One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity (The 2 Volumes)

718 Pages·2017·11.12 MB·English

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Published by
World Scientific Publishing Co. Pte. Ltd.
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Library of Congress Cataloging-in-Publication Data
Names: Ni, Wei-Tou, 1944– editor.
Title: One hundred years of general relativity : from genesis and empirical
foundations to gravitational waves, cosmology and quantum gravity /
editor, Wei-Tou Ni, National Tsing Hua University, Hsinchu.
Description: Singapore ; Hackensack, NJ : World Scientific, [2015] | Includes
bibliographical references.
Identifiers: LCCN 2015032705| ISBN 9789814635127 (set : alk. paper) |
ISBN 981463512X (set : alk. paper) | ISBN 9789814678483 (v.1 : alk. paper) |
ISBN 9814678481 (v.1 : alk. paper) | ISBN 9789814678490 (v.2 : alk. paper) |
ISBN 981467849X (v.2 : alk. paper)
Subjects: LCSH: General relativity (Physics)--History. | Gravitational waves. |
Cosmology. | Quantum gravity.
Classification: LCC QC173.6 .O54 2015 | DDC 530.11--dc23
LC record available at http://lccn.loc.gov/2015032705
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
The cover figure is adapted from a figure by David J. Champion (MPI for Radioastronomy).
The articles in this two-volume set were previously published in various issues of
International Journal of Modern Physics D.
Copyright © 2017 by World Scientific Publishing Co. Pte. Ltd.
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KahFee - One Hundred Years of General Relativity.indd 1 13-03-17 11:50:54 AM
May 4, 2017 9:45 b2167-foreword
Foreword
GeneralRelativity(GR)isfoundedontheobservationofMercuryperihelionpreces-
sion anomaly discoveredby Le Verrier and improved by Newcomb, the Michelson–
Morley experiment, and the precision Eo¨tvo¨s experiment. Its theoretical basis is
based on Special Relativity (previously called the restricted theory of relativity),
Einstein Equivalence Principle (EEP) and the realization that the metric is the
dynamical quantity of gravity together with the Principle of General Covariance
andthe absence ofother dynamicalquantities.The establishmentofGR in 1915is
acommunityeffortwithAlbertEinsteinclearlyplayingthe dominantrole.Forone
hundred years, its applicability through solar system to cosmology is prevailing.
If one includes the cosmological constant (proposed in 1917 by Einstein) in GR,
there have not been any fully established non-applicable places. The only possible
potential exception is the missing mass (dark matter)-deficient acceleration issue.
Darkenergy andquantumgravityareneeded inthe presenttheoreticalfoundation
of physics; however, more experimental clues are needed. The framework applica-
bility of GR is already demonstrated in theoretical inflation models with quantum
fluctuationsleadingtostructureformationwithexperimentallyobservedspectrum.
To celebrate the GR centennial, we solicit the writing of 23 chapters in these
two volumes consisting of five parts:
Part I. Genesis, Solutions and Energy.
Part II. Empirical Foundations.
Part III. Gravitational Waves.
Part IV. Cosmology.
Part V. Quantum Gravity.
Volume 1 consistsof PartI, PartII andPartIII; Volume 2 consists ofPartIV and
Part V.
In Part I, Valerie Messager and Christophe Letellier start in Chapter 1 with a
genesis of special relativity to set the stage. They rely on the original literature to
make the development clear and connected. Thanks to many thorough researches
in the last 50 years, the path to general relativity is clear. A concise exposition of
the path is presented in Chapter 2. In Chapter 3, Christian Heinicke and Friedrich
Hehl present the historical development and detailed properties of the basic and
fundamental spherical Schwarzschild and axisymmetric Kerr solutions. In Chap-
ter4,Chiang-MeiChen,JamesNesterandRoh-SungTungexpoundthe important
and useful concept of energy with its many facets and various applications.
v
May 4, 2017 9:45 b2167-foreword
vi Foreword
In Part II, the empirical foundations of GR are examined. First, the corner-
stone Einstein Equivalence Principle (EEP) is explored. Ever since about 100ps
(thetimeofelectroweakphasetransitionortheequivalent/substitute)atthequasi-
equilibrium Higgs/intermediate boson energy scale from the Big Bang (or equiva-
lent/substitute), photons and charged particles are abundant. With the premetric
formulationofelectrodynamics,weexaminethetestsofEEPviathemetric-induced
spacetime constitutive tensor density. The non-birefringence of the cosmic electro-
magnetic wave propagation in spacetime is observed to ultrahigh precision. This
constrains the spacetime constitutive tensor density to Maxwell–Lorentz (metric)
form plus a scalar (dilaton) degree of freedom and a pseudoscalar (axion) degree
of freedom to high precision. The accurate agreement of cosmic microwave back-
groundspectrum with the Planck spectrum constrainsthe fractionalchange of the
cosmic dilaton to be less than 8×10−4. The Galileo weak equivalence principle
(WEP) experiments (Eo¨tvo¨s-type experiments) constrain the fractional dilatonic
change in the solar system to be less than 10−10. Accompanying the axion degree
of freedom is the rotation of linear polarization in the cosmic propagation of elec-
tromagnetic waves called cosmic polarization rotation (CPR). Sperello di Serego
Alighieri reviews the constraints from radio galaxy observations and CMB polar-
izationobservationsto giveageneralconstraintof0.02radfor the mean(uniform)
CPR and also a constraint of 0.02 rad for the CPR fluctuations. In many inflation
models dilatons and axions play important roles; these investigations are crucial
to give clues or constraints on the models. Frequency and time are the most pre-
cisemetrologicalquantities.Theirusesingravityexperimentsareunavoidable.The
use of GR in time synchronization and in GPS, GLONNESS, Galileo and Beidou
becomes a folk talk. There aretwo goodwaysto compareprecisionclocks:(i) fiber
links;(ii)spaceopticallinksusinglaserranging.E´tienneSamainexpoundsthespace
optical link approach and addresses the laser ranging missions T2L2 (Time trans-
fer by Laser link), LRO (Lunar Reconnaissance Orbiter) and LTT (Laser Time
Transfer) together with future space mission proposals for fundamental physics,
solarsystemscience/navigationinwhichlaserlinksareofprimeimportance.Solar-
systemobservationprovidesthe originalimpetus and the first confirmationof GR.
Chapter 8 summarizes the progress of classical solar system tests and explores its
potential in the future. Improvement of three or more orders of magnitude is still
possible.
Perhaps the most dramatic development in testing relativistic gravity and in
improvingthedynamicalfoundationsofgeneralrelativityisthediscoveryandobser-
vationofpulsars,binarypulsars,millisecondpulsarsanddoublepulsarssince1967,
1974, 1982 and 2003 respectively. Richard Manchester reviews the pulsar observa-
tioninitsrelationwithgravityinChapter9withabriefintroductiontobasicpulsar
properties and pulsar timing. He presents a rather thorough account of dynamical
testsofGRandthe strongequivalenceprinciple togetherwith alucidbutin-depth
accountofGW detectionusing pulsar timing arrays(PTAs). See frontcoverfor an
illustrative schematic of a PTA.
May 4, 2017 9:45 b2167-foreword
Foreword vii
In 1916 Einstein predicted gravitational waves (GWs) in GR almost immedi-
ately after his founding of it. The existence of gravitational waves is the direct
consequence of general relativity and unavoidable consequences of all relativistic
gravitytheories with finite velocity of propagation.Their importance in GR is like
that electromagnetic waves in Maxwell–Lorentz theory of electromagnetism. Ein-
stein’s general relativity and relativistic gravity theories predict the existence of
gravitational waves. Gravitational waves propagate in spacetime forming ripples
of spacetime geometry. In the introductory chapter of Part III, Kazuaki Kuroda,
Wei-Ping Pan and I review and summarize the complete GW spectrum, the meth-
ods of detection, and the detection sensitivities in various frequency bands with
a brief introduction to GW sources. At the time Einstein predicted GWs in GR,
heestimatedthatGWs wereexperimentallynotdetectabledueto feeblestrengths.
However,thankstoonehundredyearsofdevelopmentofexperimentalmethodsand
technology together with the discovery of various astrophysical compact objects
and cosmological sources, GWs are now on the verge of detection in three fre-
quency bands. The very low frequency band (10fHz–300pHz) GWs are on the
vergeofdetectionbythe PTAs;RichardManchestercoversthis partinhischapter
on pulsars and gravity in Part II. As mentioned in Chapter 10, the observation of
PTAs has already constrained the isotropic GW background to a level excluding
most current models of supermassive black hole formation. This is a strong signal
that PTA observation is on the verge of detecting GWs. The high frequency band
(10Hz–100kHz) GWs are on the verge of detection by ground-based interferome-
ters; Kazuaki Kuroda addresses the detection methods and the sources in the sec-
ondchapterofPartIII.Theextremelylow(Hubble)frequencyband(1aHz–10fHz)
GWs may also be onthe vergeof detection by CMB polarizationobservations;the
present status is briefly reviewed in the introduction chapter of Part III. The low
frequency band (100nHz–100mHz) and the middle frequency band detections will
have the greatest S/N ratios according to the present expectation. We review the
sources,goalsensitivities, various missionproposalstogether with the current sup-
porting activities in the third chapter of Part III. The GW quadrupole radiation
formula has already been verified by the binary pulsar observations. In the next
hundred years we will see great discoveries and immense focused activities toward
the establishment and flourish of GW astronomy and GW cosmology.GW physics
and GW astronomy will become a precision discipline in the coming century.
The development of cosmologyis most dramatic during the last hundred years.
FromKapteynuniversein1915ofobserveddiskstarsystemof10kpcdiameterand
2kpcthicknesswiththeSunnearitscentertofull-fledgedprecisioncosmologynow
is monumentalinthe humanhistory.It is fortunatethat the developmentofobser-
vational cosmology has GR theory as a theoretical basis and goes hand-in-hand
with the developmentof generalrelativity.This is fortunate both for observational
cosmology and for GR. Using the CosmologicalPrinciple Einstein looked into cos-
mological solutions in GR in 1917. The fast development of observational distance
ladder around that time soon extends the reach of astronomy to modern cosmos.
May 4, 2017 9:45 b2167-foreword
viii Foreword
Studies in the fundamental issues on the origins of cosmos lead to anthropological
principle, cosmic inflation, and cosmic landscape scenarios.The cosmos is believed
to be open in (extended beyond) the Hubble distance scale. Part III consists of
seven chapters: Martin Bucher and I present some introductory remarks with a
discussion of missing mass-deficient acceleration issue in the first chapter; Marc
Davis reviews the observation and evolution of cosmic structure; Martin Bucher
give a rather comprehensive exposition of the physics (almost on every aspect of
cosmology)of CMB;XiangcunMeng, YanGao andZhanwenHanreview the SNIa
as a standardizable distance candle, its nature, its progenitors and its role in the
cosmology together with related current issues; Toshifumi Futamase on the gravi-
tationallensingincosmology;K.SatoandJuni’ichioncosmicinflationwithabrief
historicalexposition on the development in Japanand Russia;David Chernoff and
Henry Tye on inflation and cosmic strings from the point of view of string theory.
The quest for a satisfactory quantum description of gravity began very early.
Einstein thought that quantum effects must modify general relativity in his first
paper on GWs in 1916. Klein argued that the quantum theory must ultimately
modify the roleof spatiotemporalconcepts in fundamental physicsin 1927.PartV
onQuantumGravityconsistsof4chapters.Chapter20givesabird’s-eyesurveyon
the development of fundamental ideas of quantum gravity together with possible
observations of quantum gravitational effects in the foreseeable future. The classi-
cal age (1958–1969;according to the chronologicalclassification of Rovelli) started
withADMcanonicalformalismandconcludedwithDeWitt–Wheeler equationand
DeWitt’s derivation of Feynman rules for perturbative GR. In the middle ages
(1970–1983),thediscoveryofblackholethermodynamicsandHawking’sderivation
ofblack hole radiationradically affectedour understanding ofgeneralrelativity.In
the renaissance period (1984–1994), there are two influential developments. From
thecovariantapproach,attemptstogetridofinfinitiesmergeintostringtheory.The
use of strings and branes extends the theoretical framework of quantum field the-
ory. From the canonical approach, background-independent loop quantum gravity
emerged20yearsafterDeWitt–Wheelerequation.InChapter21,RichardWoodard
starts with experiences of two personal academic careers through the classical and
middle ages, advocates that the cosmological data from the epoch of primordial
inflation is catalyzing the maturation of quantum gravity from speculation into a
hard science, explains why quantum gravitational effects from primordial inflation
are observable, reviews what has been done in perturbative quantum gravity, tells
uswhatthefutureholdsboththeoreticallyandobservationally,anddiscusseswhat
thistellsusaboutquantumgravity.InChapter22,StevenCarlipreviewsthediscov-
ery of black hole thermodynamics and summarizes the many independent ways of
obtaining the thermodynamic and statistical mechanical properties of black holes.
This has offered us some early hints about the nature of quantum gravity. Steven
then describes some of the remainingpuzzles, including the nature of the quantum
microstates, the problem of universality, and the information loss paradox. In the
last chapter, Dah-Wei Chiou gives us a rather self-contained introductory review
May 4, 2017 9:45 b2167-foreword
Foreword ix
on loop quantum gravity — a background-independent nonperturbative approach
to a consistent quantum theory of gravity placing emphasis on the fundamental
ideas and their significance. The review presents the canonical formulation of loop
quantum gravity as the central topic and covers briefly the spin foam theory, the
relation to black hole thermodynamics and the loop quantum cosmology with cur-
rent directions and open issues summarized.
Although we do not yet have a consistent calculable quantum gravity theory
which has a good degree of completeness like quantum electrodynamics or quan-
tumchromodynamics,theeffortstofindonealreadyledtotheconsistentrenormal-
ization of the gauge theory in 1960’s. The new development since 1980’s together
withmoreunderstandingandfurtherdevelopmentofperturbationtheorymaygive
cluesto a consistenttheory.During these endeavors,the questfor a well-developed
quantum gravity phenomenology including the quest to find a correct inflationary
(or non-inflationary) scenario may play a significant role.
Thehopeisthatwewillhaveonewithinageneration.This bookiswrittenand
assembled for graduate students and general scientific-oriented readers alike. Each
chapter is basically a review article. The five Parts are interconnected. Different
combinationscanbedesignedforspecialtopicsforgraduatestudentsandadvanced
undergraduates. For example, following combinations are suitable for each topic
named:
(i) Basics (Selected Topics in GR): Part I, Chapters 8, 9, 10, 13, 20;
(ii) EmpiricalFoundations(EmpiricalFoundationsofRelativisticGravity):Chap-
ter 2, Part II, Chapters 10, 11, 13, 14, 16, 20;
(iii) Gravitational Waves: Chapters 2, 9, Part III, Chapters 15, 18, 19;
(iv) Cosmology:Chapters 5, 6, 10, 12, Part IV, Chapter 20;
(v) Quantum Gravity: Chapters 3, 4, 10, 18, 19, Part V.
There can be various other combinations too.
We are grateful to all contributors for agreeing to write comprehensive reviews
to make this publication possible. We would also like to thank all the referees for
their valuable comments and suggestions: Martin Bucher, Stephen Carlip, Dah-
Wei Chiou, Sperello di SeregoAlighieri, Angela Di Virgilio,John Eldridge,Jeremy
Gray, Friedrich Hehl, Jim Hough, Ekaterina Koptelova, Ettore Majorana, James
Nester,UlrichSchreiber,AlexeiStarobinsky,DavidTanner,RichardWoodard,An-
Ming Wu, Masahide Yamaguchi. We thank the World Scientific staff, especially
Dr.K.K.PhuaandKahFeeNgfortheirgeneroussupportincompletingthebook.
We dedicate this two-volume GR centennial book to the founders of GR and
variouscommunitieswhohavecontributedtothisdramaticcenturyofdevelopment
and applications of GR.
Wei-Tou Ni
November, 2015
May 4, 2017 9:45 b2167-foreword
x Foreword
Note Added in Proof
After the foreword was written, LIGO Scientific and Virgo Collaborations
announcedinFebruary2016andinJune2016the firstdirectdetectionsofgravita-
tionalwaves(GWs)byLIGOHanfordandLIGOLivingstondetectorsinSeptember
2015andinDecember 2015.With the LIGO discoveryannouncements,twoimpor-
tantthingsareverified:(i)GWsaredirectlydetectedinthesolar-system;(ii)Black
holes (BHs), binary BHs and BH coalescences are discovered and measured exper-
imentally and directly with the distances reached more than 1 billion light years.
These discoveries constitute the best celebration of the centennial of the genesis of
generalrelativity. We refer the readers to Refs. 1 and 2 for the discovery and Refs.
3 and 4 for a brief history of gravitationalwave research.
A web page will be set up for updates of the reviews of these two volumes.
Please see http://astrod.wikispaces.com/ for announcement.
References
1. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Observation of gravi-
tational waves from a binary black hole merger, Phys. Rev. Lett. 116 (2016) 061102.
2. B. P. Abbott et al. (LIGO Scientificand Virgo Collaborations), GW151226: Observa-
tion of gravitational waves from a 22-solar-mass binary black hole coalescence, Phys.
Rev. Lett. 116 (2016) 241103.
3. J. L.Cervantes-Cota, S. Galindo-Uribarri and G.F. Smoot, A brief history of gravita-
tional waves, Universe 2(22) (2016) 09400.
4. C.-M. Chen, J. M. Nester, W.-T. Ni, A brief history of gravitational wave research,
Chinese Journal of Physics 55 (2017) 142–169.