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The Gravitational Constant: Generalized Gravitational Theories and Experiments NATO Science Series The Gravitational Constant: Generalized Gravitational Theories and Experiments NATO Science Series A Series presenting the results of scientific meetings supported under the NATO Science Programme. The Series is published by lOS Press, Amsterdam, and Kluwer Academic Publishers in conjunction with the NATO Scientific Affairs Division Sub-Series I. Life and Behavioural Sciences lOS Press II. Mathematics, Physics and Chemistry Kluwer Academic Publishers III. Computer and Systems Science lOS Press IV. Earth and Environmental Sciences Kluwer Academic Publishers V. Science and Technology Policy lOS Press The NATO Science Series continues the series of books published formerly as the NATO ASI Series. The NATO Science Programme offers support for collaboration in civil science between scientists of countries of the Euro-Atlantic Partnership Council. The types of scientific meeting generally sl)pported are "Advanced Study Institutes" and "Advanced Research Workshops", although other types of meeting are supported from time to time. The NATO Science Series collects together the results of these meetings. The meetings are co-organized bij scientists from NATO countries and scientists from NATO's Partner countries - countries of the CIS and Central and Eastern Europe. Advanced Study Institutes are high-level tutorial courses offering in-depth study of latest advances in a field. Advanced Research Workshops are expert meetings aimed at critical assessment of a field, and identification of directions for future action. As a consequence of the restructuring of the NATO Science Programme in 1999, the NATO Science Series has been re-organised and there are currently Five Sub-series as noted above. Please consult the following web sites for information on previous volumes published in the Series, as well as details of earlier Sub-series. http://www.nato.int/science http://www.wkap.nl http://www.iospress.nl http://www.wtv-books.de/nato-pco.htm I -~­ '-V7 I Series II: Mathematics, Physics and Chemistry - Vol. 141 The Gravitational Constant: Generalized Gravitational Theories and Experiments edited by Venzo de Sabbata University of Bologna, Italy George T. Gillies University of Virginia, U.S.A. and Vitaly N. Melnikov Moscow University, Russia Springer Science+Business Media, LLC Proceedings of the NATO Advanced Study Institute on The Gravitational Constant: Generalized Gravitational Theories and Experiments Erice, Italy April3Q-May 10, 2003 A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-1-4020-1956-2 ISBN 978-1-4020-2242-5 (eBook) DOI 10.1007/978-1-4020-2242-5 Published by Kluwer Academic Publishers, P.O. Box 17, 3300 M Dordrecht, The Netherlands. Sold and distributed in North, Central and South America by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers, P.O. Box 322, 3300 AH Dordrecht, The Netherlands. Printed on acid-free paper All Rights Reserved © 2004 Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2004 Softcover reprint of the hardcover 1st edition 2004 No part of this work 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, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. CONTENTS Preface ..................................................... vii Welcome ...................................................... ix Memorial day: Peter G. Bergmann ............................ xiii Screening and Absorption of Gravitation in Pre-Relativistic and Relativistic Theories .................... 1 Horst-Heino von Borzeszkowski, T. Chrobok and Hans-Jurgen Treder Conformal Frames and D-Dimensional Gravity ................... 39 Kirill A.Bronnikov and Vitaly N.Melnikov Graviton Exchange and the Gravitational Constant ............. 65 Michael J.Clark Some base for Quantum Gravity .. : ............................. 81 Venzo de Sabbata and Luca Ronchetti Brane-inspired models in Gravitation and Cosmology .......... 113 Dmitri Gal'tsov Experimental test of a Time-Temperature formulation of the Uncertainty Principle ................................ 139 George T.Gillies and S.W.Allison The Newtonian Gravitational Constant: Present Status and Directions for future Research .......................... 149 George T.Gillies and C.S.Unnikrishnan Toward testing the Fundamental physics by SNIa data ......... 157 Wlodzimierz Godlowski, Marek Szydlowski and Wojciech czaja Investigation of Schmutzer's Exact External spherically Symmetric Static solution for a Central Body within the framework of the 5-Dimensional Projective Unified Field theory ...................................................... 193 Alexander Gorbatsievich On exact solutions in Multidimensional Gravity with antisymmetric forms ......................................... 205 Vladimir D.Ivashchuk 50 Gravity and the discrepant G measurements ................ 233 Jean-Paul Mbelek v vi 2-component cosmological models with perfect fluid and scalar field: exact solutions ........................... 247 Vitaly N.Melnikov and V.R.Gravilov Constraints on Non-Newtonian Gravity from recent Casimir Force measurements .................................. 269 Vladimir M.Mostepanenko Searching for Scalar-Tensor Gravity with Lunar Laser Ranging ......................................... 289 Kenneth Nordtvedt Is a hypothetical Long Range Spin Interaction Observable with a Laboratory Detector? ..................... 313 Rogers C.Ritter and George T.Gillies Prospects for a Space-Based determination of G wi th an error below 1 PPM .................................... 331 Alvin J.Sanders and George T.Gillies Projective Unified Field Theory revisited and adapted to the new measured values (WMAP). New results refer to approximate static interior and exterior solution of a spherically symmetric perfect fluid sphere with applications to celestial bodies, Einstein effects with particular treatment of the perihelion shift of Mercury including the quadrupole moment of the sun ............................ 341 Ernst Schmutzer The Interface of Quantum Mechanics and Gravity .............. 381 C.S.Unnikrishnan Quaternionic Program ........................................ 395 Alexander P.Yefremov Subject Index ............................................... 411 PREFACE This XVIII Course of the International School of Gravitation and Cosmology held in Erice from April 30 to May 10, 2003, has been very successful and has provided an up-to-date understanding of the progress and current problems on the Gravitational constant both on "Generalized Gravitational Theories and Experiments" either in Laboratory with Casimir force measurements, or in space at solar system distances and in Cosmological observations. We have had a qualified participation of more than fifty ASI research-workers on different fields (theoretical and experimental physicists, astrophysicists, astronomers, cosmologists from a variety of backgrounds, mathematicians) coming from various NATO and partner NATO countries (as, for instance, Belarius, Bulgaria, France, Germany, Israel, Italy, Kyrgyzistan, Latvia, Norway, Poland, Russia, Turkey, U.K., USA) . We had lectures on different aspects of the state and prediction of unified theories of the physical interactions including gravitation as a cardinal link, on the role of experimental gravitation and observational cosmology in discriminating between them, on the problem of precise measurements and stability of fundamental physical constants in space and time, and of the gravitational constant in particular. Thus we have had timely lectures in recent advances in unified and scalar-tensor theories, theories in diverse dimensions and their observational windows, gravitational experiments in space, rotational and torsional effects in gravity, basic problems in cosmology, early universe as an arena for testing unified models; basis for Quantum Gravity, brane-inspired models in Gravitation and Cosmology. vii viii Moreover we have considered cosmological variations of G, absorption and screening in prerelativistic and relativistic theories, constraints of Non-Newtonian Gravity from the recent Casimir Force measurements. Search for scalar-tensor Gravi ty with Lunar laser ranging. Special attention has been paid to the increasing role of fundamental gravitational experiments in space, the role of basic standards and determination of cosmological parameters, prediction of 5-dimensional projective unified field theory on cosmological, astrophysical and quantum effects, long range spin interaction, space-based determination of G, interface of quantum mechanics and gravity, Quaternion program. Besides the theoretical aspect, a large part of the Course was devoted to the examination of laboratory experiments and space experiments for the measurement of big G and tests of the equivalence principle including the measurement of big G using a superconductor gravimeter. We wish to thank all the lecturers and seminar speakers who did some much time to make the School successful, and all participants for contributing to the very scientific and human atmosphere. Venzo de Sabbata (Director of the School) Erice, 1 May 2003 WELCOME Only some points before the Gillies lecture It is
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