Topics in Theoretical and Experimental Gravitation Physics

Transcription

1 Topics in Theoretical and Experimental Gravitation Physics

2 NATO ADVANCED STUDY INSTITUTES SERIES A series of edited volumes comprising multifaceted studies of contemporary scientific issues by some of the best scientific minds in the world, assembled in cooperation with NATO Scientific Affairs Division. Series B: Physics RECENT VOLUMES IN THIS SERIES Volume 19 - Volume 20 - Volume Volume 22 - Volume 23 - Volume 24 - Volume 25 - Volume 26 - Volume 27 - Volume 28 - Volume 29 - Defects and Their Structure in Nonmetallic Solids edited by B. Henderson and A. E. Hughes Physics of Structurally Disordered Solids edited by Shashanka S. Mitra Superconductor Applications: SQUIDs and Machines edited by Brian B. Schwartz and Simon Foner Nuclear Magnetic Resonance in Solids edited by Lieven Van Gerven Photon Correlation Spectroscopy and Velocimetry edited by E. R. Pike and H. Z. Cummins Electrons in Finite and Infinite Structures edited by P. Phariseau and L. Scheire Chemistry and Physics of One-Dimensional Metals edited by Heimo 1. Keller New Developments in Quantum Field Theory and Statistical Mechanics-Cargese 1976 edited by Maurice Levy and Pronob Mitter Topics in Theoretical and Experimental Gravitation Physics Edited by V. De Sabbata and J. Weber Material Characterization Using Ion Beams Edited by J. P. Thomas and A. Cachard Electron-Phonon Interactions and Phase Transitions Edited by Tormod Riste The series is published by an international board of publishers in conjunction with NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics New York and London C Mathematical and D_ Reidel Publishing Company Physical Sciences Dordrecht and Boston D Behavioral and Sijthoff Interna tional Publishing Company Social Sciences Leiden E Applied Sciences Noordhoff International Publishing Leiden

3 Topics in Theoretical and Experimental Gravitation Physics Edited by V. De Sabbata Institute of Physics University of Bologna Bologna, Italy and Institute of Physics University of Ferrara Ferrara, Italy and 1. Weber University of Maryland College Park, Maryland and University of California at Irvine Irvine, California PLENUM PRESS LONDON AND NEW YORK Published in cooperation with NATO Scientific Affairs Division

4 Library of Congress Cataloging in Publication Data International School of Cosmology and Gravitation, Erice, Italy, Topics in theoretical and experimental gravitation physics. (NATO advanced study institutes series: Series B, Physics; 27) "Proceedings of the International School of Cosmology and Gravitation held in Erice, Trapani, Sicily, March 13-25, 1975." Includes indexes. 1. Gravitation-Congresses. I. De Sabbata, V. II. Weber, Joseph, III. Title. IV. Series. QC178.I ' ISBN-13: e-isbn-13: DOl: / Proceedings of the International School of Cosmology and Gravitation held in Erice, Trapani, Sicily, March 13-25, 1975 "Ettore Majorana" International Centre for Scientific Culture Antonino Zichichi - Director International School of Cosmology and Gravitation Venzo De Sabbata -Director Fourth Course: "Gravitational Waves" Joe Weber - Director 1977 Plenum Press, New York Softcover reprint of the hardcover Ist edition 1977 A Division of Plenum Publishing Corporation 227 West 17th Street, New York, N.Y All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher

5 Preface During the period March 13-25, 1975, the IV course of the International School of Cosmology and Gravitation was held at Erice, Sicily and devoted primarily to gravitational waves. A number of participants have prepared their lectures for publication here. These include topics in Gravitational Radiation, Gravitational Radiation Antennas and Data Analyses, Singularities in General Relativity Theory, the Bimetric Theory of Gravitation, Tachyons, and General Relativity and Quantum Theory. V. De Sabbata and J. Weber v

6 Contents Opening ReII1arks, J. Weber... ix The Generation of Gravitational Waves: A Review of Computational Techniques, K.S. Thorne 1 Effects of Gravitational Radiation upon Electromagnetic Waves in a Dispersive Medium, B. Bertotti and R. Catenacci 63 Gravitational Waves and Their Interaction with Electromagnetic Field, V. De Sabbata. 69 Shock Waves in General Relativity, A. Papapetrou 83 Editorial Connnents The Detection of Gravitational Waves and Quantum Nondisturbtive Measurements, V. Braginsky 105 Onedimensional Analysis and Computer Simulation of a Weber Antenna, G.V. Pallottino 123 Comments on the Gravitational Radiation Experiments, J. Weber 135 Estimated Sensitivity of the Low Temperature Gravitational Wave Antenna in Rome, G. Pizzella 139 The L.S.U. Low Temperature Gravity Wave Experiment, W.O. Hamilton, T.P. Bernat, D.G. Blair, W.C. Oelfke 149 Optimal Detection of Signals through Linear Devices with Thermal Noise Sources and Application to the Munich Frascati Weber-Type Gravitational Wave Detectors, P. Kafka Synchrotron Radiation and Astrophysics, A.A. Sokolov 243 vii

7 vm CONTENTS Editorial Comments: Development of Singularities 25l On the Behavior of Physical Clocks in the Vicinity of Singularities of a Gravitational Field, C. M~ler 253 Editorial Comments Bimetric Theory of Gravitation, N. Rosen 273 Speculative Remarks on Physics in General and Relativity in Particular., A. Mercier Gravitation and Tachyons, E. Recami 305 General Relativity and Quantum Theory, E. Schmutzer 323 Author Index Subject Index

8 OPENING REMARKS J. Weber University of California at Irvine and University of Maryland, College Park This appears to be the first school course devoted primarily to gravitational radiation. It is very appropriate to have a school of relativity and cosmology here in Erice. Probably the first work on the stress tensor of a fluid was done here by Archimedes. The great Italian physicists of modern times, Galileo, Fermi and Majorana, continue to be an inspiration to all of us. We are very fortunate to be working in the field of General Relativity. Landau remarked that Einstein's achievement was the most perfect and most beautiful of all theories. The difficult mathematics has been a challenge to the greatest theoretical physicists in the world. The great weakness of the gravitational interaction orders weaker than the weak interactions,makes possible experiments difficult, interesting and challenging. The other lecturers are truly great physicists who are skilled in communicating their ideas to students. Each lecturer has a unique philosophy of doing physics and this school provides a splendid opportunity for students to become familiar with the different philosophies of doing physics. The early work of Einstein, and Eddington predicted gravitational radiation, using the linearized field equations. For many years, there appeared to be no hope of doing meaningful experiments. We can admire the work of research workers during the period This was a field pursued purely out of intellectual curiosity. To test a theory one first thinks in terms of laboratory experiments. For electrons the quantity ix

9 x J. WEBER Gm e and this implies that in lowest order only one graviton is emitted for 1043 photons. Experiments of the type done by Hertz are therefore very difficult. Serious work began on antennas to receive astronomical sources of radiation, in It still appeared that no sources existed with sufficient intensity to make direct observations possible. The displacement sensitivity x of an antenna with mass m, angular normal mode frequency w is given by and for hw > kt Here e is a coupling factor, Q l is the quality factor of the normal mode of an antenna, and Q2 is the quality factor of some device which couples the energy out. By going to very low temperatures great increases in sensitivity are possible, and this makes more sources of gravitational radiation accessible. The Einstein Eddington formula for the radiation from a spinning rod is p (1) where P is the radiated power G is the constant of gravitation I is the amplitude of the quadrupole moment w is the angular frequency c is the speed of light. This formula is very discouraging because the very small quantity G a coupling constant -- appears in the numerator, while the very large quantity c5 appears in the denominator.

10 OPENING REMARKS xi For a binary star (1) may be written p=gmrw 5 c where m is the mass. F.J. Dyson* was the first to point out that (2) transforms in a very interesting way for an extreme relativistic system. In this case (2) Gm 2 4/ - 2 mc r m r.. 2 4c, G c = wr Substituting these gives us P => G 2 m c -2- '" r 5 c G In fact Dyson's more precise result is ** P c 5G This stupendous amount of radiation might be expected in say a gravitational collapse, and was part of the motivation for the coincidence experiments search for radiation starting in Finally, the very important discoveries of astronomy--the quasars, pulsars, and x ray sources refocussed attention on very early work of Chandresekhar, Oppenheimer and Vo1kcoff and Landau on neutron stars, black holes, and related very important gravitational radiation. We thank Professors De Sabbata, Zichichi, NATO, NSF, Gravity Research Foundation, the Italian Ministry of Public Education, the Italian Ministry of Scientific and Technological Research, the National Research Council of Italy, the Regional Sicilian Government and many countries for making this school possible. Thank you. *F.J. Dyson in Interstellar Communication p. 118, edited by AGW Cameron, W.A. Benjamin Inc **L. Smarr's Computer Analyses suggest that the gravitational radiation from relativistic sources may be much smaller