Breakdown of Einstein's Equivalence Principle PDF
Preview Breakdown of Einstein's Equivalence Principle
B1948 Governing Asia TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk BB11994488__11--AAookkii..iinndddd 66 99//2222//22001144 44::2244::5577 PPMM 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. BREAKDOWN OF EINSTEIN’S EQUIVALENCE PRINCIPLE Copyright © 2023 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. 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ISBN 978-981-125-358-4 (hardcover) ISBN 978-981-125-359-1 (ebook for institutions) ISBN 978-981-125-360-7 (ebook for individuals) For any available supplementary material, please visit https://www.worldscientific.com/worldscibooks/10.1142/12759#t=suppl Typeset by Stallion Press Email: [email protected] Printed in Singapore YYoonnggQQii -- 1122775599 -- BBrreeaakkddoowwnn ooff EEiinnsstteeiinn EEqquuiivvaalleennccee PPrriinncciippllee..iinndddd 11 99//99//22002222 44::4466::0088 ppmm September12,2022 11:21 BreakdownofEintein’sEquivalencePrinciple-9inx6in b4567-fm pagev The editor dedicates his own contributions to the book to his wife, Natalia, for her loving support and patience. v B1948 Governing Asia TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk BB11994488__11--AAookkii..iinndddd 66 99//2222//22001144 44::2244::5577 PPMM September12,2022 11:21 BreakdownofEintein’sEquivalencePrinciple-9inx6in b4567-fm pagevii (cid:2)c 2023 World Scientific Publishing Company https://doi.org/10.1142/9789811253591 fmatter Preface From a historical point of view, the Equivalence Principle was first clearly formulated by Galileo Galilei (see Fig. 1) as the independence of a body’s accelerationin the Earth’s gravitational field on the body’s mass. Accord- ing to the popular legend, he dropped cannonballs of different sizes from the Leaning Tower of Pisa and found that they hit the groundat the same time. This wasapproximately400–450yearsago. Usingmodernlanguage, Galilei established the equivalence of inertial, m , and gravitational, m , i g masses with the accuracy about |m −m |/m ≤ 2×10−2. Much less is i g i knownabouthispredecessor,GreekphilosopherJohnPhiloponus,whoper- formedlesssophisticatedbutsimilarexperimentsapproximately1500years ago. Newtonian physics accepted Galileo’s Equivalence Principle and the first successful theory of gravity, created by Isaac Newton, explained the mainfeaturesofourplanetarysystem,includingtheempiricalKeplerlaws. In 1916, Albert Einstein (see Fig. 2) published his theory of General Relativity, which is based on Einstein’s Equivalence Principle. Before he elaborated General Relativity, in 1911, he had formulated the Equivalence Principle in the following way. Einstein considered two reference frames, K and K(cid:2), where K was placed in a uniform gravitational field. K(cid:2) was not in a gravitational field, but it was uniformly accelerated. He wrote: “As long as we restrictourselvesto pure mechanical processesinthe realm where Newton’s mechanics holds sway, we are certain of the equivalence of the systems K and K(cid:2). But this view of ours will not have any deeper significance unless the systems K and K(cid:2) are equivalent with respect to all physical processes, that is, unless the laws of nature with respect to K are in entire agreement with those with respect to K(cid:2). By assuming this to be so, we arrive at a principle which, if it is really true, has great heuristic importance. By theoretical considerationof processes which take vii September12,2022 11:21 BreakdownofEintein’sEquivalencePrinciple-9inx6in b4567-fm pageviii viii Preface Fig.1. GalileoGalilei(1564–1642) (drawingofNataliaLebed). Fig.2. AlbertEinstein(1879–1955) (drawingofNataliaLebed). September12,2022 11:21 BreakdownofEintein’sEquivalencePrinciple-9inx6in b4567-fm pageix Preface ix placerelativelytoasystemofreferencewithuniformacceleration,weobtain information as to the career of processes in a homogeneous gravitational field.” Wenotethatmodernphysicsdistinguishesbetweenthreevariantsofthe Equivalence Principle: weak Equivalence Principle, Einstein’s Equivalence Principle, and strong Equivalence Principle. The weak Equivalence Prin- ciple is equivalent to the so-called universality of a free fall and is related to the original Galileo experiments. This variant has been confirmed with greataccuracyfor ordinarysolid-state bodies. In the recentspace mission, MICROSCOPEoftheFrenchspaceagencyCNES,theexperimentalequip- mentconsistedoftwocylindricalshells: largercylindricalshellandsmaller one. The smaller shell, made of platinum and rhodium, was placed inside the largerone, made of titanium andaluminum. In more than 2 years and 5 months, physicists on the Earth observed a relative motion of the cylin- ders and found that they were accelerated with the same quantity with accuracy better than |m −m |/m ≤ 10−16. We can say that the Equiv- i g i alence Principle is one of the best established laws in physics. Moreover, twomorespacemissionsarecurrentlyintheirdesignphases: SatelliteTest of the Equivalence Principle (STEP) and Galileo Galilei (GG). The STEP mission is being developed by an international team ofcollaboratorsunder theleadershipofStanfordUniversity,whereastheGGisanItalianproject. The missions would be operated in a similar way as the MICROSCOPE experiment. To improve the accuracyof measurements, the STEP mission woulduseuptofourpairsofcylindersinsteadofjustonepair. Inaddition, a tank of liquid helium would keep the temperature of the cylinders con- stant. The shell masses would also be surrounded with a superconducting shell. According to theoretical preliminary estimates, the STEP mission would allow to confirm or to disconfirm the Equivalence Principle with accuracy |m −m |/m ∼10−18. The peculiarity of the GG space mission i g i is that the satellite would quickly spin about its main axis, which provides the accuracy of the measurements of about |m −m |/m ∼10−17. i g i It is easy to understand that a violation of the weak (i.e. Galileo’s) Equivalence Principle means that Einstein’s Equivalence Principle is also violated, but the opposite statement is not true. In this book, we consider such unexpected special situations, where Einstein’s Equivalence Principle or weak Equivalence Principle are violated from theoretical point of view and briefly discuss the possible experimental methods to detect such viola- tions.
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