DOCSLIB.ORG

Thermodynamics of Relativity 301 6.1 Does the Inertia of a Body Depend on Its Heat Content?

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Thermodynamics of Relativity 301 6.1 Does the Inertia of a Body Depend on Its Heat Content? 8083.9789814340489-tp.indd 1 8/29/11 4:59 PM This page intentionally left blank Bernard H Lavenda Universita’ degli Studi di Camerino, Italy World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI 8083.9789814340489-tp.indd 2 8/29/11 4:59 PM Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. A NEW PERSPECTIVE ON RELATIVITY An Odyssey in Non-Euclidean Geometries Copyright © 2012 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-981-4340-48-9 ISBN-10 981-4340-48-0 Typeset by Stallion Press Email: [email protected] Printed in Singapore. YeeSern - A New Perspective on Relativity.pmd1 10/14/2011, 9:08 AM Aug. 26, 2011 11:17 SPI-B1197 A New Perspective on Relativity b1197-fm In memory of Franco Fraschetti (1924–2009) v Aug. 26, 2011 11:17 SPI-B1197 A New Perspective on Relativity b1197-fm This page intentionally left blank Aug. 26, 2011 11:17 SPI-B1197 A New Perspective on Relativity b1197-fm Preface Electrodynamics was the next oasis after thermodynamics which saw a confluence of physicists and mathematicians, many of whom had been protagonists in thermodynamics. Just as thermodynamics had an offspring, quantum theory,so too did electrodynamics, namely the theory of relativity. While a single name can be attached to the origins of thermodynamics, Sadi Carnot, and that of its offspring, Max Planck, no such simplicity exists in electrodynamics and relativity. Relativity is as much about physics as it is about the human beings, and their failings, that made it. Every physics student will have heard of Maxwell’s equations but will he have also heard of Weber’s force? The stu- dent may have heard of Weber and Gauss for the units named after them, but not about their championing of Ampère’s law which threatened the supremacy of Newton’s inverse square law. The names of Helmholtz, Clau- sius and Boltzmann may be familiar from thermodynamics and statistical thermodynamics but much less known for their theories of electromag- netism. Every student of mathematics will have heard the names of Gauss and Riemann, but will he also know of their fundamental contributions to electromagnetism? Who were Abraham, Heaviside, Larmor, Liénard, Lorenz, Ritz, Schwarzschild, and Voigt? Why have their names been struck from the annals of electromagnetism? We are familiar with the priority disputes between Kelvin and Clausius in thermodynamics, but not with those in electromagnetism and relativity. A student of physics may have heard the name of Lorentz, because of his law of force and transformation, but not at the same level of Einstein. And Poincaré is known for just about everything else than his principle of relativity. The history of electromagnetism and relativity has been rewritten and in a very unflattering way. vii Aug. 26, 2011 11:17 SPI-B1197 A New Perspective on Relativity b1197-fm viii A New Perspective on Relativity By the modern historical account of electromagnetism and relativity, there were winners and losers. Maxwell is said to have triumphed over Weber and Gauss, in formulating a field theory of electromagnetism, and over Lorenz and Riemann in the formulation of his displacement current, Einstein’s absolute speed of light prevailed over Ritz’s ballistic theory of emission, Lorentz’s supremacy over Abraham and Bucherer in devising a model of the electron whose expressions for the variation of mass, momen- tum, and energy with velocity were later to be adopted in toto by relativity as a model for all matter, whether charged or not, and Einstein’s seniority in stating the principles of relativity though they were previously enunciated by Poincaré. Why were the experimentalists, Ives and Essen, so vehemently opposed to relativity? Ives viewed his verification of the second-order Doppler shift as a clear demonstration that a moving clock runs slow by the same factor that was predicted by Larmor and Lorentz, and not as a vindication of time dilatation in special relativity. Essen, who built the first cesium clock, queried what happens to the lost ticks when more ticks are transmitted than are received, independent of whether two clocks are approaching or receding from one another? Essen went so far as to query relativity as a “joke or swindle?” Most if not all monographs on relativity do not touch on these ques- tions. Not so with O’Rahilly’s Electromagnetics written in 1938. Not everyone will agree with his dispraise of Maxwell’s displacement current, or his over appraisal of Ritz, but much of what he says could not be truer today: There is far more authoritarianism in science that physicists are aware or at least publicly acknowledge. Anybody with a scientific reputation would today hesitate to criticize Einstein, except by way of outdoing him in cosmological speculations. Essen expressed similar views Students are told that the theory (relativity) must be accepted although they cannot be expected to understand it...The theory is so rigidly held that young scientists who have any regard for their careers dare not openly express their doubts. Whether there is any truth in the allegations I will leave to the reader. But what I plan to do is to present relativity from a ‘new’ point of view that treats, known and unknown, relativistic phenomena from different per- spectives. I put ‘new’ in quotation marks because the approach is really not new, but was suggested by Kaluza and Variˇcak over a century ago. What Aug. 26, 2011 11:17 SPI-B1197 A New Perspective on Relativity b1197-fm Preface ix is ‘new,’ I believe, is the wealth of physical phenomena that can be drawn from the non-Euclidean geometrical perspective. This monograph is nei- ther intended an historical account of relativity nor an essay in constructive criticism of it. Arecurring theme is that motion causes deformity and this can, under certain circumstances, catapult us into non-Euclidean spaces. It was also an exciting exercise to see where non-Euclidean geometries could be found, but were not appreciated as such. There are at least two eye-catching rela- tions: The product of two longitudinal Doppler shifts is the square root of the cross-ratio, and whose logarithm is hyperbolic distance, and the Beltrami metric in polar coordinates is the exact expression for the metric for the uniformly rotating disc. Gravitational phenomena rather than being a manifestation of warped space-time can be accounted for by a varying index of refraction in an inhomogeneous medium that modifies Fermat’s principle of least time. The reader will find old and new things alike — but the ‘old’ with a new interpretation. I don’t expect that everything is true to 100 percent, some things will have to be changed, modified or clarified, but, I do believe that this is a very fruitful approach that has led to the questioning of many fundamental aspects of relativity. According to Riemann, physics is the search for a geometric mani- fold upon which physical processes occur. The line element of constant curvature, 1 dx2 , (R) + 1 2 1 4 α x appearing in his Habilitation Dissertation, when written in polar coordinates is precisely the metric for a uniformly rotating disc with constant negative curvature, α<0. When charge is added, it becomes the Liénard expression for the rate of energy loss due to radiation. The role of the longitudinal Doppler shift means that space and time do not appear separately but only in a ratio, as a homogeneous coor- dinate. It is the difference in longitudinal Doppler shifts that is responsi- ble for the slowing down of clocks in relative motion. Einstein elevated c, the velocity of light in vacuo, to a universal constant. The fact that c is a constant, even to observers in relative motion, is tantamount to making it a unit of measurement — one which is necessary for the existence of a Aug. 26, 2011 11:17 SPI-B1197 A New Perspective on Relativity b1197-fm x A New Perspective on Relativity non-Euclidean geometry. So raising c to a universal constant, as Essen has pointed out, meant that the definition of unit length or time, or both, had to be abandoned. Relativity will thus unfold in a hyperbolic space of velocities that is entirely consonant with the relativistic addition of velocities. Following the historical route spreads the honors of discovery of rel- ativity more evenly. Poincaré had arrived at the postulates of relativity at least five years before Einstein, but “because he did not fully appreciate the status of both postulates” is no argument to deny him credit. To deny Poincaré his primary role in developing the theory of relativ- ity because he held onto the aether concept is to deny Carnot the credit for discovering his principle because he still believed in caloric theory.It would never have passed my mind to say that Boltzmann’s principle is incom- plete because it deals with only part of a probability distribution, being a very large number instead of a proper fraction, whereas I have shown that the entropy is the potential of law of error for which the most probable value is the average value of the measurements, that I have detracted any credit from Boltzmann.
Load more

Recommended publications
  • Mathematical Methods of Classical Mechanics-Arnold V.I..Djvu
    V.I. Arnold Mathematical Methods of Classical Mechanics Second Edition Translated by K. Vogtmann and A. Weinstein With 269 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest V. I. Arnold K. Vogtmann A. Weinstein Department of Department of Department of Mathematics Mathematics Mathematics Steklov Mathematical Cornell University University of California Institute Ithaca, NY 14853 at Berkeley Russian Academy of U.S.A. Berkeley, CA 94720 Sciences U.S.A. Moscow 117966 GSP-1 Russia Editorial Board J. H. Ewing F. W. Gehring P.R. Halmos Department of Department of Department of Mathematics Mathematics Mathematics Indiana University University of Michigan Santa Clara University Bloomington, IN 47405 Ann Arbor, MI 48109 Santa Clara, CA 95053 U.S.A. U.S.A. U.S.A. Mathematics Subject Classifications (1991): 70HXX, 70005, 58-XX Library of Congress Cataloging-in-Publication Data Amol 'd, V.I. (Vladimir Igorevich), 1937- [Matematicheskie melody klassicheskoi mekhaniki. English] Mathematical methods of classical mechanics I V.I. Amol 'd; translated by K. Vogtmann and A. Weinstein.-2nd ed. p. cm.-(Graduate texts in mathematics ; 60) Translation of: Mathematicheskie metody klassicheskoi mekhaniki. Bibliography: p. Includes index. ISBN 0-387-96890-3 I. Mechanics, Analytic. I. Title. II. Series. QA805.A6813 1989 531 '.01 '515-dcl9 88-39823 Title of the Russian Original Edition: M atematicheskie metody klassicheskoi mekhaniki. Nauka, Moscow, 1974. Printed on acid-free paper © 1978, 1989 by Springer-Verlag New York Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag, 175 Fifth Avenue, New York, NY 10010, U.S.A.), except for brief excerpts in connection with reviews or scholarly analysis.
    [Show full text]
  • Einstein's Physical Strategy, Energy Conservation, Symmetries, And
    Einstein’s Physical Strategy, Energy Conservation, Symmetries, and Stability: “but Grossmann & I believed that the conservation laws were not satisfied” April 12, 2016 J. Brian Pitts Faculty of Philosophy, University of Cambridge [email protected] Abstract Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein’s physical strategy and the particle physics deriva- tions compare? What energy-momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his work relate to emerging knowledge (1911-14) of the canonical energy-momentum tensor and its translation-induced conservation? After initially using energy-momentum tensors hand-crafted from the gravitational field equa- ′ µ µ ν tions, Einstein used an identity from his assumed linear coordinate covariance x = Mν x to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor’s asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell’s theory (which avoids negative-energies but gets an asymmetric canonical tensor as a result) as on a scalar theory (the Newtonian limit).
    [Show full text]
  • General Relativity Requires Absolute Space and Time 1 Space
    CORE Metadata, citation and similar papers at core.ac.uk Provided by CERN Document Server General Relativity Requires Amp`ere’s theory of magnetism [10]. Maxwell uni- Absolute Space and Time fied Faraday’s theory with Huyghens’ wave the- ory of light, where in Maxwell’s theory light is Rainer W. K¨uhne considered as an oscillating electromagnetic wave Lechstr. 63, 38120 Braunschweig, Germany which propagates through the luminiferous aether of Huyghens. We all know that the classical kinematics was re- placed by Einstein’s Special Relativity [11]. Less We examine two far-reaching and somewhat known is that Special Relativity is not able to an- heretic consequences of General Relativity. swer several problems that were explained by clas- (i) It requires a cosmology which includes sical mechanics. a preferred rest frame, absolute space and According to the relativity principle of Special time. (ii) A rotating universe and time travel Relativity, all inertial frames are equivalent, there are strict solutions of General Relativity. is no preferred frame. Absolute motion is not re- quired, only the relative motion between the iner- tial frames is needed. The postulated absence of an absolute frame prohibits the existence of an aether [11]. 1 Space and Time Before Gen- According to Special Relativity, each inertial eral Relativity frame has its own relative time. One can infer via the Lorentz transformations [12] on the time of the According to Aristotle, the Earth was resting in the other inertial frames. Absolute space and time do centre of the universe. He considered the terrestrial not exist. Furthermore, space is homogeneous and frame as a preferred frame and all motion relative isotropic, there does not exist any rotational axis of to the Earth as absolute motion.
    [Show full text]
  • Complex Analysis in Industrial Inverse Problems
    Complex Analysis in Industrial Inverse Problems Bill Lionheart, University of Manchester October 30th , 2019. Isaac Newton Institute How does complex analysis arise in IP? We see complex analysis arise in two main ways: 1. Inverse Problems that are or can be reduced to two dimensional problems. Here we solve inverse problems for PDEs and integral equations using methods from complex analysis where the complex variable represents a spatial variable in the plane. This includes various kinds of tomographic methods involving weighted line integrals, and is used in medial imaging and non-destructive testing. In electromagnetic problems governed by some form of Maxwell’s equation complex analysis is typically used for a plane approximation to a two dimensional problem. 2. Frequency domain methods in which the complex variable is the Fourier-Laplace transform variable. The Hilbert transform is ubiquitous in signal processing (everyone has one implemented in their home!) due to the analytic representation of a signal. In inverse spectral problems analyticity with respect to a spectral parameter plays an important role. Industrial Electromagnetic Inverse Problems Many inverse problems involve imaging the inside from measuring on the outside. Here are some industrial applied inverse problems in electromagnetics I Ground penetrating radar, used for civil engineering eg finding burried pipes and cables. Similar also to microwave imaging (security, medicine) and radar. I Electrical resistivity/polarizability tomography. Used to locate underground pollution plumes, salt water ingress, buried structures, minerals. Also used for industrial process monitoring (pipes, mixing vessels etc). I Metal detecting and inductive imaging. Used to locate weapons on people, find land mines and unexploded ordnance, food safety, scrap metal sorting, locating reinforcing bars in concrete, non-destructive testing, archaeology, etc.
    [Show full text]
  • The Physics Surrounding the Michelson-Morley Experiment and a New Æther Theory
    The physics surrounding the Michelson-Morley experiment and a new æther theory Israel P´erez Department of Applied Physics, CINVESTAV, M´erida, Yucat´an,M´exico Abstract From the customary view the Michelson-Morley experiment is used to expose the failure of the aether theory. The key point in this experiment is the fringe shift of the interference pattern. Regularly, the fringe shift calculations are only presented from the perspective of the inertial frame where the one-way speed of light is anisotropic which gives a partial vision of the problem. In a spirit of revision of these facts we have meticulously analyzed the physics behind them. As a result, an angular effect which is based on Huyghens principle and plays a fundamental role in the reflection of light waves at moving mirrors is incorporated. Moreover, under the assumption of a null result in the experiment, on the one hand, the fringe shift conditions demand actual relativistic effects; on the other, it is confirmed that Maxwell's electrodynamics and Galilean relativity are incompatible formulations. From these two points at least three inertial theories follow: (1) the special theory of relativity (SR), (2) a new aether theory (NET) based on the Tangherlini transformations and (3) emission theories based on Ritz' modification of electrodynamics. A brief review of their physical content is presented and the problem of the aether detection as well as the propagation of light, within the context of SR and the NET, are discussed. Despite the overwhelming amount of evidences that apparently favors SR we claim that there are no strong reasons to refuse the aether which conceived as a continuous material medium, still stands up as a physical reality and could be physically associated with dark matter, the cosmic background radiation and the vacuum condensates of particle physics.
    [Show full text]
  • Mathematical Genealogy of the Union College Department of Mathematics
    Gemma (Jemme Reinerszoon) Frisius Mathematical Genealogy of the Union College Department of Mathematics Université Catholique de Louvain 1529, 1536 The Mathematics Genealogy Project is a service of North Dakota State University and the American Mathematical Society. Johannes (Jan van Ostaeyen) Stadius http://www.genealogy.math.ndsu.nodak.edu/ Université Paris IX - Dauphine / Université Catholique de Louvain Justus (Joost Lips) Lipsius Martinus Antonius del Rio Adam Haslmayr Université Catholique de Louvain 1569 Collège de France / Université Catholique de Louvain / Universidad de Salamanca 1572, 1574 Erycius (Henrick van den Putte) Puteanus Jean Baptiste Van Helmont Jacobus Stupaeus Primary Advisor Secondary Advisor Universität zu Köln / Université Catholique de Louvain 1595 Université Catholique de Louvain Erhard Weigel Arnold Geulincx Franciscus de le Boë Sylvius Universität Leipzig 1650 Université Catholique de Louvain / Universiteit Leiden 1646, 1658 Universität Basel 1637 Union College Faculty in Mathematics Otto Mencke Gottfried Wilhelm Leibniz Ehrenfried Walter von Tschirnhaus Key Universität Leipzig 1665, 1666 Universität Altdorf 1666 Universiteit Leiden 1669, 1674 Johann Christoph Wichmannshausen Jacob Bernoulli Christian M. von Wolff Universität Leipzig 1685 Universität Basel 1684 Universität Leipzig 1704 Christian August Hausen Johann Bernoulli Martin Knutzen Marcus Herz Martin-Luther-Universität Halle-Wittenberg 1713 Universität Basel 1694 Leonhard Euler Abraham Gotthelf Kästner Franz Josef Ritter von Gerstner Immanuel Kant
    [Show full text]
  • Post-Newtonian Description of Quantum Systems in Gravitational Fields
    Post-Newtonian Description of Quantum Systems in Gravitational Fields Von der QUEST-Leibniz-Forschungsschule der Gottfried Wilhelm Leibniz Universität Hannover zur Erlangung des Grades Doktor der Naturwissenschaften Dr. rer. nat. genehmigte Dissertation von M. A. St.Philip Klaus Schwartz, geboren am 12.07.1994 in Langenhagen. 2020 Mitglieder der Promotionskommission: Prof. Dr. Elmar Schrohe (Vorsitzender) Prof. Dr. Domenico Giulini (Betreuer) Prof. Dr. Klemens Hammerer Gutachter: Prof. Dr. Domenico Giulini Prof. Dr. Klemens Hammerer Prof. Dr. Claus Kiefer Tag der Promotion: 18. September 2020 This thesis was typeset with LATEX 2# and the KOMA-Script class scrbook. The main fonts are URW Palladio L and URW Classico by Hermann Zapf, and Pazo Math by Diego Puga. Abstract This thesis deals with the systematic treatment of quantum-mechanical systems situated in post-Newtonian gravitational fields. At first, we develop a framework of geometric background structures that define the notions of a post-Newtonian expansion and of weak gravitational fields. Next, we consider the description of single quantum particles under gravity, before continuing with a simple composite system. Starting from clearly spelled-out assumptions, our systematic approach allows to properly derive the post-Newtonian coupling of quantum-mechanical systems to gravity based on first principles. This sets it apart from other, more heuristic approaches that are commonly employed, for example, in the description of quantum-optical experiments under gravitational influence. Regarding single particles, we compare simple canonical quantisation of a free particle in curved spacetime to formal expansions of the minimally coupled Klein– Gordon equation, which may be motivated from the framework of quantum field theory in curved spacetimes.
    [Show full text]
  • P.W. ANDERSON Stud
    P.W. ANDERSON Stud. Hist. Phil. Mod. Phys., Vol. 32, No. 3, pp. 487–494, 2001 Printed in Great Britain ESSAY REVIEW Science: A ‘Dappled World’ or a ‘Seamless Web’? Philip W. Anderson* Nancy Cartwright, The Dappled World: Essays on the Perimeter of Science (Cambridge: Cambridge University Press, 1999), ISBN 0-521-64411-9, viii+247 pp. In their much discussed recent book, Alan Sokal and Jean Bricmont (1998) deride the French deconstructionists by quoting repeatedly from passages in which it is evident even to the non-specialist that the jargon of science is being outrageously misused and being given meanings to which it is not remotely relevant. Their task of ‘deconstructing the deconstructors’ is made far easier by the evident scientific illiteracy of their subjects. Nancy Cartwright is a tougher nut to crack. Her apparent competence with the actual process of science, and even with the terminology and some of the mathematical language, may lead some of her colleagues in the philosophy of science and even some scientists astray. Yet on a deeper level of real understanding it is clear that she just does not get it. Her thesis here is not quite the deconstruction of science, although she seems to quote with approval from some of the deconstructionist literature. She seems no longer to hold to the thesis of her earlier book (Cartwright, 1983) that ‘the laws of physics lie’. But I sense that the present book is almost equally subversive, in that it will be useful to the creationists and to many less extreme anti-science polemicists with agendas likely to benefit from her rather solipsistic views.
    [Show full text]
  • Glossary "The Difference Between Genius and Stupidity Is That Genius Has Its Limits" - Albert Einstein ( 1879 - 1955 )
    Relativity Science Calculator - Glossary "The difference between genius and stupidity is that genius has its limits" - Albert Einstein ( 1879 - 1955 ) Aberration [ aberration of (star)light, astronomical aberration, stellar aberration ]: An astronomical phenomenon different from the phenomenon of parallax whereby small apparent motion displacements of all fixed stars on the celestial sphere due to Earth's orbital velocity mandates that terrestrial telescopes must also be adjusted to slightly different directions as the Earth yearly transits the Sun. Stellar aberration is totally independent of a star's distance from Earth but rather depends upon the transverse velocity of an observer on Earth, all of which is unlike the phenomenon of parallax. For example, vertically falling rain upon your umbrella will appear to come from in front of you the faster you walk and hence the more you will adjust the position of the umbrella to deflect the rain. Finally, the fact that Earth does not drag with itself in its immediate vicinity any amount of aether helps dissuade the concept that indeed the aether exists. Star Aberration produces visual distortions of the spatial external ( spacetime ) world, a sort of faux spacetime curvature geometry. See: Celestial Sphere; also Parallax which is a totally different phenomenon. Absolute Motion, Time and Space by Isaac Newton: "Philosophiae Naturalis Principia Mathematica", by Isaac Newton, published July 5, 1687, translated from the original Latin by Andrew Motte ( 1729 ), as revised by Florian Cajori ( Berkeley,
    [Show full text]
  • A New Cosmology, Based Upon the Hertzian Fundamental Principle of Mechanics by Pascal M
    A new cosmology, based upon the Hertzian fundamental principle of mechanics by Pascal M. .Rapier Director Newtonian Science Foundation, 3154 Deseret Dr. Richmond, Calif. PRESENTADO POR EL ACADÉMICO D. JULIO PALACIOS RESUMEN Con el reciente descubrimiento de la explosión de la «estrella neutrónicaj>, y con la invalidación de la teoría de la relatividad de Einstein por el experimento de Kantor, ¡a cosmologia newtoniana adquiere capital importancia. Esta cosmología se basa en el principio fundamental de Mecánica de Hertz : Todo sistema libre, persiste r» su estado de reposo o de movimiento uniforme en el camino más corto. En consecuencia, el corrimiento hacia el rojo de las rayas espectrales resulta ser debido a una degradación de la energía, degradación que es inherente a la propa- gación de la luz, y no a un efecto de Doppler, ad hoc, como se había admitido. Ea relación entre dicho corrimiento y la luminosidad, observada en las galaxias lejanas, se deduce de dicho principio y sirve para confirmarlo. Se demuestra además que la energía que llena todo el espacio y que se atribuye a los neutrinos, es el resultado de reacciones nucleares consistentes en la emisión de partículas beta y del corrimiento hacia el rojo. Esta energía es responsable de las explosiones de las «estrellas neutrónicas». Tales explosiones sirven para recrear hidrógeno virgen a partir de los detritus estelares y para distribuirlo por todo el universo, con lo que hay una creación continua de nuevas estrellas. En consecuen- cia, dunque el universo fuese infinitamente viejo, no tiene porqué «venirse abajo». Además, la cosmología newtoniana exige que el espacio sea estable, que no se ex- panda, y que sea homogéneo, euclideo e infinito.
    [Show full text]
  • Hep-Th/9911055V4 29 Feb 2000 AS0.0+;9.0C I92-F;UBF-7;OU-TAP UAB-FT-476; NI99022-SFU; 98.80.Cq PACS:04.50.+H; Increpnst H Edfrfo H Oio Fe Gravi After Horizon Brane
    Gravity in the Randall-Sundrum Brane World. Jaume Garriga1,2 and Takahiro Tanaka1,2,3 1IFAE, Departament de Fisica, Universitat Autonoma de Barcelona, 08193 Bellaterra (Barcelona), Spain; 2Isaac Newton Institute, University of Cambridge 20 Clarkson Rd., Cambridge, CB3 0EH, UK; 3Department of Earth and Space Science, Graduate School of Science Osaka University, Toyonaka 560-0043, Japan. We discuss the weak gravitational field created by isolated matter sources in the Randall-Sundrum brane-world. In the case of two branes of opposite tension, linearized Brans-Dicke (BD) gravity is recovered on either wall, with different BD parameters. On the wall with positive tension the BD parameter is larger than 3000 provided that the separation between walls is larger than 4 times the AdS radius. For the wall of negative tension the BD parameter is always negative. In either case, shadow matter from the other wall gravitates upon us. For equal Newtonian mass, light deflection from shadow matter is 25 % weaker than from ordinary matter. For the case of a single wall of posi- tive tension, Einstein gravity is recovered on the wall to leading order, and if the source is stationary the field stays localized near the wall. We calculate the leading Kaluza-Klein corrections to the linearized gravitational field of a non-relativistic spherical object and find that the metric is different from the Schwarzschild solution at large distances. We believe that our linearized solu- tion corresponds to the field far from the horizon after gravitational collapse of matter on the brane. PACS:04.50.+h; 98.80.Cq NI99022-SFU; UAB-FT-476; OU-TAP106 arXiv:hep-th/9911055v4 29 Feb 2000 It has recently been shown [1] that something very similar to four dimensional Einstein gravity exists on a domain wall (or 3-brane) of positive tension which is embedded in a five dimensional anti-de Sitter space (AdS).
    [Show full text]
  • Post-Newtonian Approximations and Applications
    Monash University MTH3000 Research Project Coming out of the woodwork: Post-Newtonian approximations and applications Author: Supervisor: Justin Forlano Dr. Todd Oliynyk March 25, 2015 Contents 1 Introduction 2 2 The post-Newtonian Approximation 5 2.1 The Relaxed Einstein Field Equations . 5 2.2 Solution Method . 7 2.3 Zones of Integration . 13 2.4 Multi-pole Expansions . 15 2.5 The first post-Newtonian potentials . 17 2.6 Alternate Integration Methods . 24 3 Equations of Motion and the Precession of Mercury 28 3.1 Deriving equations of motion . 28 3.2 Application to precession of Mercury . 33 4 Gravitational Waves and the Hulse-Taylor Binary 38 4.1 Transverse-traceless potentials and polarisations . 38 4.2 Particular gravitational wave fields . 42 4.3 Effect of gravitational waves on space-time . 46 4.4 Quadrupole formula . 48 4.5 Application to Hulse-Taylor binary . 52 4.6 Beyond the Quadrupole formula . 56 5 Concluding Remarks 58 A Appendix 63 A.1 Solving the Wave Equation . 63 A.2 Angular STF Tensors and Spherical Averages . 64 A.3 Evaluation of a 1PN surface integral . 65 A.4 Details of Quadrupole formula derivation . 66 1 Chapter 1 Introduction Einstein's General theory of relativity [1] was a bold departure from the widely successful Newtonian theory. Unlike the Newtonian theory written in terms of fields, gravitation is a geometric phenomena, with space and time forming a space-time manifold that is deformed by the presence of matter and energy. The deformation of this differentiable manifold is characterised by a symmetric metric, and freely falling (not acted on by exter- nal forces) particles will move along geodesics of this manifold as determined by the metric.
    [Show full text]