DOCSLIB.ORG

Traceabilitv of Time Requirements

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Traceabilitv of Time Requirements tainties of the measurements themselves, The resulting uncertainty of the overall GPS and the Legal process (which is at best a statistical extrapolation and not an actual measure ment) might or might not satisfy our initial Traceabilitv of Time requirements. J The uncertainty associated with basing /ud& Levine National Institute of Standards and Technology traceability on previous calibrations exists and the University of Colorado for a mechanical artifact (a voltmeter, for example) as well, but our confidence in the stability of a properly maintained and local- 4s Faster, James Gleick notes in his recent book "A man with a watch knows what time ly available mechanical artifact usually is it is. A man with two watches is never sure." From the sundial, to the water clock, to the much higher than it is for a complex system escapement, to the pendulum, to the quartz crystal, to the atomic clock, to the Global based on a remote reference standard. The Positioning System, humanity has been obsessed with knowing what time it is. But just fact that the channel between our device fike the man with two watches, how do we know whose watch or clock is correct? In and the reference is usually not under our other words, as the rock band Chicago noted in one oftheir classic hits, "Does anyone direct control does not help matters. really know what time it is? Does anyone really care?" The answer to both questions is a Applications that require traceable meas resounding 'yes." Our modem society depends on knowing the correct time with higher urements usually have documentation 2nd higher accuracies for everything from time-stamping electronic transactions to syn- requirements as well as technical ones. chronizing telecommunications to navigating spacecrafi. "Correct" means that the time Depending on the details of the application, must be technically, and in some cases legally, traceable to national or intemational these requirements might range from main- standards. In this month's column, Dr. Judah Levine discusses these standards and the taining a simple log of the calibrations to important role GPS plays in keeping the world's timepieces both technically and legally real-time oversight or auditing by a disin- synchronized. terested third party using encrypted and Dr. Levine is a physicist in the Time and Frequency Division of the National Institute digitally signed messages. Systems that can ofStandards and Technology (NI.. formerly called the National Bureau ofStandards) support these requirements can become in Boulder, Colorado. He is also an adjoint professor in the Department ofPhysics of quite complex, because they must be pro- the University of Colorado. He received a B.A. in 1960 Yeshiva College and hm M.S. tected against both outsiders and insiders. and Ph.D. degrees from New York University in 1963 and 1966 respectively. Dr. Levine's The National Institute of Standards and research involves studies ofthe statistics offrequency standards and improving the accu- Technology (NISI') (and some other nation- racy of the distribution oftime and frequency information using both satellite and terres- al laboratories) provide onlysome of these trial methods. He is also involved in the application ofprecision measurement techniques services; other services (especially those to problems ofgeophysical interest. In collaboration with colleagues at NIST, he is intended for satisfying commercial or finan- engaged in improving methods for realizing the definition ofthe second and for distribut- cial requirements) are (or will be) provid- ing accurate time and frequency information. ed by private third parties using time sig- nals that are traceable to national standards. The Treaty of the Meter The Treaty of the Meter (Convention du Metre) is the basis for all international cooperation on questions of standards and precision metrology The treaty was signed in 1875 in Paris and was ratified by the US. Senate in 1878. The treaty was modified in 1921, and the modified version was ratified by the U.S. Senate in 1923. The modifica- "traceab1e"measurementis one that for traceability The fact that a previous time tions did not make any substantial changes A can be related to national or interna- stamp from some source was found to be to the original document. There are cur- tional standards using an unbroken chain within an acceptable tolerance of a refer- rently 49 member states of the treaty of measurements, each of which has a stat- ence standard does not by itself imply The treaty established the International ed uncertainty In this article I will describe (much less guarantee) that the current one Bureau of Weights and Measures (Bureau the traceability of time signals, with a spe- will also satisfy the same requirement. lntemational des bids et Mesures or BIPM), cial focuson the legal aspects of this ques- We can address this issue statistically which is currently located in Shes,a sub- tion. As I will show below, legal traceabili- by combining the interval since the last cal- urb of Paris. The BIPM is managed by the ty is not a purely technical question -the ibration with a statistical estimate of the International Committee of Weights and legal and technical definitions of time are stability of the reference to arrive at some Measures (Cornit6 International des kids not precisely the same (at least in the confidence interval for the current meas- et Mesures or CIPM). The President of the United States at present), and this differ- urement. The result is likely to be charac- CIPM is currently Professor J. Kovalevsky, ence could be significant in practice. terized in terms of a root mean square error, who is at the Observatoire de la CGte An unbroken chain of measurements is which is a function of the interval since the d'Azur, and the U.S. representative is Dr. a necessary but not sufficient requirement last calibration as well as of the uncer- Karen Brown, the Deputy Director of NIST GfS World January 2001 www.gpsworld.com The organizational structure defined in 4.0 . thelkaty of the Meter was initially intend- ed to deal with maintaining and calibrating ar ifact standards, such as the standard mc' ter and kilogram. The responsibilities of the BIPM were expanded over time to include other standards activities. In what follows, we will discuss only the current arrangement, which dates from 1987 when the responsibility for dealing with standards of time and frequency was transferred to the BIPM from the Bureau International de I'Heure. The CIPM appoints a number of consul- I ti tative committees to provide technical advice on questions that are referred to them. The committee that is important for -1 .o this discussion is the Consultative Commit- 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2 0 Year tee onTime and Frequency (CO,which was formerly called the Consultative CURE 1 The length of the astronomical day varies because of several different Committee for the Definition of the Second henomena including tidal friction and the exchange of angular momentum (CCDS). The CCFin turn appoints a num- etween the Earth's core, mantle, and atmosphere. This plot of the annual mean ber of working groups and subcommittees ifferences between the actual length of day and a day containing exactly to deal with specific questions. Two that 6,400 seconds (the UTC day) illustrates that during the past 100 years, the day are important for this discussion are the ased on the Earth's rotation has almost always been longer than the UTC day Working Group on International Atomic iith a maximum departure of about 4 milliseconds. Time UAI) and the subgroup on GPS and GLONASTimeTransfer Standards. neWeb 1 .o page of the BIPM has additional organiza- tional details (see "Further Reading"). In 0.8 __ particular, that page describes other rele- b vant working groups such as the one that is concerned with the realization of primary frequency standards and another which deals with time and frequency transfer using non-GPS methods such as two-way satellite time transfer. nme, Frequency, and the BIPM Althou h time and frequency were origi- nally dought of as distinct quantities with independent definitions, this distinction has not been significant for about 30 years. #en frequency standards based on atom- -0.6 ic transitions were first developed in the 1993 1994 1995 1996 1997 1998 1999 2000 2001 19%, the initial plan was to use these stan- Year ~~ ~~~ ~~ dards to realize the standard of frequency ICURE 2 The longer astronomical day requires the insertion of leap seconds inti but to maintain the standard of time astre ie UTC time scale in order to keep the difference between UT1 and UTC less nomically That method proved to be very ian 0.9 second. The five leap seconds which have occurred since 1993 are cumbersome, and the realization of the learly evident in this plot of UT1 -UTC as determined by the International Earth standards for time and frequency were otation Service. Values at 0.05 year intervals are plotted up to the beginning of unified into their current configuration on le year 2000 and at five-day intervals after that. 1 January 1972. Since 1972, the length of the second has ay defined by astronomical methods;the onds is what makes UTC a'coordinated been defined using the frequency of a ifference is removed by introducing leap time scale.) The rates of TAI and UTC ar hyperfine energystate transition in the econds as needed to keep the absolute identical between leap seconds. During th ground state of the cesium atom. iagnitude of the difference less than 0.9 past 10 years or so, the length of the UT International atomic time (TAI, using the econds.
Load more

Recommended publications
  • A Study of Ancient Khmer Ephemerides
    A study of ancient Khmer ephemerides François Vernotte∗ and Satyanad Kichenassamy** November 5, 2018 Abstract – We study ancient Khmer ephemerides described in 1910 by the French engineer Faraut, in order to determine whether they rely on observations carried out in Cambodia. These ephemerides were found to be of Indian origin and have been adapted for another longitude, most likely in Burma. A method for estimating the date and place where the ephemerides were developed or adapted is described and applied. 1 Introduction Our colleague Prof. Olivier de Bernon, from the École Française d’Extrême Orient in Paris, pointed out to us the need to understand astronomical systems in Cambo- dia, as he surmised that astronomical and mathematical ideas from India may have developed there in unexpected ways.1 A proper discussion of this problem requires an interdisciplinary approach where history, philology and archeology must be sup- plemented, as we shall see, by an understanding of the evolution of Astronomy and Mathematics up to modern times. This line of thought meets other recent lines of research, on the conceptual evolution of Mathematics, and on the definition and measurement of time, the latter being the main motivation of Indian Astronomy. In 1910 [1], the French engineer Félix Gaspard Faraut (1846–1911) described with great care the method of computing ephemerides in Cambodia used by the horas, i.e., the Khmer astronomers/astrologers.2 The names for the astronomical luminaries as well as the astronomical quantities [1] clearly show the Indian origin ∗F. Vernotte is with UTINAM, Observatory THETA of Franche Comté-Bourgogne, University of Franche Comté/UBFC/CNRS, 41 bis avenue de l’observatoire - B.P.
    [Show full text]
  • Tidal Datums and Their Applications
    U.S. DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration National Ocean Service Center for Operational Oceanographic Products and Services TIDAL DATUMS AND THEIR APPLICATIONS NOAA Special Publication NOS CO-OPS 1 NOAA Special Publication NOS CO-OPS 1 TIDAL DATUMS AND THEIR APPLICATIONS Silver Spring, Maryland June 2000 noaa National Oceanic and Atmospheric Administration U.S. DEPARTMENT OF COMMERCE National Ocean Service Center for Operational Oceanographic Products and Services Center for Operational Oceanographic Products and Services National Ocean Service National Oceanic and Atmospheric Administration U.S. Department of Commerce The National Ocean Service (NOS) Center for Operational Oceanographic Products and Services (CO-OPS) collects and distributes observations and predictions of water levels and currents to ensure safe, efficient and environmentally sound maritime commerce. The Center provides the set of water level and coastal current products required to support NOS’ Strategic Plan mission requirements, and to assist in providing operational oceanographic data/products required by NOAA’s other Strategic Plan themes. For example, CO-OPS provides data and products required by the National Weather Service to meet its flood and tsunami warning responsibilities. The Center manages the National Water Level Observation Network (NWLON) and a national network of Physical Oceanographic Real-Time Systems (PORTSTM) in major U.S. harbors. The Center: establishes standards for the collection and processing of water level and current data; collects and documents user requirements which serve as the foundation for all resulting program activities; designs new and/or improved oceanographic observing systems; designs software to improve CO-OPS’ data processing capabilities; maintains and operates oceanographic observing systems; performs operational data analysis/quality control; and produces/disseminates oceanographic products.
    [Show full text]
  • The Day and Its Hours in Ancient Jewish Astronomy. Elucidation of Medieval Rabbinic Astronomical Quotations
    The Day and its Hours in Ancient Jewish Astronomy. Elucidation of Medieval Rabbinic Astronomical Quotations. There are different ways of defining the span of time of one day. It appears that people, along the history, did not use a unique definition. According to their cultural background they counted the days differently. The astronomers had still their own way of counting days: it was from noon of one day until noon of the following day. Furthermore the different authors considered that their own definition of the day was so evident that they generally did not think necessary to specify the type of day that they used and its exact definition. It is clear that the diversity of the possibilities makes sometimes the elucidation of ancient texts difficult. We selected four sets of quotations of celebrated medieval rabbinic astronomers which are at the first glance problematic. n R’ Abraham bar Hiya, who appears to be the great specialist of Al-Battani and Ptolemy, defined his astronomical day n as beginning at noon of the Jewish civil day n – 1 and ending at noon of the Jewish civil day n. This definition seems disconcerting and in contradiction with the definition of the astronomical day which was in use from Ptolemy until the modern times. n R’ Isaac Israeli, in his book Yessod Olam, written in 1310 C.E. in Toledo, in Christian Spain, adopted the same position as bar Hiya. n R’ Abraham ibn Ezra, in his Sefer ha-Ibbur, made some statements about the moment of occurrence of the apparent vernal equinox in the year 1147 in the city of Verona in Italia and about the span of time between the apparent equinox and solstices on the one hand and the four tekufot of Adda on the other hand.
    [Show full text]
  • Structure of Physical Space and New Interaction in Nature (Theory And
    STRUCTURE OF PHYSICAL SPACE AND NEW INTERACTION IN NATURE (THEORY AND EXPERIMENTS) Yuri A. Baurov Central Research Institute of Machine Building Pionerskaya, 4 141070, Korolyov, Moscow Region, Russia In the talk, on the basis of the author’s model of formation of the observable physical space R3 in the process of dynamics of special discrete one-dimensional vectorial objects, byuons, while minimizing their potential energy of interaction in the one-dimensional space R1 formed by them, the existence of global anisotropy of observable space and new interaction in nature, is shown. The data of recent experiments are given and discussed. 1. Introduction. A wealth of works, beginning from antiquity (Aristoteles, Euclides, Democritus) and ending with authors of XX-th century, are dedicated to the structure of space and time, to the physical sense of these fundamental concepts, and their properties1. In all existing works on quantum field theory and physics of elementary particles, the space in which elementary processes occur, as a rule, is given one way or another. arXiv:hep-ph/9907239v1 5 Jul 1999 Yet we will follow another way and try to build physical space and major properties of elementary objects in this space from dynamics of a finite set of special discrete objects (so called byuons)2. Note that the development of physical comprehension of elementary processes on the base of modern superstring models3, unfortunately, also gives no evidences for how structured is the observed space itself which is obtained, according to one of the models, by means of compactification of six dimensions in a ten-dimensional space.
    [Show full text]
  • Julian Day from Wikipedia, the Free Encyclopedia "Julian Date" Redirects Here
    Julian day From Wikipedia, the free encyclopedia "Julian date" redirects here. For dates in the Julian calendar, see Julian calendar. For day of year, see Ordinal date. For the comic book character Julian Gregory Day, see Calendar Man. Not to be confused with Julian year (astronomy). Julian day is the continuous count of days since the beginning of the Julian Period used primarily by astronomers. The Julian Day Number (JDN) is the integer assigned to a whole solar day in the Julian day count starting from noon Greenwich Mean Time, with Julian day number 0 assigned to the day starting at noon on January 1, 4713 BC, proleptic Julian calendar (November 24, 4714 BC, in the proleptic Gregorian calendar),[1] a date at which three multi-year cycles started and which preceded any historical dates.[2] For example, the Julian day number for the day starting at 12:00 UT on January 1, 2000, was 2,451,545.[3] The Julian date (JD) of any instant is the Julian day number for the preceding noon in Greenwich Mean Time plus the fraction of the day since that instant. Julian dates are expressed as a Julian day number with a decimal fraction added.[4] For example, the Julian Date for 00:30:00.0 UT January 1, 2013, is 2,456,293.520833.[5] The Julian Period is a chronological interval of 7980 years beginning 4713 BC. It has been used by historians since its introduction in 1583 to convert between different calendars. 2015 is year 6728 of the current Julian Period.
    [Show full text]
  • Scattering of the Results of Measurements” of Processes of Diverse Nature Is Determined by the Earth’S Motion in the Inhomogeneous Space-Time Continuum
    January, 2009 PROGRESS IN PHYSICS Volume 1 The “Scattering of the Results of Measurements” of Processes of Diverse Nature is Determined by the Earth’s Motion in the Inhomogeneous Space-Time Continuum. The Effect of “Half-Year Palindromes” Simon E. Shnoll Institute of Theor. and Experim. Biophysics, Russian Acad. of Sciences, Pushchino, Moscow Region, 142290, Russia and Department of Physics, Moscow State University, Moscow 119992, Russia E-mail: [email protected]; [email protected] As obtained in this experimental research, the sequence of the shapes of histograms (the spectra of the amplitudes of fluctuations), measured during an astronomical day from 6 h to 18 h of the local time, is very similar (with high precision of probability) to the sequence of the histogram shapes obtained during an astronomical night from 18 h to 6 h of the local time a half of year later in exact. We call the effect that the sequences of the histogram shapes in the same half of day measured a half of year later are similar after inversion the “effect of half-year palindromes”. This means that the shapes of histograms are stable characteristics of a given region of space. In the previous work [32], we considered the phenomenon of have a half-year interval between them, i.e., histograms that “palindromes”, which stands for a high probability of simi- correspond to the measurements made when the Earth was at lar histograms to be found upon comparison of two data se- the opposite ends of a diameter of the circumsolar orbit [33]. ries: first, representing the results of measurements of 239Pu This supposition agrees with our earlier observation on sim- -decay over astronomical day (since 6 to 18 h by local, lon- ilarity between the series of daytime histograms obtained on gitude, time) and, second, measured over astronomical night the days of vernal equinox and the series of nighttime his- (since 18 to 6 h, in continuation of the first series) and in- tograms taken in the periods of autumnal equinox.
    [Show full text]
  • GPS and Leap Seconds Time to Change?
    INNOVATION GPS and Leap Seconds Time to Change? Dennis D. McCarthy, U.S. Naval Observatory William J. Klepczynski, Innovative Solutions International Since ancient times, we have used the Just as leap years keep our calendar approxi- seconds. While resetting the GLONASS Earth’s rotation to regulate our daily mately synchronized with the Earth’s orbit clocks, the system is unavailable for naviga- activities. By noticing the approximate about the Sun, leap seconds keep precise tion service because the clocks are not syn- position of the sun in the sky, we knew clocks in synchronization with the rotating chronized. If worldwide reliance on satellite how much time was left for the day’s Earth, the traditional “clock” that humans navigation for air transportation increases in hunting or farming, or when we should have used to determine time. Coordinated the future, depending on a system that may stop work to eat or pray. First Universal Time (UTC), created by adjusting not be operational during some critical areas sundials, water clocks, and then International Atomic Time (TAI) by the of flight could be a difficulty. Recognizing mechanical clocks were invented to tell appropriate number of leap seconds, is the this problem, GLONASS developers plan to time more precisely by essentially uniform time scale that is the basis of most significantly reduce the outage time with the interpolating from noon to noon. civil timekeeping in the world. The concept next generation of satellites. As mechanical clocks became of a leap second was introduced to ensure Navigation is not the only service affected increasingly accurate, we discovered that UTC would not differ by more than 0.9 by leap seconds.
    [Show full text]
  • Historical Reflections on the Work of IAU Commission 4 (Ephemerides)
    Historical Reflections on the Work of IAU Commission 4 (Ephemerides) To be Published in the Transactions of the International Astronomical Union, Volume XXIX-A George H. Kaplan, editor Contributors: J. A. Bangert, A. Fienga, W. Folkner, C. Hohenkerk, G. H. Kaplan, M. Lukashova, E. V. Pitjeva, P. K. Seidelmann, M. Sveshnikov, S. Urban, J. Vondr´ak,J. Weratschnig, J. G. Williams October 30, 2015 Abstract As part of a reorganization of the International Astronomical Union (IAU), Commission 4 (Ephemerides) went out of existence after the IAU General Assembly in August 2015. This paper presents brief discussions of some of the developments in fundamental astronomy that have influenced and been influenced by the work of Commission 4 over its 96-year history. The paper also presents notes about some of the publications of the national institutions that have played an essential role in the commission's mission. The contents of this paper were submitted for Commission 4's final report, to appear in IAU Transactions Vol. XXIX-A. Commission 4 was among the first set of commissions formed within the IAU at its founding in 1919. (Commissions were originally called \Standing Committees.") During its 96 years of service to the IAU and astronomical community in general, the commission has been fortunate to have been led by many distinguished scientists | see the list of presidents below. Presidents of Commission 4 1919{1922 P. H. Cowell 1967{1970 G. A. Wilkins 1991{1994 B. D. Yallop 1922{1928 W. S. Eichelberger 1970{1973 J. Kovalevsky 1994{1997 H. Kinoshita 1928{1932 E. W.
    [Show full text]
  • ASEN 5050 SPACEFLIGHT DYNAMICS Time Systems
    ASEN 5050 SPACEFLIGHT DYNAMICS Time Systems Dr. Steve Nerem University of Colorado - Boulder lecture7.ppt ©R.S. Nerem 2004 1 Time systems • Time is important: – Signal travel time of electromagnetic waves • Altimetry, GPS, SLR, VLBI • For positioning – Orbit determination – One nanosecond (10–9 second) is 30 cm of distance – Relative motion of celestial bodies lecture7.ppt ©R.S. Nerem 2004 2 Astronomical clocks • We commonly define time in terms of astronomical and geodetic periods: – Rotation of the Earth (day) – Revolution of the Earth around the sun (year) – Orbit of the moon around the Earth (month) – Number of bodies in the solar system visible to the naked eye or 1/4 of a lunar cycle (week) • These astronomical clocks are not consistent – The current length of a year is 365.242190 days – 1900: 365.242196 days – 2100: 365.242184 day lecture7.ppt ©R.S. Nerem 2004 3 Mechanical clocks • When mechanical clocks were less accurate than variations in astronomical clocks, astronomical clocks were used to correct mechanical clocks. – The pendulum clock was invented in the 17th century • In 1928 with the invention of the quartz clock. – Apparent that the uncertainty in the astronomical day was 10–7 due to irregularities in Earth rotation • Atomic clocks – The idea of using hyperfine quantum states of atoms for a clock was first proposed by U.S. physicist Isador Rabi in 1945. lecture7.ppt ©R.S. Nerem 2004 4 Atomic clocks • Certain atoms in a the magnetic field can exhibit one of two hyperfine states – The spin of the outermost electron of an atom either points in the same direction as the magnetic field of the nucleus, or it points opposite.
    [Show full text]
  • Lesson 9. Chronology, Daniel Flaut.Pdf
    Lesson 9. Chronology Learning tasks: by completing this unit of study, the student will be able to: ¾ Define Chronology and to highlight the key moments in its evolution as science. ¾ Identify main elements of timeline (day, hour, week, month, year). ¾ Retain some elementary notions about the calendar. I. Definition; The evolution of Chronology as science Chronology from Latin chronologia, from Ancient Greek χρόνος, chronos = time, and ­λογία, ­logia) is the Auxiliary Science of History which deal with the measuring and dividing of time, therefore with accurate dating of historical events to determine their sequence. Chronology has two major branches: Astronomical Chronology, a technical method of dating events or artifacts that are associated with astronomical phenomena, and Historical Chronology, to achieve timelines: national, universal, of different institutions and of their leaders, of various historical events. There were two systems to highlight the time: the astronomical system and the civil system, of which there were some differences. But, both systems were based on revolution movements of the Earth, the Moon and Sun. In Antiquity, historiography has shown a constant concern for establishing accurate data of events narrated, but made after the dating system used at that time. In XV­XVIII centuries, Chronology make important steps in its evolution as a scientific discipline. The problematic of Chronology began with the controversy between Joseph Justus Scaliger (August 5, 1540, Agen‐January 21, 1609, Leiden) and Denis Pétau (August 21, 1583 – December 11, 1652), which gave to Benedictines the opportunity to undertake the difficult task to clarify the research field of Chronology. They needed a long time until to draft critical chronological lists and to clarify old dating systems.
    [Show full text]
  • The Eastern Veil the Best of Monochrome
    The Journal of The Royal Astronomical Society of Canada PROMOTING ASTRONOMY IN CANADA February/février 2019 Volume/volume 113 Le Journal de la Société royale d’astronomie du Canada Number/numéro 1 [794] Inside this issue: Thermal X-Ray Emission From a Kilonova Remnant? Have You Seen a Neutron Star “Wave”? Smooth or Grained? The Loopy Explanation of Gravity Student of Star-Law The Eastern Veil The Best of Monochrome. Drawings, images in black and white, or narrow-band photography. Barry Schellenberg imaged IC 5067 which is focused on the dark nebula region within the Pelican Nebula for a total of 60 hours. February / février 2019 | Vol. 113, No. 1 | Whole Number 794 contents / table des matières Research Article / Article de recherche 33 Observing Tips: The Amateur Astronomer (oral presentation, 1966 January 26) 07 Chandra X-Ray Observations of the Neutron by Michael Burke-Gaffney Star Merger GW170817: Thermal X-Ray Emission From a Kilonova Remnant? 36 Binary Universe: Explore the Exoplanets by Samar Safi-Harb, Neil Doerksen, Adam Rogers, by Blake Nancarrow and Chris L. Fryer 39 CFHT Chronicles: 2019: 40 Years at the Top of the World Feature Articles / Articles de fond by Mary Beth Laychak 14 Smooth or Grained? The loopy explanation 42 John Percy’s Universe: Introducing AAVSO of gravity: How can general relativity and by John R. Percy quantum theory both be correct when they contradict each other? by Khalil Kurwa Departments / Départements 16 Have You Seen a Neutron Star “Wave”? 02 President’s Corner by Hassan Kurwa by Dr. Chris Gainor
    [Show full text]
  • Relativity the Special and General Theory
    RELATIVITY THE SPECIAL AND GENERAL THEORY ALBERT EINSTEIN DIGITAL REPRINT Elegant Ebooks COPYRIGHT INFORMATION Book: Relativity: The Special and General Theory Author: Albert Einstein, 1879–1955 First published: 1920 The original book is in the public domain in the United States. However, since Einstein died in 1955, it may still be under copyright in many other countries, for example, those that use the life of the author + 60 years or life + 70 years for the duration of copyright. Readers outside the United States should check their own countries’ copyright laws to be certain they can legally download this ebook. The Online Books Page has an FAQ which gives a summary of copyright durations for many other countries, as well as links to more official sources. This PDF ebook was created by José Menéndez. NOTE ON THE TEXT The text used in this ebook is from the first English translation, published in 1920, of Über die spezielle und die allgemeine Relativitätstheorie. A few misprints in the original text have been corrected, but to preserve all of the book, the original misprints are included in footnotes enclosed in square brackets and signed “J.M.” In addition, the line breaks and pagination of the original book have been reproduced, and the PDF’s page numbers are linked to page images of the book from the Google Books Library Project for easy comparison. Please note: Google’s images may not be available to people outside the U.S. and may be unavailable to U.S. residents at times. Retaining the original pagination made it possible to include a fully functional (clickable) copy of the original index.
    [Show full text]