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General Relativity
next up previous Next Quantum Physics Up Physical Theories and CausalityPrevious Conservation Laws in Modern general relativity.
http://www.ensc.sfu.ca/people/grad/brassard/personal/THESIS/node176.html

Extractions: Next: Quantum Physics Up: Physical Theories and Causality Previous: Conservation Laws in Modern With Einstein's 1905 special theory of relativity, all the states differing only by spatial or temporal translations, rotations, or Lorentz transformations are equivalent, and all the states that differ only in this way translate into the same input for the theory. All pairs of scientists with arbitrary spatio-temporal separation, arbitrary relative orientation, and arbitrary constant rectilinear relative velocity experience the same laws of nature, including the speed of light. In order to make this theory possible, a 4-dimensional Euclidean spatio-temporal geometrical framework (Michosky's space) was used where there is no meaning for the concept of simultaneous distant events, and for the instantaneous action of forces. Forces are replaced by field moving with velocity of light. With this theory, the magnetic field is explained as a relativist effect. The intellectual necessity or symmetry reasons to make a general relativist theory of mechanic was stressed by many physician before Einstein. Ernst Mach (1838-1916), in particular, advocates the necessity to have all the laws of nature to be the same. In order to find such theory, Einstein had to give up the Euclidean geometrical framework and to replace it by a 4-space Riemanian geometry where the space-time has a topography such as the surface of the earth and where it is the mass that determines the local curvature of this surface. The first law of Newton, the invariance to translation if no mass, is generalized so that any mass follows the geodesic line of space-time 4D surface of the gravitational field.
Parallel Linear General Relativity
Parallel Linear general relativity and CMB Anisotropies. Authors PaulBode 1INST1 Dept. of Physics, MIT 1ADD1 Cambridge, MA 02139
http://arcturus.mit.edu/SC95/

Extractions: Keywords: Cosmology, Applications, Parallel algorithms, Performance evaluation We have developed a code which links the primeval fluctuations in the early universe with those observable at the present time by integrating the coupled, linearized, Einstein, Boltzmann, and fluid equations governing the evolution of metric perturbations and density fluctuations; this is the most accurate treatment to date of both the physics and the numerical integration. The results are useful both for calculations of the cosmic microwave background (CMB) anisotropy and the linear power spectrum of matter fluctuations. The serial code (LINGER) is highly efficient on vector machines. Furthermore, this application is perfectly suited for coarse-grained parallelism. A portable, parallel implementation (PLINGER) using common message-passing libraries (PVM, MPI, MPL, and PVMe) has been completed; it achieves Gflop/sec rates on current parallel supercomputers such as the T3D and SP2. LINGER and PLINGER are publically available as part of the COSMICS software package.
General Term: General Relativity
general relativity. An extension of Einsteins theory of special relativity toinclude gravity and other noninertial (accelerating) frames of reference.
http://www.counterbalance.net/physgloss/grel-body.html
General Relativity
general relativity. general relativity is about gravity or the attractionthat any object has for any other object. We think of gravity
http://www.mtnmath.com/whatth/node51.html

Extractions: General Relativity General relativity is about gravity or the attraction that any object has for any other object. We think of gravity as what keeps us on the ground, The earth's gravity is a major factor in our lives. But gravity is universal. Every object attracts every other object. The prior Newtonian theory of gravity was a bit of a mystery. It required action at a distance. Einstein solved the mystery by showing that gravity warps space and time. It does so in a way that is called local . Gravity propagates through space at the speed of light. Special relativity is based on the simplifying assumption that the laws of physics are the same in any inertial frame of reference. General relativity is based on the simplifying assumption that gravity and acceleration are indistinguishable. If your ship in deep space accelerates at just the right rate you will feel the same force pushing you towards the floor that you feel on earth. Special relativity suggests that time and space measurements transform so that one cannot detect absolute motion. Philosophically (but not mathematically) special relativity denies the existence of an absolute frame of reference. General relativity suggests that mass warps space and time to appear just as they do to someone under uniform acceleration in deep space.
General Relativity
According to the principle of equivalence from general relativity, any frequencyshift which can be shown to arise from acceleration of a radiating source
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html

Extractions: Gravitational Red Shift According to the principle of equivalence from general relativity, any frequency shift which can be shown to arise from acceleration of a radiating source could also be produced by the appropriate gravitational field. Thus the expected shift in radiation frequency in a gravitational field can be related to the relativistic doppler shift experienced from an accelerating light source. Applications: Harvard tower experiment Index is just 4.92 x 10^-15 , but the Mossbauer effect with the 14.4 keV gamma ray from iron-57 has a high enough resolution to detect that difference. In the early 60's physicists Pound, Rebka,and Snyder at the Jefferson Physical Laboratory at Harvard measured the shift to within 1% of the predicted shift. By just using the expression for gravitational potential energy near the Earth, and using the m in the relativistic energy expression , the gain in energy for a photon which falls distance h is Comparing the energy shifts on the upward and downward paths gives a predicted difference The measured difference was The success of this experiment owed much to the care of Pound and Rebka in preparing the source. They electroplated cobalt-57 onto the surface of a thin sheet of iron and then heated the combination at 1220 K for an hour. The heat treatment caused the cobalt to diffuse into the iron to a depth of about 300 nm or 1000 atomic spacings. The source was then mounted on the cone of a loudspeaker driven at 10Hz to sweep the source velocity in a sinusoidal variation. The detector was a thin sheet of iron about 14 micrometers thick which was also annealed. The heat treatments were found to be crucial in obtaining high resolution.
Preface Modern Relativity Special General Black Hole Mass Energy Einstein Wormho
modernrelativity special general relativity black hole mass energy Einsteinwormhole time travel Schwarzschild modern light Aclubierre warp.
http://home.aol.com/zcphysicsms2/grpreface.htm

Extractions: General Relativity Preface Return to Modern Relativity Each section presumes that the reader has worked through the previous sections and chapters. It is also assume the reader has an understanding of mathematics through calculus and partial differential equations. The relevant tensor calculus is presented throughout as needed. Every author has his own conventions, his own way of doing general relativity. When mixing equations from this book with equations from other authors of relativity, make sure to account for the differences in definitions and conventions as needed. This book will use the following conventions. The space-time signature will be (+ - - -). Where the word mass or the letter m is used unqualified it will be defined as invariant as discussed in the section on the definition of mass. The Ricci tensor will be the contraction over the Riemann tensor's first and third indices. Except for the section on Kaluza-Klein theories, Greek superscripts and subscripts will be indices running 0,1,2,3 where will represent the time index. Indices i and j will only be spatial indices running 1,2,3. A comma will represent a partial derivative. In other words F l r will mean F l x r . A semicolon will represent the partial covariant derivative. The meaning of a covariant derivative is discussed in its section below.
Astrophysics And General Relativity
Astrophysics and general relativity, This is where the caption wouldgo if this were a real caption. Astrophysics research provides
http://www.phys.washington.edu/Department/Gradweb/Res_AstrphysGnrlReltvity.html

Extractions: This is where the caption would go if this were a real caption. Astrophysics research provides connections between several fields of physics. General relativity affects astrophysics through the theory of compact objects and violent phenomena such as quasars, gravitational collapse, and gravitational radiation and the overall expansion of the universe. Stellar astrophysics shares many topics of interest with nuclear physics. New particles, topological singularities in gauge fields (cosmic strings), phase transitions in the early universe, the creation of matter, and the unification of the fundamental forces are all topics of interest in elementary-particle research and may strongly affect knowledge of the large-scale structure of the present universe. Research topics include the following.
Ph236
Physics 236 general relativity. Sean Carroll's lecture notes for 8.962, thegraduate general relativity course taught during Spring 1996 at MIT.
http://www.pma.caltech.edu/~ph236/ph236.html

Extractions: Lectures: Tuesday, Thursday 2:30-4:00, 269 Lauritsen (An Einsten-Rosen bridge. This figure can be obtained by embedding a constant time hypersurface of the Schwarzschild spacetime in a higher-dimensional Euclidean space. For clarity, one rotational degree of freedom has been suppressed.) Richard O'Shaughnessy
Numerical Hydrodynamics In General Relativity
http://www.livingreviews.org/Articles/Volume3/2000-2font/
GENERAL RELATIVITY
Before beginning this brief article, dealing with the essential features of GeneralRelativity, we have to postulate one thing Special Relativity is supposed
http://www.gravitywarpdrive.com/General_Relativity.htm

Extractions: This is the English translation of a Web Page originally written in French , by Nymbus , who also provided the translation. I have posted it here at my own Website, with some minor personal additional comments. The content has been left untouched. Any comments or questions should be addressed to nymbus@wanadoo.fr . At times, this Web Page alludes to concepts from Einstein's Special Relativity Theory, which are explored here Reference: http://www.svsu.edu/~slaven/gr/ Before beginning this brief article, dealing with the essential features of General Relativity, we have to postulate one thing: Special Relativity is supposed to be true. Hence, General Relativity lies on Special Relativity. If the latter were proved to be false, the whole edifice would collapse. In order to understand General Relativity, we have to define how mass is defined in classical mechanics. The Two Different Manifestations of Mass: First, let's consider what represents mass in everyday life: "It's weight." In fact, we think of mass as something we can weigh, as that's how we measure it: We put the object whose mass is to be measured on a balance. What's the property of mass we use by doing this? The fact that the object and Earth attract each other. To be convinced of it, just go in your garage and try to raise your car! This kind of mass is called "gravitational mass." We call it "gravitational" because it determines the motion of every planet or of every star in the universe: Earth's and Sun's gravitational mass compels Earth to have a nearly circular motion around the latter.
General Relativity
general relativity Confuses faster than the speed of light. (1, +8), Doforces fall outside of general relativity? What am I missing?
http://www.halfbakery.com/idea/General_20Relativity

Extractions: A distant cousin to everybody, General Relativity has no fixed operating base; instead, he hops from house to house at the places of his many relatives, disguised as a traveling physicist on military assignment. A keen war-strategist, the General uses informational dominance tactics, given at near light speed to confuse his enemies with physics explanations of trains moving at the speed of light and time-traveling twin brothers. He eventually traps his more Euclidean opponents in a wormhole of confusion, and having completed his job, leaves the previous day. RayfordSteele , Apr 28 2002
General Relativity
general relativity. In general relativity we know the symmetries arespacetime symmetries, which means they work on the coordinates.
http://www-th.phys.rug.nl/~schaar/htmlreport/node3.html

Extractions: Next: Black Holes Up: Stringy Black Holes Previous: Introduction Before we are going to consider black holes in general and stringy black holes in particular, it is necessary to describe the basic structure of General Relativity. When Einstein first constructed his Relativistic theory of Gravitation it was from a geometrical point of view. Space-time was considered to be a dynamical entity that curved under the influence of matter and test-particles travelled on paths as straight as possible in this curved space-time (geodesics). Although this approach is very elegant, nowadays from a high-energy physics point of view it is perhaps more usefull to formulate the theory in a way that makes manifestly clear the connection between General Relativity and field theories describing elementary particles and their interactions. In the field theories of elementary particles (Yang Mills theories), interactions are introduced by turning a global (=coordinate independent) symmetry of the free theory, into a local (=coordinate dependent) symmetry and introducing a covariant derivative with the right transformation properties under these local symmetry transformations. The symmetries in the case of elementary particle theories are always internal, which means they work on the fields. In General Relativity we know the symmetries are space-time symmetries, which means they work on the coordinates. In the absense of gravitation the theory of Special Relativity is invariant under global Lorentz coordinate tranformations which leave the Minkowski metric tensor invariant (
Gravity: An Introduction To Einstein's General Relativity - Addison Wesley / Ben
. Einstein'stheory of general relativity is a cornerstone of modern physics.Gravity An Introduction to Einstein's general relativity.
http://www.aw.com/catalog/academic/product/1,4096,0805386629,00.html

Extractions: ABOUT THIS PRODUCT Description Table of Contents Features Appropriate Courses About the Author(s) SUPPLEMENTS Student Instructor INTERNET RESOURCES Companion Website RELATED TITLES Relativity (Physics/Astronomy) Gravity: An Introduction to Einstein's General Relativity View Larger Image James B. Hartle University of California, Santa Barbara
Early Philosophical Interpretations Of General Relativity
Early Philosophical Interpretations of general relativity. Einstein and theHistory of general relativity. (Boston, Basel, Berlin Birkhäuser).
http://plato.stanford.edu/entries/genrel-early/

Extractions: NOV 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 literati There has been a tendency, not uncommon in the case of a new scientific theory, for every philosopher to interpret the work of Einstein in accordance with his own metaphysical system, and to suggest that the outcome is a great accession of strength to the views which the philosopher in question previously held. This cannot be true in all cases; and it may be hoped that it is true in none. It would be disappointing if so fundamental a change as Einstein has introduced involved no philosophical novelty.
General Relativity
Astronomy. 1.11 general relativity. Special gravity. The cornerstone of generalrelativity is something known as the principle of equivalence.
http://www.herts.ac.uk/astro_ub/a13_ub.html
Field Equations & Equations Of Motion
Field Equations Equations of Motion (general relativity). Let me now presenta heuristic approach to the equations of general relativity.
http://www.grc.nasa.gov/WWW/K-12/Numbers/Math/Mathematical_Thinking/field_equati

Extractions: Proficiency Tests Mathematical Thinking in Physics Aeronauts 2000 CONTENTS Introduction Fermi's Piano Tuner Problem How Old is Old? If the Terrestrial Poles were to Melt... ... A Note on the Centrifugal and Coriolis Accelerations as Pseudo Accelerations - PDF File On Expansion of the Universe - PDF File (General Relativity) Velocity is a vector (tensor) or vector (tensor) field. In familiar notation, the velocity v is represented by v = v i e i where v i represent the components of the velocity, and e i represent basis (unit) vectors in the selected coordinate system. (As usual in tensor notation, summation is assumed over all repeated indices unless otherwise specified.) Acceleration is the first time-derivative of velocity, and involves derivatives of both the v i and the e i a = d v /dt = (dv i /dt) e i + v i (d e i /dt) . The second term may be further expanded as v i (d e i /dt) = v i i j k dx j /dt e k where i j k are the appropriate Christoffel symbols. Substituting, the expression for acceleration becomes
Altvw100
John G. Cramer Analog Column Alternate View 100 general relativity withoutBlack Holes. general relativity without Black Holes. by John G. Cramer.
http://www.npl.washington.edu/AV/altvw100.html

Extractions: "The Alternate View" columns of John G. Cramer Alternate View Column AV-100 Keywords: alternative general relativity Yilmaz theory black holes Published in the April-2000 issue of the explicit permission of the author. This page now has an access count of: This column is a milestone. It's the 100 th Alternate View column that I've written for Analog over a period of 16 years beginning in 1983. I was on a sabbatical in Berlin when Stan recruited me to write the column after Jerry Pournelle, my predecessor as AV columnist, decided to step down. The AV columns are a soapbox that was too attractive to pass up, and I've used them to promote an interst in science and to feed cutting-edge science ideas, primarily in the areas of physics and astrophysics, to the readers and writers of science fiction. Nevertheless, a small group of dissident theoretical physicists has recently been pointing out certain problems with orthodox GR and advocating a modification that has interesting consequences. It's this GR variant that I want to focus on here. In standard GR, gravity is considered to be "geometrical", to be a consequence of the curvature of space produced by nearby mass-energy.. If a mass or an energy-containing field is present in space, GR predicts that the space will become distorted. This distortion or curvature of space produces gravitational effects like the attraction between masses and the gravitational bending of light rays.
PhysicsWeb - Slingshot Test For General Relativity
Slingshot test for general relativity 4 April 2001. Physicists are hopingto make a new test of Einstein's General Theory of Relativity
http://physicsweb.org/article/news/5/4/1/1

Extractions: 4 April 2001 Physicists are hoping to make a new test of Einstein's General Theory of Relativity by measuring the effect of the Sun's gravity on a passing spacecraft. James Longuski of Purdue University and colleagues have devised a new formula to calculate the distortion of space from the deflection of a spacecraft's path as it skims the Sun (J M Longuski et al Phys. Rev. Lett. 2942). The researchers are optimistic that imminent refinements in measurement technology will allow them to carry out the most sensitive test of the theory yet. In 1915, Einstein proposed that gravity actually distorts the fabric of space. His calculations perfectly explained certain astronomical observations that Newtonian physics could not account for - such as the apparently exaggerated precession of Mercury's orbit. "General relativity is at the heart of everything in cosmology", says team member Ephraim Fischbach, "so it's very important we continue to test it to make sure its predictions are correct". The Small Interstellar Probe mission currently under consideration by NASA needs to perform a close fly-by of the Sun to gather enough momentum to propel itself outside the solar system. This 'slingshot' manoeuvre will take the craft to within 4 solar radii of the Sun. The probe's chief goal is to establish the composition of interstellar space, but Longuski and colleagues hope it will be able to include their experiment. "We can't get as precise a measurement by merely observing the planets in their orbits", Longuski told PhysicsWeb, "but we can control this experiment by selecting a trajectory for the spacecraft".
Gravity Probe B
Gravity Probe B is the relativity gyroscope experiment being developed by NASA and Stanford University Category Science Physics relativity 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/
Einstein, Albert. 1920. Relativity: The Special And General Theory
The physicist and humanitarian took his place beside the great teachers with thepublication of relativity The Special and general Theory, Einsteins own
http://www.bartleby.com/173/

Extractions: Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia 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 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

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