Donald Salisbury, Austin College Department of Physics and Max Planck Insitute for the History of Science
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Of the American Mathematical Society August 2017 Volume 64, Number 7
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society August 2017 Volume 64, Number 7 The Mathematics of Gravitational Waves: A Two-Part Feature page 684 The Travel Ban: Affected Mathematicians Tell Their Stories page 678 The Global Math Project: Uplifting Mathematics for All page 712 2015–2016 Doctoral Degrees Conferred page 727 Gravitational waves are produced by black holes spiraling inward (see page 674). American Mathematical Society LEARNING ® MEDIA MATHSCINET ONLINE RESOURCES MATHEMATICS WASHINGTON, DC CONFERENCES MATHEMATICAL INCLUSION REVIEWS STUDENTS MENTORING PROFESSION GRAD PUBLISHING STUDENTS OUTREACH TOOLS EMPLOYMENT MATH VISUALIZATIONS EXCLUSION TEACHING CAREERS MATH STEM ART REVIEWS MEETINGS FUNDING WORKSHOPS BOOKS EDUCATION MATH ADVOCACY NETWORKING DIVERSITY blogs.ams.org Notices of the American Mathematical Society August 2017 FEATURED 684684 718 26 678 Gravitational Waves The Graduate Student The Travel Ban: Affected Introduction Section Mathematicians Tell Their by Christina Sormani Karen E. Smith Interview Stories How the Green Light was Given for by Laure Flapan Gravitational Wave Research by Alexander Diaz-Lopez, Allyn by C. Denson Hill and Paweł Nurowski WHAT IS...a CR Submanifold? Jackson, and Stephen Kennedy by Phillip S. Harrington and Andrew Gravitational Waves and Their Raich Mathematics by Lydia Bieri, David Garfinkle, and Nicolás Yunes This season of the Perseid meteor shower August 12 and the third sighting in June make our cover feature on the discovery of gravitational waves -
A Brief History of Gravitational Waves
universe Review A Brief History of Gravitational Waves Jorge L. Cervantes-Cota 1, Salvador Galindo-Uribarri 1 and George F. Smoot 2,3,4,* 1 Department of Physics, National Institute for Nuclear Research, Km 36.5 Carretera Mexico-Toluca, Ocoyoacac, C.P. 52750 Mexico, Mexico; [email protected] (J.L.C.-C.); [email protected] (S.G.-U.) 2 Helmut and Ana Pao Sohmen Professor at Large, Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, 999077 Hong Kong, China 3 Université Sorbonne Paris Cité, Laboratoire APC-PCCP, Université Paris Diderot, 10 rue Alice Domon et Leonie Duquet, 75205 Paris Cedex 13, France 4 Department of Physics and LBNL, University of California; MS Bldg 50-5505 LBNL, 1 Cyclotron Road Berkeley, 94720 CA, USA * Correspondence: [email protected]; Tel.:+1-510-486-5505 Academic Editors: Lorenzo Iorio and Elias C. Vagenas Received: 21 July 2016; Accepted: 2 September 2016; Published: 13 September 2016 Abstract: This review describes the discovery of gravitational waves. We recount the journey of predicting and finding those waves, since its beginning in the early twentieth century, their prediction by Einstein in 1916, theoretical and experimental blunders, efforts towards their detection, and finally the subsequent successful discovery. Keywords: gravitational waves; General Relativity; LIGO; Einstein; strong-field gravity; binary black holes 1. Introduction Einstein’s General Theory of Relativity, published in November 1915, led to the prediction of the existence of gravitational waves that would be so faint and their interaction with matter so weak that Einstein himself wondered if they could ever be discovered. -
Towards a Theory of Gravitational Radiation Or What Is a Gravitational Wave?
Recent LIGO announcement Gravitational radiation theory: summary Prehistory: 1916-1956 History: 1957-1962 Towards a theory of gravitational radiation or What is a gravitational wave? Paweł Nurowski Center for Theoretical Physics Polish Academy of Sciences King’s College London, 28 April 2016 1/48 Recent LIGO announcement Gravitational radiation theory: summary Prehistory: 1916-1956 History: 1957-1962 Plan 1 Recent LIGO announcement 2 Gravitational radiation theory: summary 3 Prehistory: 1916-1956 4 History: 1957-1962 2/48 Recent LIGO announcement Gravitational radiation theory: summary Prehistory: 1916-1956 History: 1957-1962 LIGO detection: Its relevance the first detection of gravitational waves the first detection of a black hole; of a binary black-hole; of a merging process of black holes creating a new one; Kerr black holes exist; black holes with up to 60 Solar masses exist; the most energetic process ever observed important test of Einstein’s General Theory of Relativity new window: a birth of gravitational wave astronomy 3/48 Recent LIGO announcement Gravitational radiation theory: summary Prehistory: 1916-1956 History: 1957-1962 LIGO detection: Its relevance the first detection of gravitational waves the first detection of a black hole; of a binary black-hole; of a merging process of black holes creating a new one; Kerr black holes exist; black holes with up to 60 Solar masses exist; the most energetic process ever observed important test of Einstein’s General Theory of Relativity new window: a birth of gravitational wave astronomy -
Vector and Tensor Analysis, 1950, Harry Lass, 0177610514, 9780177610516, Mcgraw- Hill, 1950
Vector and tensor analysis, 1950, Harry Lass, 0177610514, 9780177610516, McGraw- Hill, 1950 DOWNLOAD http://bit.ly/1CHWNWq http://www.powells.com/s?kw=Vector+and+tensor+analysis DOWNLOAD http://goo.gl/RBcy2 https://itunes.apple.com/us/book/Vector-and-tensor-analysis/id439454683 http://bit.ly/1lGfW8S Vector & Tensor Analysis , U.Chatterjee & N.Chatterjee, , , . Tensor Calculus A Concise Course, Barry Spain, 2003, Mathematics, 125 pages. A compact exposition of the theory of tensors, this text also illustrates the power of the tensor technique by its applications to differential geometry, elasticity, and. The Art of Modeling Dynamic Systems Forecasting for Chaos, Randomness and Determinism, Foster Morrison, Mar 7, 2012, Mathematics, 416 pages. This text illustrates the roles of statistical methods, coordinate transformations, and mathematical analysis in mapping complex, unpredictable dynamical systems. It describes. Partial differential equations in physics , Arnold Sommerfeld, Jan 1, 1949, Mathematics, 334 pages. Partial differential equations in physics. Tensor Calculus , John Lighton Synge, Alfred Schild, 1978, Mathematics, 324 pages. "This book is an excellent classroom text, since it is clearly written, contains numerous problems and exercises, and at the end of each chapter has a summary of the. Vector and tensor analysis , Harry Lass, 1950, Mathematics, 347 pages. Abstract Algebra and Solution by Radicals , John Edward Maxfield, Margaret W. Maxfield, 1971, Mathematics, 209 pages. Easily accessible undergraduate-level text covers groups, polynomials, Galois theory, radicals, much more. Features many examples, illustrations and commentaries as well as 13. Underwater Missile Propulsion A Selection of Authoritative Technical and Descriptive Papers, Leonard Greiner, 1968, Fleet ballistic missile weapons systems, 502 pages. -
Professor Andrzej Trautman
PredictingPredicting GrGr avitational avitational WavesWaves briefly speaking THE MAGAZINE OF THE PASK 52 3/55/2017 PROF. ANDRZEJ TRAUTMAN e talk to Professor Andrzej W Trautman, Full Member of the Polish Academy of Sciences and Emeritus Professor at the University of Warsaw, about the consequences of the general theory of relativity, the theoretical foundations of gravitational waves and the difficulties in proving their existence. THE MAGAZINE 53 OF THE PAS 3/55/2017 Briefly Speaking ANDRZEJ TRAUTMAN: I should start by saying that of my work at the Polytechnic that I was able to start although I have worked on gravitational waves, it was simultaneous studies at the University. only on the theory. Over fifty years ago I searched for solutions of Einstein’s equations that may describe You were born in central Warsaw and you still gravitational waves and studied their properties. I had live in the city now, but you spent several years always assumed that their existence would one day be after the war wandering round Europe with your confirmed, and I was right. mother. During the Warsaw uprising we were deported to ACADEMIA: Let’s start by talking about what Germany. It was one of the worst periods of my life your research focuses on. – filled with hunger, filth, lice. We came back to Po- I graduated from the Warsaw Polytechnic, so I’m ac- land, but our apartment in Warsaw was destroyed and tually an engineer. I first met Professor Leopold Infeld, we spent a few months in Lublin where my father’s a theoretical physicist, towards the end of my studies. -
How the Green Light Was Given for Gravitational Wave Search
HOW THE GREEN LIGHT WAS GIVEN FOR GRAVITATIONAL WAVE SEARCH C DENSON HILL AND PAWELNUROWSKI Abstract. The recent detection of gravitational waves by the LIGO/VIRGO team [1] is an incredibly impressive achievement of experimental physics. It is also a tremendous success of the theory of General Relativity. It confirms the existence of black holes; shows that binary black holes exist; that they may collide and that during the merging process gravitational waves are produced. These are all predictions of General Relativity theory in its fully nonlinear regime. The existence of gravitational waves was predicted by Albert Einstein in 1916 within the framework of linearized Einstein theory. Contrary to common belief, even the very definition of a gravitational wave in the fully nonlinear Einstein theory was provided only after Einstein's death. Actually, Einstein had arguments against the existence of nonlinear gravitational waves (they were erroneous but he did not accept this), which virtually stopped develop- ment of the subject until the mid 1950s. This is what we refer to as the Red Light for gravitational waves research. In the following years, the theme was picked up again and studied vigor- ously by various experts, mainly Herman Bondi, Felix Pirani, Ivor Robinson and Andrzej Trautman, where the theoretical obstacles concerning gravita- tional wave existence were successfully overcome, thus giving the Green Light for experimentalists to start designing detectors, culminating in the recent LIGO/VIRGO discovery. In this note we tell the story of this theoretical breakthrough. Particular attention is given to the fundamental 1958 papers of Trautman [19, 20], which seem to be lesser known outside the circle of General Relativity experts. -
A Brief History of Gravitational Waves
Review A Brief History of Gravitational Waves Jorge L. Cervantes-Cota 1, Salvador Galindo-Uribarri 1 and George F. Smoot 2,3,4,* 1 Department of Physics, National Institute for Nuclear Research, Km 36.5 Carretera Mexico-Toluca, Ocoyoacac, Mexico State C.P.52750, Mexico; [email protected] (J.L.C.-C.); [email protected] (S.G.-U.) 2 Helmut and Ana Pao Sohmen Professor at Large, Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, 999077 Kowloon, Hong Kong, China. 3 Université Sorbonne Paris Cité, Laboratoire APC-PCCP, Université Paris Diderot, 10 rue Alice Domon et Leonie Duquet 75205 Paris Cedex 13, France. 4 Department of Physics and LBNL, University of California; MS Bldg 50-5505 LBNL, 1 Cyclotron Road Berkeley, CA 94720, USA. * Correspondence: [email protected]; Tel.:+1-510-486-5505 Abstract: This review describes the discovery of gravitational waves. We recount the journey of predicting and finding those waves, since its beginning in the early twentieth century, their prediction by Einstein in 1916, theoretical and experimental blunders, efforts towards their detection, and finally the subsequent successful discovery. Keywords: gravitational waves; General Relativity; LIGO; Einstein; strong-field gravity; binary black holes 1. Introduction Einstein’s General Theory of Relativity, published in November 1915, led to the prediction of the existence of gravitational waves that would be so faint and their interaction with matter so weak that Einstein himself wondered if they could ever be discovered. Even if they were detectable, Einstein also wondered if they would ever be useful enough for use in science. -
A Contextual Analysis of the Early Work of Andrzej Trautman and Ivor
A contextual analysis of the early work of Andrzej Trautman and Ivor Robinson on equations of motion and gravitational radiation Donald Salisbury1,2 1Austin College, 900 North Grand Ave, Sherman, Texas 75090, USA 2Max Planck Institute for the History of Science, Boltzmannstrasse 22, 14195 Berlin, Germany October 10, 2019 Abstract In a series of papers published in the course of his dissertation work in the mid 1950’s, Andrzej Trautman drew upon the slow motion approximation developed by his advisor Infeld, the general covariance based strong conservation laws enunciated by Bergmann and Goldberg, the Riemann tensor attributes explored by Goldberg and related geodesic deviation exploited by Pirani, the permissible metric discontinuities identified by Lich- nerowicz, O’Brien and Synge, and finally Petrov’s classification of vacuum spacetimes. With several significant additions he produced a comprehensive overview of the state of research in equations of motion and gravitational waves that was presented in a widely cited series of lectures at King’s College, London, in 1958. Fundamental new contribu- tions were the formulation of boundary conditions representing outgoing gravitational radiation the deduction of its Petrov type, a covariant expression for null wave fronts, and a derivation of the correct mass loss formula due to radiation emission. Ivor Robin- son had already in 1956 developed a bi-vector based technique that had resulted in his rediscovery of exact plane gravitational wave solutions of Einstein’s equations. He was the first to characterize shear-free null geodesic congruences. He and Trautman met in London in 1958, and there resulted a long-term collaboration whose initial fruits were the Robinson-Trautman metric, examples of which were exact spherical gravitational waves. -
SCIENTIFIC REPORT for the 5 YEAR PERIOD 1993–1997 INCLUDING the PREHISTORY 1991–1992 ESI, Boltzmanngasse 9, A-1090 Wien, Austria
The Erwin Schr¨odinger International Boltzmanngasse 9 ESI Institute for Mathematical Physics A-1090 Wien, Austria Scientific Report for the 5 Year Period 1993–1997 Including the Prehistory 1991–1992 Vienna, ESI-Report 1993-1997 March 5, 1998 Supported by Federal Ministry of Science and Transport, Austria http://www.esi.ac.at/ ESI–Report 1993-1997 ERWIN SCHRODINGER¨ INTERNATIONAL INSTITUTE OF MATHEMATICAL PHYSICS, SCIENTIFIC REPORT FOR THE 5 YEAR PERIOD 1993–1997 INCLUDING THE PREHISTORY 1991–1992 ESI, Boltzmanngasse 9, A-1090 Wien, Austria March 5, 1998 Table of contents THE YEAR 1991 (Paleolithicum) . 3 Report on the Workshop: Interfaces between Mathematics and Physics, 1991 . 3 THE YEAR 1992 (Neolithicum) . 9 Conference on Interfaces between Mathematics and Physics . 9 Conference ‘75 years of Radon transform’ . 9 THE YEAR 1993 (Start of history of ESI) . 11 Erwin Schr¨odinger Institute opened . 11 The Erwin Schr¨odinger Institute An Austrian Initiative for East-West-Collaboration . 11 ACTIVITIES IN 1993 . 13 Short overview . 13 Two dimensional quantum field theory . 13 Schr¨odinger Operators . 16 Differential geometry . 18 Visitors outside of specific activities . 20 THE YEAR 1994 . 21 General remarks . 21 FTP-server for POSTSCRIPT-files of ESI-preprints available . 22 Winter School in Geometry and Physics . 22 ACTIVITIES IN 1994 . 22 International Symposium in Honour of Boltzmann’s 150th Birthday . 22 Ergodicity in non-commutative algebras . 23 Mathematical relativity . 23 Quaternionic and hyper K¨ahler manifolds, . 25 Spinors, twistors and conformal invariants . 27 Gibbsian random fields . 28 CONTINUATION OF 1993 PROGRAMS . 29 Two-dimensional quantum field theory . 29 Differential Geometry . 29 Schr¨odinger Operators . -
SCIENTIFIC REPORT for the YEAR 1999 ESI, Boltzmanngasse 9, A-1090 Wien, Austria
The Erwin Schr¨odinger International Boltzmanngasse 9 ESI Institute for Mathematical Physics A-1090 Wien, Austria Scientific Report for the Year 1999 Vienna, ESI-Report 1999 March 1, 2000 Supported by Federal Ministry of Science and Transport, Austria ESI–Report 1999 ERWIN SCHRODINGER¨ INTERNATIONAL INSTITUTE OF MATHEMATICAL PHYSICS, SCIENTIFIC REPORT FOR THE YEAR 1999 ESI, Boltzmanngasse 9, A-1090 Wien, Austria March 1, 2000 Honorary President: Walter Thirring, Tel. +43-1-3172047-15. President: Jakob Yngvason: +43-1-31367-3406. [email protected] Director: Peter W. Michor: +43-1-3172047-16. [email protected] Director: Klaus Schmidt: +43-1-3172047-14. [email protected] Administration: Ulrike Fischer, Doris Garscha, Ursula Sagmeister. Computer group: Andreas Cap, Gerald Teschl, Hermann Schichl. International Scientific Advisory board: Jean-Pierre Bourguignon (IHES), Giovanni Gallavotti (Roma), Krzysztof Gawedzki (IHES), Vaughan F.R. Jones (Berkeley), Viktor Kac (MIT), Elliott Lieb (Princeton), Harald Grosse (Vienna), Harald Niederreiter (Vienna), ESI preprints are available via ‘anonymous ftp’ or ‘gopher’: FTP.ESI.AC.AT and via the URL: http://www.esi.ac.at. Table of contents Statement on Austria’s current political situation . 2 General remarks . 2 Winter School in Geometry and Physics . 2 ESI - Workshop Geometrical Aspects of Spectral Theory . 3 PROGRAMS IN 1999 . 4 Functional Analysis . 4 Nonequilibrium Statistical Mechanics . 7 Holonomy Groups in Differential Geometry . 9 Complex Analysis . 10 Applications of Integrability . 11 Continuation of programs from 1998 and earlier . 12 Guests via Director’s shares . 13 List of Preprints . 14 List of seminars and colloquia outside of conferences . 25 List of all visitors in the year 1999 . -
Gravitational Waves
Gravitational waves 27.10.20 1/52 General schedule ⋆ History ⋆ Gravity research before modern scientific revolution, ⋆ Gravity and gravitational waves from Newton to Einstein, ⋆ After Einstein - brief overview of the XX century. ⋆ Introduction to general relativity ⋆ Detection principles ⋆ Detectors ⋆ Binary black-hole system ⋆ Bursts and continuous waves ⋆ Rates and populations, stochastic GW background, cosmology ⋆ Testing general relativity ⋆ Data analysis: waveforms and detection ⋆ Data analysis: parameter estimation 2/52 Fundamental interactions (known so far) Standard Model of elementary particles Organized by their strength (coupling): ⋆ Strong interactions (1), ⋆ 1 Electromagnetism ( 137 ), ⋆ Weak interactions (10−9), ⋆ Gravitation (10−38) ⋆ not included in the Standard Model, ⋆ the weakest ”force”, ⋆ does the graviton really exist? 3/52 Before modern scientific revolution Aristotle (384-322 BCE): ⋆ There is no effect of motion without a cause, ⋆ massive bodies move according to their tendency in natural motion, i.e., towards the centre of the universe, which happens to be the center of Earth, ⋆ cause of tendency: inner gravitas or heaviness, ⋆ 4 elements on Earth, proposed earlier by Empedocles (490-430 BCE), æther in heavens, ⋆ natural state of objects is to be at rest. 4/52 Before modern scientific revolution Aristotle (384-322 BCE): ⋆ natural and ”violent” (unnatural) motion (→ continuous force needed to move bodies) ⋆ speed of falling bodies is ⋆ proportional to their weight, ⋆ inversely proportional to the resistance of the medium (→ infinite speed in vacuum?), Vitruvius (1st century BCE): ⋆ gravity depends on substance’s ’nature’ (specific gravity) ↔ Archimedes, buoyancy 4/52 India, Islamic world; theory of impetus ⋆ Brahmagupta (598-668 CE) describes gravity as an attractive force, ⋆ 6th century, John Philoponus of Alexandria: the theory of impetus to explain motion of objects against gravity. -
Relativistic Astrophysics: the View from Texas in Baltimore (Review)
btropliysica/ Letters, 1981, Vol. 22, pp. 21-30 C> 1981 Gordon and Breach, Science Publishers, Inc. 0004-6388/81/2201-002 I $06.5010 Printed in the United States of America Relativistic Astrophysics: The View from Texas in Baltimore (Review) V. L. TRIMBLE Department of Physics, University of'Ca/ifornia. Irvine CA 92717 and Astronomy Program, University of Maryland College Park MD 20742 S. P. MARAN Laborarory for Astronomy and Solar Physics. NASA Goddard Space Flight Center, Greenbelt MD 20771 (Received July 7, 1981) · INTRODUCTION quantum theory and cannot be turned into one. It 0 is not renormalizable. That is, many seemingly The phrase relativistic astrophysics" was in sensible calculations yield infinite answers, and vented by Ivor Robinson, the late Alfred Schild, there is no coherent prescription for subtracting and Englebert Schucking on July 4th, 1963, as the infinite part to leave a finite, correct answer, part of the title of a symposium they were then in the way that quantum electrodynamics deals organizing at Dallas ("Conference on Gravita with the infinities of electromagnetism. tional Collapse and Other Topics in Relativistic 0 Even at the classical level, there may be linger Astrophysics ). The glory of the name, according ing doubts: Thomas Van Flandern (U.S. Naval to Robinson (who claims to have been out of the Observatory) finds, primarily from precise timings room at the crucial moment), was that no one of lunar occultations, that the constant of gravity knew what it meant, so they could have anything is decreasing by 3 parts in 10 11 per year, which is they wanted at the conference.