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26-2 Spacetime and the Spacetime Interval We Usually Think of Time and Space As Being Quite Different from One Another
Answer to Essential Question 26.1: (a) The obvious answer is that you are at rest. However, the question really only makes sense when we ask what the speed is measured with respect to. Typically, we measure our speed with respect to the Earth’s surface. If you answer this question while traveling on a plane, for instance, you might say that your speed is 500 km/h. Even then, however, you would be justified in saying that your speed is zero, because you are probably at rest with respect to the plane. (b) Your speed with respect to a point on the Earth’s axis depends on your latitude. At the latitude of New York City (40.8° north) , for instance, you travel in a circular path of radius equal to the radius of the Earth (6380 km) multiplied by the cosine of the latitude, which is 4830 km. You travel once around this circle in 24 hours, for a speed of 350 m/s (at a latitude of 40.8° north, at least). (c) The radius of the Earth’s orbit is 150 million km. The Earth travels once around this orbit in a year, corresponding to an orbital speed of 3 ! 104 m/s. This sounds like a high speed, but it is too small to see an appreciable effect from relativity. 26-2 Spacetime and the Spacetime Interval We usually think of time and space as being quite different from one another. In relativity, however, we link time and space by giving them the same units, drawing what are called spacetime diagrams, and plotting trajectories of objects through spacetime. -
The Sundial, Beyond the Form and Time
ISAMA BRIDGES The International Society of the Mathematical Connections Arts, Mathematics, and Architecture in Art, Music, and Science The Sundial, Beyond the Form and Time ... Andrzej Zarzycki 227 Brighton Street Belmont, MA 02478 E-mail: [email protected] Abstract Architecture (iir" k 1-t].lk" ch ... r) n. 1. The art and science of designing and erecting buildings. Can a building inspire scientific thinking? Can an architectural structure reflect the complexity of the universe? Is there a relationship between the artistic and scientific? This paper discusses an approach to design, which uses an architectural structure as a research apparatus to pursue scientifically driven beauty. Architecture could be defined as the man-made universe - the universe whose primary function was to shelter us from elements, animals and other people. Broadly speaking, to protect us from the "outer Uni verse". It is not surprising that the evolution of architecture follows the same trajectories as the evolution of our thinking and perception ofthe surrounding world. However, somewhere along the lines of history, archi tecture acquired another purpose and began to playa new role in our self-awareness. In ancient, medieval and even modem times, we have viewed architecture as a medium to express, symbolize, and address the meaning of our existence. Ancient temples reveal an intimate knowledge of geometry and human perception by purposefully distorting their forms to balance visual illusions. Medieval cathedrals manifested greatness of God through art and structural achievements, while contemporary monu ments address the social and philosophical aspirations of a present-day society. As a result of this centuries long evolution~ we now associate architecture with its less utilitarian and more symbolic values. -
Course Descriptions
COURSE DESCRIPTIONS American Multicultural Studies (AMCS) AMCS 273 AMERICAN DIVERSITY: PAST, PRESENT, FUTURE (4) This course explores the relationships between race, ethnicity, and identity through AMCS 165A HUMANITIES LEARNING COMMUNITY (4) close readings of social, historical, and cultural texts. At the heart of the course is AMCS 165 A/B is a year long course, which features weekly lectures and small an exploration of how race and ethnicity have impacted collective understandings seminars. It constitutes a Humanities Learning Community (HLC) for any first-year of this nation’s morals and values. Satisfies GE Area C2. Only one course numbered student. The learning objectives of the HLC will satisfy A3 (Critical Thinking) and 273 in the Arts & Humanities will be considered for credit. Prerequisite: completion C3 (Comparative Perspectives and/or Foreign Languages) GE Areas, and fulfills GE of GE Category A2 (ENGL 101 or ENGL 100B) required. Ethnic Studies. C- or better required in the second semester for A3 credit. AMCS 301 AFRICANA LECTURE SERIES (1) AMCS 165B HUMANITIES LEARNING COMMUNITY (4) A weekly lecture series offering presentations and discussions that focus on AMCS 165 A/B is a year long course, which features weekly lectures and small historical and contemporary topics relating to people of African descent. This seminars. It constitutes a Humanities Learning Community (HLC) for any first-year includes, but is not limited to, African Americans, Continental Africans, Afro-Carib- student. The learning objectives of the HLC will satisfy A3 (Critical Thinking) and beans, and Afro-Latinos. This lecture series is in honor of Dr. LeVell Holmes and C3 (Comparative Perspectives and/or Foreign Languages) GE Areas, and fulfills GE his contributions to the Sonoma State University community. -
Time Reversal Symmetry in Cosmology and the Creation of a Universe–Antiuniverse Pair
universe Review Time Reversal Symmetry in Cosmology and the Creation of a Universe–Antiuniverse Pair Salvador J. Robles-Pérez 1,2 1 Estación Ecológica de Biocosmología, Pedro de Alvarado, 14, 06411 Medellín, Spain; [email protected] 2 Departamento de Matemáticas, IES Miguel Delibes, Miguel Hernández 2, 28991 Torrejón de la Calzada, Spain Received: 14 April 2019; Accepted: 12 June 2019; Published: 13 June 2019 Abstract: The classical evolution of the universe can be seen as a parametrised worldline of the minisuperspace, with the time variable t being the parameter that parametrises the worldline. The time reversal symmetry of the field equations implies that for any positive oriented solution there can be a symmetric negative oriented one that, in terms of the same time variable, respectively represent an expanding and a contracting universe. However, the choice of the time variable induced by the correct value of the Schrödinger equation in the two universes makes it so that their physical time variables can be reversely related. In that case, the two universes would both be expanding universes from the perspective of their internal inhabitants, who identify matter with the particles that move in their spacetimes and antimatter with the particles that move in the time reversely symmetric universe. If the assumptions considered are consistent with a realistic scenario of our universe, the creation of a universe–antiuniverse pair might explain two main and related problems in cosmology: the time asymmetry and the primordial matter–antimatter asymmetry of our universe. Keywords: quantum cosmology; origin of the universe; time reversal symmetry PACS: 98.80.Qc; 98.80.Bp; 11.30.-j 1. -
Some Aspects Geographical - Historically Thinking in the Context of the Time: Review of Literature
ISSN 1678-7226 Bulatović , J.; Rajović , G. (52 - 72) Rev. Geogr. Acadêmica v.14, n.2 (xii.2020) SOME ASPECTS GEOGRAPHICAL - HISTORICALLY THINKING IN THE CONTEXT OF THE TIME: REVIEW OF LITERATURE ALGUNOS ASPECTOS GEOGRÁFICOS - PENSAMIENTO HISTÓRICO EN EL CONTEXTO DEL TIEMPO: REVISIÓN DE LA LITERATURA ALGUNS ASPECTOS GEOGRÁFICOS - PENSANDO HISTORICAMENTE NO CONTEXTO DA ÉPOCA: REVISÃO DA LITERATURA Jelisavka Bulatović Department of Textile Design, Technology and Management, Academy of Technical-Art Professional Studies, Serbia. [email protected] Goran Rajović International Network Center for Fundamental and Applied Research, Washington, USA Volgograd State University, Volgograd, Russian Federation [email protected] ABSTRACT The main objective of this paper confirm the importance understanding that are historical events and geographical factors in interdependence, that everything that relates with human population and vital for it takes place the geographical area that are a key factor in historical events organization and transformation of space. Acording to Komušanac and Šterc (2011) "one of the basic problems of theoretical considerations historical geography from its beginnings as an independent discipline was unclear positioning of its subject - content base and defining its limits within the frame of the system of scientific geography. Theoretic analysis of historical and geographical aspects of research is determined by the historical - geographic factors, and their interactive relationship is set as a prerequisite -
The Time Wave in Time Space: a Visual Exploration Environment for Spatio
THE TIME WAVE IN TIME SPACE A VISUAL EXPLORATION ENVIRONMENT FOR SPATIO-TEMPORAL DATA Xia Li Examining Committee: prof.dr.ir. M. Molenaar University of Twente prof.dr.ir. A.Stein University of Twente prof.dr. F.J. Ormeling Utrecht University prof.dr. S.I. Fabrikant University of Zurich ITC dissertation number 175 ITC, P.O. Box 217, 7500 AE Enschede, The Netherlands ISBN 978-90-6164-295-4 Cover designed by Xia Li Printed by ITC Printing Department Copyright © 2010 by Xia Li THE TIME WAVE IN TIME SPACE A VISUAL EXPLORATION ENVIRONMENT FOR SPATIO-TEMPORAL DATA DISSERTATION to obtain the degree of doctor at the University of Twente, on the authority of the rector magnificus, prof.dr. H. Brinksma, on account of the decision of the graduation committee, to be publicly defended on Friday, October 29, 2010 at 13:15 hrs by Xia Li born in Shaanxi Province, China on May 28, 1977 This thesis is approved by Prof. Dr. M.J. Kraak promotor Prof. Z. Ma assistant promoter For my parents Qingjun Li and Ruixian Wang Acknowledgements I have a thousand words wandering in my mind the moment I finished this work. However, when I am trying to write them down, I lose almost all of them. The only word that remains is THANKS. I sincerely thank all the people who have been supporting, guiding, and encouraging me throughout my study and research period at ITC. First, I would like to express my gratitude to ITC for giving me the opportunity to carry out my PhD research. -
TIME GEOGRAPHY and SPACE–TIME PRISM Conceptualization in the 1960S
context. Basic time geographic concepts, such Time geography and as events being sparsely distributed in time and space–time prism space, limited time availability, and trading time for space to access activities, seem mundane, Harvey J. Miller since they are common and correspond with The Ohio State University, USA everyday experience. But this is why time geog- raphy is needed: these seemingly banal but utterly Time geography is a constraints-oriented crucial factors in our scientific explanations of approach to understanding human activities in human behavior should not be neglected. Time space and time. Time geography recognizes that geography provides a framework that demands humans have fundamental spatial and temporal recognition of the fundamental constraints limitations: people can physically only be in one underlying human experience and also provides place at a time and activities occur at a sparse set an effective conceptual system for keeping track of places for limited durations. Participating in an of these conditions. activity requires allocating scarce available time Time geography originates from Professor to access and conduct the activity. Constraints Torsten Hägerstrand (1916–2004), a Swedish on activity participation include the location and geographer who spent his career at the Univer- timing of anchors that compel presence (such as sity of Lund. He nurtured the ideas for a long home and work), the time budget for access and time, but time geography emerged dramatically activity, and the ability to trade time for space in to the international scientific community with using mobility or information and communication a now-famous 1969 presidential address to the technologies (ICTs). -
The Expression of Orientations in Time and Space With
The Expression of Orientations in Time and Space with Flashbacks and Flash-forwards in the Series "Lost" Promotor: Auteur: Prof. Dr. S. Slembrouck Olga Berendeeva Master in de Taal- en Letterkunde Afstudeerrichting: Master Engels Academiejaar 2008-2009 2e examenperiode For My Parents Who are so far But always so close to me Мои родителям, Которые так далеко, Но всегда рядом ii Acknowledgments First of all, I would like to thank Professor Dr. Stefaan Slembrouck for his interest in my work. I am grateful for all the encouragement, help and ideas he gave me throughout the writing. He was the one who helped me to figure out the subject of my work which I am especially thankful for as it has been such a pleasure working on it! Secondly, I want to thank my boyfriend Patrick who shared enthusiasm for my subject, inspired me, and always encouraged me to keep up even when my mood was down. Also my friend Sarah who gave me a feedback on my thesis was a very big help and I am grateful. A special thank you goes to my parents who always believed in me and supported me. Thanks to all the teachers and professors who provided me with the necessary baggage of knowledge which I will now proudly carry through life. iii Foreword In my previous research paper I wrote about film discourse, thus, this time I wanted to continue with it but have something new, some kind of challenge which would interest me. After a conversation with my thesis guide, Professor Slembrouck, we decided to stick on to film discourse but to expand it. -
The Space-Time Cube As an Effective Way of Representing and Analysing the Streetscape Along a Pedestrian Route in an Urban Environment
SHS Web of Conferences 64, 03005 (2019) https://doi.org/10.1051/shsconf/20196403005 EAEA14 2019 The space-time cube as an effective way of representing and analysing the streetscape along a pedestrian route in an urban environment Thomas Leduc1,*, Vincent Tourre2, and Myriam Servières2 1AAU-CRENAU, CNRS, École Nationale Supérieure d’Architecture de Nantes, France 2AAU-CRENAU, École Centrale de Nantes, France Abstract. The graphical representation of a complex polygonal object, such as an isovist field (i.e. a 2D isovist in its evolution over time along a pedestrian path in an urban environment) is a hard research issue that was stated in the late 1970s by Benedikt [1]. The generalized space-time cube from Bach and al. [2] is a conceptual framework allowing to propose innovative implementations for the analysis and the display of this complex object. The purpose of this article is to situate, within this formal framework, all the graphical representation solutions that have already been developed for isovist fields. It also aims to identify the problems raised by each of these solutions (spatial anchoring, arbitrary sampling, etc.) and to propose related solutions. 1 Introduction and state of the art 1.1 Urban space analysis and visibility issues Because a strong trend at work today is to develop and design cities that allow people to adapt and mitigate phenomena related to major issues, such as climate change, several new criteria have emerged for the design of sustainable and healthy cities. These new criteria have to do with walkability, role of the streetscape in encouraging the development of pedestrian mobility, physical activity and well-being. -
Spacetime Symmetries and the Cpt Theorem
SPACETIME SYMMETRIES AND THE CPT THEOREM BY HILARY GREAVES A dissertation submitted to the Graduate School|New Brunswick Rutgers, The State University of New Jersey in partial fulfillment of the requirements for the degree of Doctor of Philosophy Graduate Program in Philosophy Written under the direction of Frank Arntzenius and approved by New Brunswick, New Jersey May, 2008 ABSTRACT OF THE DISSERTATION Spacetime symmetries and the CPT theorem by Hilary Greaves Dissertation Director: Frank Arntzenius This dissertation explores several issues related to the CPT theorem. Chapter 2 explores the meaning of spacetime symmetries in general and time reversal in particular. It is proposed that a third conception of time reversal, `geometric time reversal', is more appropriate for certain theoretical purposes than the existing `active' and `passive' conceptions. It is argued that, in the case of classical electromagnetism, a particular nonstandard time reversal operation is at least as defensible as the standard view. This unorthodox time reversal operation is of interest because it is the classical counterpart of a view according to which the so-called `CPT theorem' of quantum field theory is better called `PT theorem'; on this view, a puzzle about how an operation as apparently non- spatio-temporal as charge conjugation can be linked to spacetime symmetries in as intimate a way as a CPT theorem would seem to suggest dissolves. In chapter 3, we turn to the question of whether the CPT theorem is an essentially quantum-theoretic result. We state and prove a classical analogue of the CPT theorem for systems of tensor fields. This classical analogue, however, ii appears not to extend to systems of spinor fields. -
1 How Could Relativity Be Anything Other Than Physical?
How Could Relativity be Anything Other Than Physical? Wayne C. Myrvold Department of Philosophy The University of Western Ontario [email protected] Forthcoming in Studies in History and Philosophy of Modern Physics. Special Issue: Physical Relativity, 10 years on Abstract Harvey Brown’s Physical Relativity defends a view, the dynamical perspective, on the nature of spacetime that goes beyond the familiar dichotomy of substantivalist/relationist views. A full defense of this view requires attention to the way that our use of spacetime concepts connect with the physical world. Reflection on such matters, I argue, reveals that the dynamical perspective affords the only possible view about the ontological status of spacetime, in that putative rivals fail to express anything, either true or false. I conclude with remarks aimed at clarifying what is and isn’t in dispute with regards to the explanatory priority of spacetime and dynamics, at countering an objection raised by John Norton to views of this sort, and at clarifying the relation between background and effective spacetime structure. 1. Introduction Harvey Brown’s Physical Relativity is a delightful book, rich in historical details, whose main thrust is to an advance a view of the nature of spacetime structure, which he calls the dynamical perspective, that goes beyond the familiar dichotomy of substantivalism and relationism. The view holds that spacetime structure and dynamics are intrinsically conceptually intertwined and that talk of spacetime symmetries and asymmetries is nothing else than talk of the symmetries and asymmetries of dynamical laws. Brown has precursors in this; I count, for example, Howard Stein (1967) and Robert DiSalle (1995) among them. -
History of Sundials
History of Sundials The earliest record of the sundial dates back as early as 3500 BCE. At this time the ancient Egyptians were building tall, slender monuments from stone, called obelisks, which cast shadows that functioned like a sundial. Obelisks enabled people to divide the day into morning and afternoon, and they also showed the longest and shortest days of the year when the shadow they cast was longest or shortest at noon. Later on, additional markers were added around the base of the obelisk to indicate further subdivisions of time. Possibly the first portable timepiece came into use around 1500 BCE. Still a sundial, this was another Egyptian invention and it divided the day into ten parts plus two “twilight hours” in the morning and evening; was this the origin of the “twelve hour day” that we know today? Around 600 BCE the Egyptians came up with another invention, the merkhet (the oldest known astronomical tool), which allowed them to tell the time at night when there was no sun to cast a shadow. The merkhet worked in a similar way to a sundial: you would line up a pair of them in a north-south direction using the Pole Star, and then as certain stars crossed that line you would be able to tell what time it was. In the pursuit of year-round accuracy sundials gradually developed from their original shape, of a flat or vertical plate or surface, to much more elaborate forms. One version was a bowl-shape, cut into a block of stone, with a central vertical pointer (gnomon) whose shadow fell on lines marking sets of hour lines for different seasons.