Exploring the Invisible Universe : From Black Holes to Superstrings

488 Pages·2015·20.96 MB·English

by  Belal E Baaquie

EXPLORING THE INVISIBLE
U N I V E R S E
From Black Holes to Superstrings
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EXPLORING THE INVISIBLE
U N I V E R S E
From Black Holes to Superstrings
Belal E Baaquie
Frederick H Willeboordse
National University of Singapore
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI
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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
Library of Congress Cataloging-in-Publication Data
Baaquie, B. E., author.
Exploring the invisible universe : from black holes to superstrings / Belal E. Baaquie (National University
of Singapore, Singapore), Frederick H. Willeboordse (National University of Singapore).
pages cm
Includes bibliographical references and index.
ISBN 978-9814618670 (hardcover : alk. paper)
1. Physics--Popular works. I. Willeboordse, Frederick H., author. II. Title.
QC24.5.B33 2015
523.1--dc23
2014032724
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
The cover image is an adaptation of two images.
Credit of the original images goes to NASA and ESO/MPE/Marc Schartmann.
Copyright © 2015 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
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In-house Editor: Ng Kah Fee
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Email: [email protected]
Printed in Singapore
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Preface
TheUniversesurroundsandpermeatesusinallpossibleways.Wegoaboutourdaily
lives concentrating mainly on matters that directly affect us, and for good reasons
since therelentlesschallengesforsurvivalhaveto be constantlysurmounted.Those
of us who look upon the Universe only as it directly appears to us — and from the
perspectiveofoursurvivalneeds—areonlyapprehendingthevisiblemanifestation
andappearanceoftheUniverse.Fromthispointofview,wewillnotbeabletograsp
theunderlyinguniversallawsofNatureandneitherwillweencounterthemysterious
and invisible realms of the Universe.
The invisible and unseen domains and phenomena of the Universe are beyond
our direct perception and do not appear in the manifest Universe. However, if we
turnourattentionandthinkingtowardstheinvisibleUniverse,towardstheunseen,
imperceptible and hidden realms of the Universe, then these realms will become
real and comprehensible to us.
As the title of the book indicates, we explore the invisible Universe, and
especially those hidden and imperceptible phenomena that can never, in principle,
be directly perceived by our five senses. The guiding lights for making a scientific
journey to these invisible domains are our conceptual and mathematical notions
of the underlying universal laws of Nature — which in turn are founded on
experimental and observational results.
The laws of Nature, and in particular, the laws of Physics, are our main theo-
retical instruments in exploring and grasping the invisible realms and phenomena
oftheUniverse.Itisforthisreasonthatweexpendconsiderableeffortindiscussing
and elaborating the theoretical edifice of Physics. Except for the first chapter on
fields, the analysis is carried out in the context of a specific problem so that the
reader’s attention remains grounded on phenomena.
Black holes are astrophysical objects that, in principle, cannot be observed
directly. The flow of time ceases on the boundary of the black hole: this is just
one of the mysterious properties of black holes that are difficult to comprehend or
accept. We explore the properties of black holes from a theoretical point of view
and then show how our concepts lead to the interpretations of observations that
indirectly point to the remarkable properties of these otherwise invisible objects.
v
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vi Exploring the Invisible Universe
In journeying from black holes to superstrings, we encounter many unexpected
properties of our Universe, such as the fact that gravity is geometry, and that the
Universe at the cosmic scale comprises almost entirely of dark energy and dark
matter — entities that are unseen and cannot be directly perceived. The coming
into existence of the Universe throws light on the eternal question of “how it all
came to be?” and unlocks many of the mysteries relating to the formation and
evolution of galaxies,stars and planets.
On a journey inwards, to the microscopic essence of materiality, we peel away
layers upon layers of phenomena to finally encounter the point-like constituents of
matter, namely the quarks and leptons as well as the four fundamental forces. We
are then faced with the enigma and paradox that the constituents of the nuclei of
all atoms, namely the quarks, are permanently confined inside the nucleus.
A further journey inwards — to ultra-microscopic realms — leads us to the
unveiling of another hidden entity, namely the superstring. Superstrings exist in
higher dimensions of spacetime that are hidden and invisible but have observable
and tell-tale signals in our four dimensional Universe. At the frontiers of Physics,
superstrings provide a consistent mathematical theory that purports to show that
allofphysicalreality—fromquarkstoquasars,andincludingspacetimeitself—is
the manifestation of the hidden and unseen realm of the superstring. The Universe
that we observe and live in is a vanishingly small reflection of the truly immense
and colossalhigher dimensional Universe that superstrings inhabit.
With the complete superstring unification and synthesis of all aspects of our
invisible, mysterious and enigmatic Universe, we bring our book to a closure.
Witnessing, observing and marveling at the invisible, subtle and intriguing
Universe that we live in — full of mysteries,surprises and enigmas — by using our
conceptualandmathematicalconstructsisoneofthegreatabilitiesofmankind.To
develop the possibility of this theoreticalconsciousness into reality is, of course,up
to every individual. It is our hope that this book will demonstrate how fascinating
it is to unlock some of the mysteries of the invisible Universe, and that it will lead
the reader, especially the younger generation, to continue on the path of further
exploring the invisible Universe.
Belal E. Baaquie and Frederick H. Willeboordse
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Acknowledgments
The writing of this book has been a long project, going through many phases. We
wouldliketo recordourdeepappreciationto ShihChoongFongfor encouragingus
toembarkonthisprojectandwewereinspiredbyhisreadingofscience—supported
bymathematicsandexperiments—thatisdrivenbyintuitionandphysicalinsights.
Wewouldliketothankourcolleaguesfornumerouscommentsandextensivehelp
in the preparation of this book. We thank Phua Kok Khoo for his warm support
and encouragement. Without pretense of completeness and with apologies for the
manyomitted,weexpressourgratitudetoThomasOsipowicz,PhilChan,Kenneth
Hong, Ngee Pong Chang, Munawar Karim, Kerson Huang, Tan Meng Chwan, Bal
Menon, Xin Du and a special thanks to Edward Teo for many fruitful discussions
ongravity.They havebeenindefatigableinterlocutors,alwayswilling togenerously
share their valuable knowledge of Physics that has greatly helped to clarify many
concepts. We are indebted to Rafi Rashid for a careful reading of the draft; his
prescientobservationsandincisivecommentsbroughtmanyideasintoasharpfocus
and are greatly appreciated. We would like to thank Ng Kah Fee for his valuable
contributions in the publication of this book.
Oneofus(BEB)wouldliketoacknowledgediscussionswithlateJamalN.Islam,
rangingovermanyyears,onEinstein’stheoryofgravity;heclarifiedtheideaofhow
localcoordinatepatchesdefine spacetime curvature,whichis achievedinone single
strokebydirectlyworkingwiththemetrictensor.Heexplainedindetailtherotating
gravitationalfieldsthatconstitutetheKerrsolutionanditsremarkablysimpleform
when written in the Schild coordinates. My thanks to JayantV. Narlikar for many
discussions on cosmology, inflation and the early Universe. Thanks are also due to
ZahurAhmedandKamalZ.Islamfortheirencouragementandsupport.Andlastly,
mylatefatherMuhammadAbdulBaaquie,whowasaGoldMedalistinPhysics,has
beenalifelonginspirationtodoscienceandnowordscanexpressmyindebtedness
to him.
We would like to thank our families for their unflagging and constant support
for an undertaking that has taken many years to complete.
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Contents
Preface v
Acknowledgments vii
1. Synopsis 1
2. Fields 5
2.1 The Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 What is a Field? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Pressure Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1 Propagating pressure field . . . . . . . . . . . . . . . . . . 9
2.4 Electric and Magnetic Fields . . . . . . . . . . . . . . . . . . . . . 11
2.4.1 Magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5 The Electromagnetic Field . . . . . . . . . . . . . . . . . . . . . . 14
2.5.1 Electromagnetic waves . . . . . . . . . . . . . . . . . . . . 15
2.5.2 Maxwell’s field equations . . . . . . . . . . . . . . . . . . 16
2.6 Do Fields Need a Medium? . . . . . . . . . . . . . . . . . . . . . . 18
2.6.1 Action at a distance . . . . . . . . . . . . . . . . . . . . . 19
2.7 Lorentz Transformations . . . . . . . . . . . . . . . . . . . . . . . 20
2.8 Gravitational Field . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.9 Quantum Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.9.1 Feynman diagrams . . . . . . . . . . . . . . . . . . . . . . 26
2.10 Quantum Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.10.1 Casimir effect and Lamb shift . . . . . . . . . . . . . . . . 29
2.11 Unification of Particles and Interactions. . . . . . . . . . . . . . . 31
2.12 The Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3. The Geometry of Space 35
3.1 The Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Is Space Curved? . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
ix