THE IMPACT of WORLD WAR I on RELATIVITY: a PROGRESS REPORT by Virginia Trimble University of California Irvine, Las Cumbres Obse
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Ricci, Levi-Civita, and the Birth of General Relativity Reviewed by David E
BOOK REVIEW Einstein’s Italian Mathematicians: Ricci, Levi-Civita, and the Birth of General Relativity Reviewed by David E. Rowe Einstein’s Italian modern Italy. Nor does the author shy away from topics Mathematicians: like how Ricci developed his absolute differential calculus Ricci, Levi-Civita, and the as a generalization of E. B. Christoffel’s (1829–1900) work Birth of General Relativity on quadratic differential forms or why it served as a key By Judith R. Goodstein tool for Einstein in his efforts to generalize the special theory of relativity in order to incorporate gravitation. In This delightful little book re- like manner, she describes how Levi-Civita was able to sulted from the author’s long- give a clear geometric interpretation of curvature effects standing enchantment with Tul- in Einstein’s theory by appealing to his concept of parallel lio Levi-Civita (1873–1941), his displacement of vectors (see below). For these and other mentor Gregorio Ricci Curbastro topics, Goodstein draws on and cites a great deal of the (1853–1925), and the special AMS, 2018, 211 pp. 211 AMS, 2018, vast secondary literature produced in recent decades by the world that these and other Ital- “Einstein industry,” in particular the ongoing project that ian mathematicians occupied and helped to shape. The has produced the first 15 volumes of The Collected Papers importance of their work for Einstein’s general theory of of Albert Einstein [CPAE 1–15, 1987–2018]. relativity is one of the more celebrated topics in the history Her account proceeds in three parts spread out over of modern mathematical physics; this is told, for example, twelve chapters, the first seven of which cover episodes in [Pais 1982], the standard biography of Einstein. -
Charles Darwin: a Companion
CHARLES DARWIN: A COMPANION Charles Darwin aged 59. Reproduction of a photograph by Julia Margaret Cameron, original 13 x 10 inches, taken at Dumbola Lodge, Freshwater, Isle of Wight in July 1869. The original print is signed and authenticated by Mrs Cameron and also signed by Darwin. It bears Colnaghi's blind embossed registration. [page 3] CHARLES DARWIN A Companion by R. B. FREEMAN Department of Zoology University College London DAWSON [page 4] First published in 1978 © R. B. Freeman 1978 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the permission of the publisher: Wm Dawson & Sons Ltd, Cannon House Folkestone, Kent, England Archon Books, The Shoe String Press, Inc 995 Sherman Avenue, Hamden, Connecticut 06514 USA British Library Cataloguing in Publication Data Freeman, Richard Broke. Charles Darwin. 1. Darwin, Charles – Dictionaries, indexes, etc. 575′. 0092′4 QH31. D2 ISBN 0–7129–0901–X Archon ISBN 0–208–01739–9 LC 78–40928 Filmset in 11/12 pt Bembo Printed and bound in Great Britain by W & J Mackay Limited, Chatham [page 5] CONTENTS List of Illustrations 6 Introduction 7 Acknowledgements 10 Abbreviations 11 Text 17–309 [page 6] LIST OF ILLUSTRATIONS Charles Darwin aged 59 Frontispiece From a photograph by Julia Margaret Cameron Skeleton Pedigree of Charles Robert Darwin 66 Pedigree to show Charles Robert Darwin's Relationship to his Wife Emma 67 Wedgwood Pedigree of Robert Darwin's Children and Grandchildren 68 Arms and Crest of Robert Waring Darwin 69 Research Notes on Insectivorous Plants 1860 90 Charles Darwin's Full Signature 91 [page 7] INTRODUCTION THIS Companion is about Charles Darwin the man: it is not about evolution by natural selection, nor is it about any other of his theoretical or experimental work. -
Glossary Glossary
Glossary Glossary Albedo A measure of an object’s reflectivity. A pure white reflecting surface has an albedo of 1.0 (100%). A pitch-black, nonreflecting surface has an albedo of 0.0. The Moon is a fairly dark object with a combined albedo of 0.07 (reflecting 7% of the sunlight that falls upon it). The albedo range of the lunar maria is between 0.05 and 0.08. The brighter highlands have an albedo range from 0.09 to 0.15. Anorthosite Rocks rich in the mineral feldspar, making up much of the Moon’s bright highland regions. Aperture The diameter of a telescope’s objective lens or primary mirror. Apogee The point in the Moon’s orbit where it is furthest from the Earth. At apogee, the Moon can reach a maximum distance of 406,700 km from the Earth. Apollo The manned lunar program of the United States. Between July 1969 and December 1972, six Apollo missions landed on the Moon, allowing a total of 12 astronauts to explore its surface. Asteroid A minor planet. A large solid body of rock in orbit around the Sun. Banded crater A crater that displays dusky linear tracts on its inner walls and/or floor. 250 Basalt A dark, fine-grained volcanic rock, low in silicon, with a low viscosity. Basaltic material fills many of the Moon’s major basins, especially on the near side. Glossary Basin A very large circular impact structure (usually comprising multiple concentric rings) that usually displays some degree of flooding with lava. The largest and most conspicuous lava- flooded basins on the Moon are found on the near side, and most are filled to their outer edges with mare basalts. -
Review Study on “The Black Hole”
IJIRST –International Journal for Innovative Research in Science & Technology| Volume 2 | Issue 10 | March 2016 ISSN (online): 2349-6010 Review Study on “The Black Hole” Syed G. Ibrahim Department of Engineering Physics (Nanostructured Thin Film Materials Laboratory) Prof. Ram Meghe College of Engineering and Management, Badnera 444701, Maharashtra, India Abstract As a star grows old, swells, then collapses on itself, often you will hear the word “black hole” thrown around. The black hole is a gravitationally collapsed mass, from which no light, matter, or signal of any kind can escape. These exotic objects have captured our imagination ever since they were predicted by Einstein's Theory of General Relativity in 1915. So what exactly is a black hole? A black hole is what remains when a massive star dies. Not every star will become a black hole, only a select few with extremely large masses. In order to have the ability to become a black hole, a star will have to have about 20 times the mass of our Sun. No known process currently active in the universe can form black holes of less than stellar mass. This is because all present black hole formation is through gravitational collapse, and the smallest mass which can collapse to form a black hole produces a hole approximately 1.5-3.0 times the mass of the sun .Smaller masses collapse to form white dwarf stars or neutron stars. Keywords: Escape Velocity, Horizon, Schwarzschild Radius, Black Hole _______________________________________________________________________________________________________ I. INTRODUCTION Soon after Albert Einstein formulated theory of relativity, it was realized that his equations have solutions in closed form. -
The Emergence of Gravitational Wave Science: 100 Years of Development of Mathematical Theory, Detectors, Numerical Algorithms, and Data Analysis Tools
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 53, Number 4, October 2016, Pages 513–554 http://dx.doi.org/10.1090/bull/1544 Article electronically published on August 2, 2016 THE EMERGENCE OF GRAVITATIONAL WAVE SCIENCE: 100 YEARS OF DEVELOPMENT OF MATHEMATICAL THEORY, DETECTORS, NUMERICAL ALGORITHMS, AND DATA ANALYSIS TOOLS MICHAEL HOLST, OLIVIER SARBACH, MANUEL TIGLIO, AND MICHELE VALLISNERI In memory of Sergio Dain Abstract. On September 14, 2015, the newly upgraded Laser Interferometer Gravitational-wave Observatory (LIGO) recorded a loud gravitational-wave (GW) signal, emitted a billion light-years away by a coalescing binary of two stellar-mass black holes. The detection was announced in February 2016, in time for the hundredth anniversary of Einstein’s prediction of GWs within the theory of general relativity (GR). The signal represents the first direct detec- tion of GWs, the first observation of a black-hole binary, and the first test of GR in its strong-field, high-velocity, nonlinear regime. In the remainder of its first observing run, LIGO observed two more signals from black-hole bina- ries, one moderately loud, another at the boundary of statistical significance. The detections mark the end of a decades-long quest and the beginning of GW astronomy: finally, we are able to probe the unseen, electromagnetically dark Universe by listening to it. In this article, we present a short historical overview of GW science: this young discipline combines GR, arguably the crowning achievement of classical physics, with record-setting, ultra-low-noise laser interferometry, and with some of the most powerful developments in the theory of differential geometry, partial differential equations, high-performance computation, numerical analysis, signal processing, statistical inference, and data science. -
DMAAC – February 1973
LUNAR TOPOGRAPHIC ORTHOPHOTOMAP (LTO) AND LUNAR ORTHOPHOTMAP (LO) SERIES (Published by DMATC) Lunar Topographic Orthophotmaps and Lunar Orthophotomaps Scale: 1:250,000 Projection: Transverse Mercator Sheet Size: 25.5”x 26.5” The Lunar Topographic Orthophotmaps and Lunar Orthophotomaps Series are the first comprehensive and continuous mapping to be accomplished from Apollo Mission 15-17 mapping photographs. This series is also the first major effort to apply recent advances in orthophotography to lunar mapping. Presently developed maps of this series were designed to support initial lunar scientific investigations primarily employing results of Apollo Mission 15-17 data. Individual maps of this series cover 4 degrees of lunar latitude and 5 degrees of lunar longitude consisting of 1/16 of the area of a 1:1,000,000 scale Lunar Astronautical Chart (LAC) (Section 4.2.1). Their apha-numeric identification (example – LTO38B1) consists of the designator LTO for topographic orthophoto editions or LO for orthophoto editions followed by the LAC number in which they fall, followed by an A, B, C or D designator defining the pertinent LAC quadrant and a 1, 2, 3, or 4 designator defining the specific sub-quadrant actually covered. The following designation (250) identifies the sheets as being at 1:250,000 scale. The LTO editions display 100-meter contours, 50-meter supplemental contours and spot elevations in a red overprint to the base, which is lithographed in black and white. LO editions are identical except that all relief information is omitted and selenographic graticule is restricted to border ticks, presenting an umencumbered view of lunar features imaged by the photographic base. -
The Principle of Equivalence As a Criterion of Identity Ryan Samaroo
Forthcoming in Synthese The Principle of Equivalence as a Criterion of Identity Ryan Samaroo Somerville College, Woodstock Road, Oxford, OX2 6HD, United Kingdom [email protected] Dedicated to the memory of William (Bill) Demopoulos Abstract In 1907 Einstein had the insight that bodies in free fall do not “feel” their own weight. This has been formalized in what is called “the principle of equivalence.” The principle motivated a critical analysis of the Newtonian and special-relativistic concepts of inertia, and it was indispensable to Einstein’s development of his theory of gravitation. A great deal has been written about the principle. Nearly all of this work has focused on the content of the principle and whether it has any content in Einsteinian gravitation, but more remains to be said about its methodological role in the development of the theory. I argue that the principle should be understood as a kind of foundational principle known as a criterion of identity. This work extends and substantiates a recent account of the notion of a criterion of identity by William Demopoulos. Demopoulos argues that the notion can be employed more widely than in the foundations of arithmetic and that we see this in the development of physical theories, in particular space-time theories. This new account forms the basis of a general framework for applying a number of mathematical theories and for distinguishing between applied mathematical theories that are and are not empirically constrained. 1. Introduction “The principle of equivalence,” which Einstein originally used to refer to one particular statement, has come to refer to a number of interrelated principles in the theory of gravitation.1 1 Einstein’s first formulation of the principle can be found in his article “On the Relativity Principle and the Conclusions Drawn from It” (1907, p. -
August 2017 Posidonius P & Luther
A PUBLICATION OF THE LUNAR SECTION OF THE A.L.P.O. EDITED BY: Wayne Bailey [email protected] 17 Autumn Lane, Sewell, NJ 08080 RECENT BACK ISSUES: http://moon.scopesandscapes.com/tlo_back.html FEATURE OF THE MONTH – AUGUST 2017 POSIDONIUS P & LUTHER Sketch and text by Robert H. Hays, Jr. - Worth, Illinois, USA March 5, 2017 01:28-01:48; UT, 15 cm refl, 170x, seeing 7-8/10. I drew these craters on the evening of March 4/5, 2017 while the moon was hiding some Hyades stars. This area is in northeast Mare Serenitatis west of Posidonius itself. Posidonius P is the largest crater on this sketch. The smaller crater south of P is Posidonius F and Posidonius G is the tiny pit to the north. There is a halo around Posidonius G, but this crater is noticeably north of the halo's center. A very low round swelling is northeast of Posidonius G. Luther is the crater well to the west of Posidonius P. All four of these craters are crisp, symmetric features, differing only in size. There are an assortment of elevations near Luther. The peak Luther alpha is well to the west of Luther, and showed dark shadowing at this time. All of the other features near Luther are more subtle than Luther alpha. One mound is between Luther and Luther alpha. Two more mounds are north of Luther, and a low ridge is just east of this crater. A pair of very low mounds are south of Luther. These are the vaguest features depicted here, and may be too conspicuous on the sketch. -
Math, Physics, and Calabi–Yau Manifolds
Math, Physics, and Calabi–Yau Manifolds Shing-Tung Yau Harvard University October 2011 Introduction I’d like to talk about how mathematics and physics can come together to the benefit of both fields, particularly in the case of Calabi-Yau spaces and string theory. This happens to be the subject of the new book I coauthored, THE SHAPE OF INNER SPACE It also tells some of my own story and a bit of the history of geometry as well. 2 In that spirit, I’m going to back up and talk about my personal introduction to geometry and how I ended up spending much of my career working at the interface between math and physics. Along the way, I hope to give people a sense of how mathematicians think and approach the world. I also want people to realize that mathematics does not have to be a wholly abstract discipline, disconnected from everyday phenomena, but is instead crucial to our understanding of the physical world. 3 There are several major contributions of mathematicians to fundamental physics in 20th century: 1. Poincar´eand Minkowski contribution to special relativity. (The book of Pais on the biography of Einstein explained this clearly.) 2. Contributions of Grossmann and Hilbert to general relativity: Marcel Grossmann (1878-1936) was a classmate with Einstein from 1898 to 1900. he was professor of geometry at ETH, Switzerland at 1907. In 1912, Einstein came to ETH to be professor where they started to work together. Grossmann suggested tensor calculus, as was proposed by Elwin Bruno Christoffel in 1868 (Crelle journal) and developed by Gregorio Ricci-Curbastro and Tullio Levi-Civita (1901). -
Marcel Grossmann Awards
MG15 MARCEL GROSSMANN AWARDS ROME 2018 ICRANet and ICRA MG XV MARCEL GROSSMANN AWARDS ROME 2018 and TEST The 15th Marcel Grossmann Meeting – MG XV 2nd July 2018, Rome (Italy) Aula Magna – University “Sapienza” of Rome Institutional Awards Goes to: PLANCK SCIENTIFIC COLLABORATION (ESA) “for obtaining important constraints on the models of inflationary stage of the Universe and level of primordial non-Gaussianity; measuring with unprecedented sensitivity gravitational lensing of Cosmic Microwave Background fluctuations by large-scale structure of the Universe and corresponding B- polarization of CMB, the imprint on the CMB of hot gas in galaxy clusters; getting unique information about the time of reionization of our Universe and distribution and properties of the dust and magnetic fields in our Galaxy” - presented to Jean-Loup Puget, the Principal Investigator of the High Frequency Instrument (HFI) HANSEN EXPERIMENTAL PHYSICS LABORATORY AT STANFORD UNIVERSITY “to HEPL for having developed interdepartmental activities at Stanford University at the frontier of fundamental physics, astrophysics and technology” - presented to Research Professor Leo Hollberg, HEPL Assistant Director Individual Awards Goes to LYMAN PAGE “for his collaboration with David Wilkinson in realizing the NASA Explorer WMAP mission and as founding director of the Atacama Cosmology Telescope” Goes to RASHID ALIEVICH SUNYAEV “for the development of theoretical tools in the scrutinising, through the CMB, of the first observable electromagnetic appearance of our Universe” Goes to SHING-TUNG YAU “for the proof of the positivity of total mass in the theory of general relativity and perfecting as well the concept of quasi-local mass, for his proof of the Calabi conjecture, for his continuous inspiring role in the study of black holes physics” Each recipient is presented with a silver casting of the TEST sculpture by the artist A. -
Historical Painting Techniques, Materials, and Studio Practice
Historical Painting Techniques, Materials, and Studio Practice PUBLICATIONS COORDINATION: Dinah Berland EDITING & PRODUCTION COORDINATION: Corinne Lightweaver EDITORIAL CONSULTATION: Jo Hill COVER DESIGN: Jackie Gallagher-Lange PRODUCTION & PRINTING: Allen Press, Inc., Lawrence, Kansas SYMPOSIUM ORGANIZERS: Erma Hermens, Art History Institute of the University of Leiden Marja Peek, Central Research Laboratory for Objects of Art and Science, Amsterdam © 1995 by The J. Paul Getty Trust All rights reserved Printed in the United States of America ISBN 0-89236-322-3 The Getty Conservation Institute is committed to the preservation of cultural heritage worldwide. The Institute seeks to advance scientiRc knowledge and professional practice and to raise public awareness of conservation. Through research, training, documentation, exchange of information, and ReId projects, the Institute addresses issues related to the conservation of museum objects and archival collections, archaeological monuments and sites, and historic bUildings and cities. The Institute is an operating program of the J. Paul Getty Trust. COVER ILLUSTRATION Gherardo Cibo, "Colchico," folio 17r of Herbarium, ca. 1570. Courtesy of the British Library. FRONTISPIECE Detail from Jan Baptiste Collaert, Color Olivi, 1566-1628. After Johannes Stradanus. Courtesy of the Rijksmuseum-Stichting, Amsterdam. Library of Congress Cataloguing-in-Publication Data Historical painting techniques, materials, and studio practice : preprints of a symposium [held at] University of Leiden, the Netherlands, 26-29 June 1995/ edited by Arie Wallert, Erma Hermens, and Marja Peek. p. cm. Includes bibliographical references. ISBN 0-89236-322-3 (pbk.) 1. Painting-Techniques-Congresses. 2. Artists' materials- -Congresses. 3. Polychromy-Congresses. I. Wallert, Arie, 1950- II. Hermens, Erma, 1958- . III. Peek, Marja, 1961- ND1500.H57 1995 751' .09-dc20 95-9805 CIP Second printing 1996 iv Contents vii Foreword viii Preface 1 Leslie A. -
Glossary of Lunar Terminology
Glossary of Lunar Terminology albedo A measure of the reflectivity of the Moon's gabbro A coarse crystalline rock, often found in the visible surface. The Moon's albedo averages 0.07, which lunar highlands, containing plagioclase and pyroxene. means that its surface reflects, on average, 7% of the Anorthositic gabbros contain 65-78% calcium feldspar. light falling on it. gardening The process by which the Moon's surface is anorthosite A coarse-grained rock, largely composed of mixed with deeper layers, mainly as a result of meteor calcium feldspar, common on the Moon. itic bombardment. basalt A type of fine-grained volcanic rock containing ghost crater (ruined crater) The faint outline that remains the minerals pyroxene and plagioclase (calcium of a lunar crater that has been largely erased by some feldspar). Mare basalts are rich in iron and titanium, later action, usually lava flooding. while highland basalts are high in aluminum. glacis A gently sloping bank; an old term for the outer breccia A rock composed of a matrix oflarger, angular slope of a crater's walls. stony fragments and a finer, binding component. graben A sunken area between faults. caldera A type of volcanic crater formed primarily by a highlands The Moon's lighter-colored regions, which sinking of its floor rather than by the ejection of lava. are higher than their surroundings and thus not central peak A mountainous landform at or near the covered by dark lavas. Most highland features are the center of certain lunar craters, possibly formed by an rims or central peaks of impact sites.