October 2001. http://www.math.rutgers.edu/events/bbconf.html

58. 2001: A Spacetime Odyssey Two theories revolutionized the 20th century view of space and time Einstein's general Theory of relativity and Quantum Mechanics. Their union has spawned elementary particle theories with extra spacetime dimensions, the inflationary model of bigbang cosmology, dark matter in the universe, radiation from quantum black holes and the fuzzy spacetime geometry of superstrings and M-theory. http://www.umich.edu/~mctp/sto2001/

Conference Home Scientific Program Schedule of Talks Students ... MCTP Inaugural Conference of the Michigan Center for Theoretical Physics May 21-25, 2001 University of Michigan, Ann Arbor Two theories revolutionized the 20th century view of space and time: Einstein's General Theory of Relativity and Quantum Mechanics. Their union has spawned elementary particle theories with extra spacetime dimensions, the inflationary model of big-bang cosmology, dark matter in the universe, radiation from quantum black holes and the fuzzy spacetime geometry of superstrings and M-theory. These developments, derived from the 19th century mathematics of Riemannian geometry and Lie groups, have in their turn inspired new directions in the pure mathematics of topology and knot theory. In view of the mission of the Michigan Center for Theoretical Physics to provide a venue for interdisciplinary studies in the mathematical sciences, this Inaugural Conference will bring together Astronomers, Cosmologists, Particle Physicists and Mathematicians to share their different perspectives on the 21st century view of spacetime. Invited speakers include: John Bahcall (IAS) Jacob Bekenstein (Jerusalem) Stanley Deser (Brandeis) Paul Frampton (UNC, Chapel Hill)

59. NOVA Online/Einstein Revealed/Relativity (Lightman Essay) that light rays from distant stars were deflected by the gravity of the sun in justthe amount he had predicted in his theory of gravity, general relativity. http://www.pbs.org/wgbh/nova/einstein/relativity/

Relativity and the Cosmos by Alan Lightman In November of 1919, at the age of 40, Albert Einstein became an overnight celebrity, thanks to a solar eclipse. An experiment had confirmed that light rays from distant stars were deflected by the gravity of the sun in just the amount he had predicted in his theory of gravity, General Relativity. General Relativity was the first major new theory of gravity since Isaac Newton's, more than two hundred and fifty years earlier. Einstein became a hero, and the myth building began. Headlines appeared in newspapers all over the world. On November 8, 1919, for example, the London Times had an article headlined: "The Revolution In Science/Einstein Versus Newton." Two days later, The New York Times' headlines read: "Lights All Askew In The Heavens/Men Of Science More Or Less Agog Over Results Of Eclipse Observations/Einstein Theory Triumphs." The planet was exhausted with World War I, eager for some sign of humankind's nobility, and suddenly here was a modest scientific genius, seemingly interested only in pure intellectual pursuits. What was General Relativity? Einstein's earlier theory of time and space, Special Relativity, proposed that distance and time are not absolute. The ticking rate of a clock depends on the motion of the observer of that clock; likewise for the length of a "yard stick." Published in 1915, General Relativity proposed that gravity, as well as motion, can affect the intervals of time and of space.

60. PhysicsWeb - A Quantum Leap For Cosmology 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 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 Previous Physics World November 2001 Next 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.

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