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Demystifying Special Relativity; the K-Factor Angel Darlene Harb
Demystifying Special Relativity; the K-Factor Angel Darlene Harb University of Texas at San Antonio, TX, U.S.A. ABSTRACT This paper targets upper-level high school students and incoming college freshmen who have been less exposed to Special Relativity (SR). The goal is to spark interest and eliminate any feelings of intimidation one might have about a topic brought forth by world genius Albert Einstein. For this purpose, we will introduce some ideas revolving around SR. Additionally, by deriving the relationship between the k-factor and relative velocity, we hope that students come to an appreciation for the impact of basic mathematical skills and the way these can be applied to quite complex models. Advanced readers can directly jump ahead to the section discussing the k-factor. keywords : relative velocity, world lines, space-time 1 Introduction 1.1 A Morsel of History Throughout time, scientists have searched for ’just the right’ model comprised of laws, assumptions and theories that could explain our physical world. One example of a leading physical law is: All matter in the universe is subject to the same forces. It is important to note, this principle is agreeable to scientists, not because it is empirically true, but because this law makes for a good model of nature. Consequently, this law unifies areas like mechanics, electricity and optics traditionally taught separate from each other. Sir Isaac Newton (1643-1727) contributed to this principle with his ’three laws of motion.’ They were so mathematically elegant, that the Newtonian model dominated the scientific mind for nearly two centuries. -
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 -
6.61.2.5 Essential Earth Learning Concepts for Teachers and Students
6.61.2.5 Essential Earth Learning Concepts for Teachers and Students Mario M. Yanez Executive Director of Earth Learning, Inc. in Miami, FL [email protected] Keywords: Change, Interdependence, Earth, Evolution, Humanity, Learning, Life Community, Sustainability Contents 1.0 Introduction 2.0 Essential Concepts 2.1 There is no environment 2.2 Earth is alive 2.3 Evolution is not a theory 2.4 Earth is learning and teaching 2.5 Earth is Slow, Culture is Fast 2.6 Earth is Primary, Humans are Derivative 2.7 Sustainability requires living in place 2.8 Earth is a recycling planet 2.9 There are no second chances 2.10 Humanity must be the change 3.0 Conclusion Glossary: Bioregion A unique but integral geographical subsystem of Earth, most often a watershed, that provides a contextual container for life, one whose living boundaries are permeable and exist for the purpose of identity not separation. Carrying Capacity The ability of a bioregion or the planet to sustain given populations and their associated consumption and waste production. Co-evolution When two or more entities adapt to each other in a given place over long periods of time; requires the acquisition of local knowledge of what works and what does not work Ecological footprint A representation of the amount of land, ocean, energy, and natural materials necessary to feed human activities and assimilate their waste for any given population. Linear Progress The misconception that it is possible and necessary for humans to achieve unlimited material growth and accumulation of material wealth; linear progress is a consumptive practice, which ignores that we live on one materially finite planet who’s ecosystems are being altered, drastically diminishing their capacity to support life. -
The Quasi-Steady State Cosmology
Acta Scientiarum 22(5):1241-1248, 2000. ISSN 1415-6814. The quasi-steady state cosmology Jayant V. Narlikar Inter-University Center for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune 411 007. India. ABSTRACT. This paper begins with a discussion of the shortcomings of standard cosmology, and then outlines an alternative cosmology called the Quasi-Steady State Cosmology (QSSC). The theoretical framework and observational tests of the QSSC are next described. Finally some tests which can distinguish between the standard big bang cosmology and the QSSC are briefly mentioned. Key words: cosmological models, observational tests, alternative cosmologies, creation of matter, microwave background, light nuclear abundances. RESUMO. A cosmologia do estado quase-estacionário. D is cut e m-se em primeiro lugar as falhas na cosmologia oficial, seguido por uma breve descrição da cosmologia alternativa chamada Cosmologia do Estado Quase Constante. Descrevem-se também o arcabouço teórico e os testes referentes a CEQC. Por último, são mencionados os testes que testemunham a distinção entre a cosmologia oficial do Big Bang e a CEQC. Palavras-chave: modelos cosmológicos, testes de observação, cosmologias alternativas, criação de matéria, fundo de microondas, abundâncias nucleares de luz. Modern cosmology began in 1917 with particles moving at near-light speeds. They felt that Einstein's model of the universe in which the the physical conditions during a short era were ideal universe was assumed to be homogeneous and for nuclear fusion making all the chemical elements isotropic and also static. The general belief in a static from protons and neutrons. However, they soon universe in which the galaxies etc., are at rest was so encountered a basic difficulty that made it clear that strong that when in 1922 Aleksandr Friedmann this programme could not be carried out, because of proposed expanding models of the cosmos, they the absence of stable nuclei at mass numbers 5 and were largely ignored by everybody, including 8. -
Edward Milne's Influence on Modern Cosmology
ANNALS OF SCIENCE, Vol. 63, No. 4, October 2006, 471Á481 Edward Milne’s Influence on Modern Cosmology THOMAS LEPELTIER Christ Church, University of Oxford, Oxford OX1 1DP, UK Received 25 October 2005. Revised paper accepted 23 March 2006 Summary During the 1930 and 1940s, the small world of cosmologists was buzzing with philosophical and methodological questions. The debate was stirred by Edward Milne’s cosmological model, which was deduced from general principles that had no link with observation. Milne’s approach was to have an important impact on the development of modern cosmology. But this article shows that it is an exaggeration to intimate, as some authors have done recently, that Milne’s rationalism went on to infiltrate the discipline. Contents 1. Introduction. .........................................471 2. Methodological and philosophical questions . ..................473 3. The outcome of the debate .................................476 1. Introduction In a series of articles, Niall Shanks, John Urani, and above all George Gale1 have analysed the debate stirred by Edward Milne’s cosmological model.2 Milne was a physicist we can define, at a philosophical level, as an ‘operationalist’, a ‘rationalist’ and a ‘hypothetico-deductivist’.3 The first term means that Milne considered only the observable entities of a theory to be real; this led him to reject the notions of curved space or space in expansion. The second term means that Milne tried to construct a 1 When we mention these authors without speaking of one in particular, we will use the expression ‘Gale and co.’ 2 George Gale, ‘Rationalist Programmes in Early Modern Cosmology’, The Astronomy Quarterly,8 (1991), 193Á218. -
ISI Student Text.Book
11 Astronomy Chapter 30 What is Frequently in the news we hear about discoveries that involve space. In fact, our knowledge of the solar system and beyond is expanding each year because of advancements in technology. In recent years, space probes have been sent to most of Astronomy? the planets in the solar system and we have seen them “up close” for the very first time. Long before the invention of the telescope, ancient civilizations made observations of the heavens that helped people keep track of time and the seasons. In this chapter, you will learn about tools and language of astronomy. 30.1 Cycles on Earth How do we keep track of time? In this Investigation, you will build a solar clock and discover the variables involved with using the sun to keep track of time. You will also observe the lunar cycle over the course of a month and construct a daily calendar based on changes in the moon’s appearance. 30.2 Tools of Astronomy How does a telescope work? In this Investigation, you will build a simple telescope and use it to observe objects around your school. Through this exercise, you will find out how a telescope works. Next, you will use your telescope to observe the surface of the moon. Finally, you will try a more difficult task—observing the planet Jupiter and some of its moons. 587 Chapter 30: What is Astronomy? Learning Goals In this chapter, you will: ! Relate keeping track of time to astronomical cycles. ! Predict how the moon will appear based on its orbital position. -
Elementary General Relativity Version 3.35
Elementary General Relativity Version 3.35 Alan Macdonald Luther College, Decorah, IA USA mailto:[email protected] http://faculty.luther.edu/∼macdonal c To Ellen “The magic of this theory will hardly fail to impose itself on anybody who has truly understood it.” Albert Einstein, 1915 “The foundation of general relativity appeared to me then [1915], and it still does, the greatest feat of human thinking about Nature, the most amazing combination of philosophical penetration, physical intuition, and mathematical skill.” Max Born, 1955 “One of the principal objects of theoretical research in any depart- ment of knowledge is to find the point of view from which the subject appears in its greatest simplicity.” Josiah Willard Gibbs “There is a widespread indifference to attempts to put accepted the- ories on better logical foundations and to clarify their experimental basis, an indifference occasionally amounting to hostility. I am con- cerned with the effects of our neglect of foundations on the educa- tion of scientists. It is plain that the clearer the teacher, the more transparent his logic, the fewer and more decisive the number of ex- periments to be examined in detail, the faster will the pupil learn and the surer and sounder will be his grasp of the subject.” Sir Hermann Bondi “Things should be made as simple as possible, but not simpler.” Albert Einstein Contents Preface 1 Flat Spacetimes 1.1 Spacetimes . 11 1.2 The Inertial Frame Postulate . 14 1.3 The Metric Postulate . 18 1.4 The Geodesic Postulate . 25 2 Curved Spacetimes 2.1 History of Theories of Gravity . -
John Archibald Wheeler Man with Picturesque Imagination
GENERAL ARTICLE John Archibald Wheeler Man with Picturesque Imagination Jayant V Narlikar John Archibald Wheeler was a researcher and teacher par excellence who was responsible for popularizing the theory of general relativity amongst the academics in the United States. This article tries to provide glimpses of his contribu- tions to gravitation as also some of the work of Jayant V Narlikar is a his distinguished students. cosmologist and theoretical astrophysicist. He was a John Wheeler, a theoretical physicist par excellence, is research student and a best known to the present generation of physics stu- long-time collaborator of dents as the senior author of the mammoth book called Fred Hoyle. He is the Gravitation, the other two (younger) authors being his Founder Director of students Charlie Misner and Kip Thorne. If you open IUCCA and is currently an emeritus professor there. this book (hereafter referred to as MTW) on any page He has made strong efforts at random, you will see what I call Wheeler's stamp. to promote teaching and This is the property of `picturesqueness' which applies research in astronomy in not only to the diagrams but also to the language. You the universities. He has would ¯nd it hard to believe that the writer is describing written extensively in English and Marathi to some intricate idea in relativity. popularize science. Though his early research work was in the areas of atomic and nuclear physics, and he was amongst the large group of scientists involved with the making of the atom bomb under the top secret Manhattan Project, in the post- war era, John Wheeler gradually changed his interests to gravitation and relativity. -
A Lunar Farside Low Radio Frequency Array for Dark Ages 21-Cm Cosmology Authors: Jack O
A Lunar Farside Low Radio Frequency Array for Dark Ages 21-cm Cosmology Authors: Jack O. Burns (University of Colorado Boulder), Gregg Hallinan (California Institute of Technology), Tzu-Ching Chang (Jet Propulsion Laboratory/Caltech), Marin Anderson (JPL/Caltech), Judd Bowman (ASU), Richard Bradley (NRAO), Steven Furlanetto (UCLA), Alex Hegedus (U. Michigan), Justin Kasper (U. Michigan), Jonathon Kocz (Caltech), Joseph Lazio (JPL/Caltech), Jim Lux (JPL/Caltech), Robert MacDowall (NASA Goddard), Jordan Mirocha (McGill U.), Issa Nesnas (JPL/Caltech), Jonathan Pober (Brown U.), Ronald Polidan (Lunar Resources), David Rapetti (ARC/USRA/CU), Andres Romero-Wolf (JPL/Caltech), Anže Slosar (Brookhaven National Laboratory), Albert Stebbins (Fermilab), Lawrence Teitelbaum (JPL/Caltech), Martin White (UC Berkeley/Lawrence Berkeley National Laboratory) A NASA Probe mission study produced a viable engineering design for an initial farside radio array that consists of 3 components: a commercial lander carrying the base station, four JPL Axel rovers to deploy antenna nodes, and a 128×2 (two orthogonal polarizations) node antenna array. The array will be deployed in a spiral pattern as shown in the upper right. Tethers connect the lander to the nodes, providing communications and power. NASA’s Gateway may serve as a data relay to Earth. ABSTRACT – Focus Area 1: lunar farside radio telescope to explore the early universe An array of low-frequency dipole antennas on the lunar farside surface will probe a unique, unexplored epoch in the early Universe called the Dark Ages. It begins at Recombination when neutral hydrogen atoms formed, first revealed by the cosmic microwave background. This epoch is free of stars and astrophysics, so it is ideal to investigate high energy particle processes including dark matter (e.g., warm dark matter, self-annihilation, nongravitational interactions with baryons), early Dark Energy, neutrinos, and cosmic strings. -
How Fast Are You Moving When You Are Sitting Still? by Andrew Fraknoi Foothill College & the Astronomical Society of the Pacific
© 2007, Astronomical Society of the Pacific No. 71 • Spring 2007 www.astrosociety.org/uitc 390 Ashton Avenue, San Francisco, CA 94112 How Fast Are You Moving When You Are Sitting Still? by Andrew Fraknoi Foothill College & the Astronomical Society of the Pacific hen, after a long day of running around, you Stream is part of contains more water than all the rivers of finally find the time to relax in your favorite the world put together. It is circulated by the energy of our Warmchair, nothing seems easier than just sitting turning planet. still. But have you ever considered how fast you are really moving when it seems you are not moving at all? Daily Motion When we are on a smoothly riding train, we sometimes get the illusion that the train is standing still and the trees or buildings are moving backwards. In the same way, because we “ride” with the spinning Earth, it appears to us that the Sun and the stars are the ones doing the moving as day and night alternate. But actually, it is our planet that turns on its axis once a day—and all of us who live on the Earth’s surface are moving with it. How fast do we turn? To make one complete rotation in 24 hours, a point near the equator of the Earth must move at close to 1000 miles per hour (1600 km/hr). The speed gets less as you move north, but it’s still a good clip throughout the United States. Because gravity holds us tight to the surface of our planet, we move with the Earth and don’t notice its rotation1 in everyday life. -
Euclid Mapping the Geometry of the Dark Universe
ESA/SRE(2011)12 July 2011 Euclid Mapping the geometry of the dark Universe Definition Study Report European Space Agency 1 Euclid Mapping the geometry of the dark Universe Definition Study Report ESA/SRE(2011)12 July 2011 September 2011 (Revision 1) 2 On the front cover: composite of a fragment from Raphael’s fresco “The School of Athens” in the Stanza della Segnatura of the Vatican Palace depicting the Greek mathematician Euclid of Alexandria, a simulation of the cosmic web by Springel et al, and an image of Abell 1689; the composition is made by Remy van Haarlem (ESA/ESTEC). 3 Euclid Mission Summary Main Scientific Objectives Understand the nature of Dark Energy and Dark Matter by: Reach a dark energy FoM > 400 using only weak lensing and galaxy clustering; this roughly corresponds to 1 sigma errors on wp and wa of 0.02 and 0.1, respectively. Measure γ, the exponent of the growth factor, with a 1 sigma precision of < 0.02, sufficient to distinguish General Relativity and a wide range of modified-gravity theories Test the Cold Dark Matter paradigm for hierarchical structure formation, and measure the sum of the neutrino masses with a 1 sigma precision better than 0.03eV. Constrain ns, the spectral index of primordial power spectrum, to percent accuracy when combined with Planck, and to probe inflation models by measuring the non-Gaussianity of initial conditions parameterised by fNL to a 1 sigma precision of ~2. SURVEYS Area (deg2) Description Wide Survey 15,000 (required) Step and stare with 4 dither pointings per step. -
Enigmas of the Universe Syllabus.Pdf
Enigmas of the Universe Chris Impey, Associate Dean and University Distinguished Professor Overview: Astronomy has seen tremendous progress in the past century. Large telescopes on the ground and in space now give us views of the universe across the electromagnetic spectrum. Powerful computers can handle exponentially increasing volumes of data and they allow simulations of remote objects and extreme astrophysics. We know how stars work, how many galaxies there are, and how to find exoplanets. Yet there is much we don’t know, and areas where our physical understanding is weak. This course is a report from the frontiers of astronomy and physics research on five aspects of the universe where profound questions remain unanswered. Meetings: Typical structure is a 50 minute lecture, then a 10 minute break, a 40 minute lecture, then 20 minutes for questions and discussion. Short descriptions of the five topics follow. The Big Bang. How did the universe begin? There’s ample observational support for the idea that the universe expanded from a hot, dense state billions of years ago. But the nature of dark matter and dark energy are unknown and the situation just after the big bang is shrouded in mystery. Black Holes. What happens in extreme regions of space-time? Nature can make black holes ranging from ten to ten billion times the Sun’s mass and the recent detection of gravitational waves confirms that black holes exist. However, gravity theory is challenged in trying to explain black holes. The God Particle. Where does mass come from? The detection of the Higgs particle filled in the missing piece of the Standard Model of particle physics.