100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

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208 C. M. Willated with dynamical fields that couple to matter directly are also not metrictheories.2.1. Tests of the weak equivalence principleTo test the weak equivalence principle, one compares the acceleration oftwo laboratory-sized bodies of different composition in an external gravitationalfield. A measurement or limit on the fractional difference in accelerationbetween two bodies yields a quantity η ≡ 2|a 1 − a 2 |/|a 1 + a 2 |, calledthe “Eötvös ratio”, named in honor of Baron von Eötvös, the Hungarianphysicist whose experiments carried out with torsion balances at the endof the 19th century were the first high-precision tests of WEP 5 . Later classicexperiments by Dicke and Braginsky 6,7 improved the bounds by severalorders of magnitude. Additional experiments were carried out during the1980s as part of a search for a putative “fifth force”, that was motivated inpart by a reanalysis of Eötvös’ original data (the range of bounds achievedduring that period is shown schematically in the region labeled “fifth force”in Figure 1).In a torsion balance, two bodies of different composition are suspendedat the ends of a rod that is supported by a fine wire or fibre. One then looksfor a difference in the horizontal accelerations of the two bodies as revealedby a slight rotation of the rod. The source of the horizontal gravitationalforce could be the Sun, a large mass in or near the laboratory, or, as Eötvösrecognized, the Earth itself.The best limit on η currently comes from the “Eöt-Wash” experimentscarried out at the University of Washington, which used a sophisticatedtorsion balance tray to compare the accelerations of bodies of different compositiontoward the Earth, the Sun and the galaxy 8 . Another strong boundcomes from Lunar laser ranging (LLR), which checks the equality of freefall of the Earth and Moon toward the Sun 9 . The results from laboratoryand LLR experiments are:η Eöt−Wash < 4 × 10 −13 , η LLR < 5 × 10 −13 . (1)In fact, by using laboratory materials whose composition mimics that ofthe Earth and Moon, the Eöt-Wash experiments 8 permit one to infer anunambiguous bound from Lunar laser ranging on the universality of accelerationof gravitational binding energy at the level of 1.3 × 10 −3 (test ofthe Nordtvedt effect – see Sec. 3.2 and Table 1.)In the future, the Apache Point Observatory for Lunar Laser-rangingOperation (APOLLO) project, a joint effort by researchers from the
Was Einstein Right? 20910 -810 -9EötvösRennerFree-fallη10 -1010 -11PrincetonBoulderFifth-forcesearchesEöt-Wash10 -12MoscowLLREöt-Wash10 -13η= a 1 -a 2(a 1+a 2)/210 -14 YEAR OF EXPERIMENT19801970196019401920190019902000Fig. 1. Selected tests of the Weak Equivalence Principle, showing bounds on the fractionaldifference in acceleration of different materials or bodies. “Free-fall” and Eöt-Washexperiments, along with numerous others between 1986 and 1990, were originally performedto search for a fifth force. The dark line and the shading below it show evolvingbounds on WEP for the Earth and the Moon from Lunar laser ranging (LLR).Universities of Washington, Seattle, and California, San Diego, plans touse enhanced laser and telescope technology, together with a good, highaltitudesite in New Mexico, to improve the Lunar laser-ranging bound byas much as an order of magnitude 10 .High-precision WEP experiments, can test superstring inspired modelsof scalar-tensor gravity, or theories with varying fundamental constants inwhich weak violations of WEP can occur via non-metric couplings. Theproject MICROSCOPE, designed to test WEP to a part in 10 15 has beenapproved by the French space agency CNES for a possible 2008 launch. A
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Published byWorld Scientific Publis
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viA. Ashtekarof space-time that eme
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viiiA. AshtekarGravitational waves
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xA. Ashtekarhappy, schizophrenic at
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xviContents9. Receiving Gravitation
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4 J. Stachel(2) the change over tim
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6 J. StachelFig. 2respectively. Fur
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8 J. Stachelof string theory, M-the
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10 J. StachelLogically, it would se
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12 J. Stachelupon by no (net) exter
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14 J. Stachelof the incompatibility
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16 J. Stachelis an important differ
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18 J. Stachelbetween physical conce
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20 J. Stachel10. Four-Dimensional F
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22 J. Stachelderivative of the metr
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24 J. Stachel(b) General relativity
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26 J. Stachelfour-dimensional analo
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28 J. Stachelply the lessons learne
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30 J. Stachelmanifold appropriate f
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32 J. Stachelwhich merely defines t
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34 J. Stacheldynamical process as a
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36 J. Stachel9. J. Stachel, Special
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Part IIEinstein’s UniverseRamific
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40 H. Nicolai• Higher dimensions
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42 H. Nicolaiadvance, and possibly
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44 H. NicolaiBianchi identities are
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46 H. NicolaiIt does not appear pos
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48 H. NicolaiThe other SL(2, R), of
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50 H. Nicolai3.1. BKL dynamics and
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52 H. Nicolaidegrees of freedom, th
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54 H. Nicolaiin the valley. The Ham
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56 H. NicolaiThe main feature of th
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58 H. Nicolai4. Basics of Kac Moody
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60 H. Nicolaifor indefinite A. It i
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62 H. NicolaiThe level l = 0 sector
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64 H. NicolaiConsequently, the repr
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66 H. Nicolaiwhere the abelian part
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68 H. Nicolaiconstant momenta Π yi
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70 H. Nicolaiσ-model side is suppo
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72 H. NicolaiReferences1. H.A. Buch
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74 H. Nicolai44. G. Neugebauer and
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CHAPTER 3THE NATURE OF SPACETIME SI
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78 A. D. Rendallspacetime to define
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80 A. D. RendallOne of the most imp
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82 A. D. Rendalltheorems was an elu
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84 A. D. Rendallsymmetric solution
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86 A. D. Rendallback into a curvatu
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88 A. D. Rendallspace and there are
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The Nature of Spacetime Singulariti
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CHAPTER 4BLACK HOLES - AN INTRODUCT
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Black Holes 95It follows that ˙v d
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Black Holes 973221100-1-1-2-200-5-3
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Black Holes 99calculation of the de
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Black Holes 101family of null geode
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Black Holes 105(3) Ω is positive o
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Black Holes 107In dimension 3 + 1 t
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Black Holes 109A fundamental theore
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Black Holes 111(4) The Kerr black h
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Black Holes 113˚g ab =˚g ab (x a
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Black Holes 115It is a folklore the
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Black Holes 117⃗x 4 = −⃗x 3
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Black Holes 119Work partially suppo
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Black Holes 121totically flat space
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Black Holes 12376. R.C. Myers and M
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The Physical Basis of Black Hole As
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Probing Space-Time Through Numerica
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Probing Space-Time Through Numerica
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Page 193 and 194: CHAPTER 7UNDERSTANDING OUR UNIVERSE
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Page 223 and 224: CHAPTER 8WAS EINSTEIN RIGHT? TESTIN
Page 225: Was Einstein Right? 207We begin in
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Page 231 and 232: Was Einstein Right? 213The SME and
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Page 235 and 236: Was Einstein Right? 217of VLBI data
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Page 243 and 244: Was Einstein Right? 22510. J. G. Wi
Page 245 and 246: Was Einstein Right? 22761. C. M. Wi
Page 247 and 248: Receiving Gravitational Waves 229th
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Page 251 and 252: Receiving Gravitational Waves 233Th
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Page 257 and 258: Receiving Gravitational Waves 239th
Page 259 and 260: Receiving Gravitational Waves 241to
Page 261 and 262: Receiving Gravitational Waves 243In
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Page 265 and 266: Receiving Gravitational Waves 247a
Page 267 and 268: Receiving Gravitational Waves 249ab
Page 269 and 270: Receiving Gravitational Waves 251Fi
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Page 275 and 276: CHAPTER 10RELATIVITY IN THE GLOBAL
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Relativity in the Global Positionin
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Part IIIBeyond EinsteinUnifying Gen
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CHAPTER 11SPACETIME IN SEMICLASSICA
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Spacetime in Semiclassical Gravity
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CHAPTER 12SPACE TIME IN STRING THEO
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Space Time in String Theory 313limi
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Space Time in String Theory 315luti
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Space Time in String Theory 317In s
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Space Time in String Theory 319of t
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Space Time in String Theory 321an o
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Space Time in String Theory 323arbi
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Space Time in String Theory 325an e
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Space Time in String Theory 327in a
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Space Time in String Theory 329doma
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Space Time in String Theory 331a tu
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Space Time in String Theory 333bran
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Space Time in String Theory 335is a
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Space Time in String Theory 337thes
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Space Time in String Theory 339The
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Space Time in String Theory 341gene
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Space Time in String Theory 343are
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Space Time in String Theory 345tion
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Space Time in String Theory 34723.
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Space Time in String Theory 34955.
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Gravity, Geometry and the Quantum 3
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£¢¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡
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Loop Quantum Cosmology 383inflation
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Loop Quantum Cosmology 385gravitati
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Loop Quantum Cosmology 387Secondly,
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Loop Quantum Cosmology 389sically d
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Loop Quantum Cosmology 391states an
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Loop Quantum Cosmology 393represent
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Loop Quantum Cosmology 3954.2.1. Di
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Loop Quantum Cosmology 397question
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Loop Quantum Cosmology 399exist. Th
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Loop Quantum Cosmology 401in the ex
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Loop Quantum Cosmology 403λ max or
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Loop Quantum Cosmology 405This happ
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Loop Quantum Cosmology 407Loop quan
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Loop Quantum Cosmology 409to obtain
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Loop Quantum Cosmology 411familiar
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Loop Quantum Cosmology 41334. M. Bo
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CHAPTER 15CONSISTENT DISCRETE SPACE
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Consistent Discrete Space-Time 417v
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Consistent Discrete Space-Time 419I
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Consistent Discrete Space-Time 421a
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Consistent Discrete Space-Time 423F
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Consistent Discrete Space-Time 4250
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Consistent Discrete Space-Time 4272
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Consistent Discrete Space-Time 429i
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Consistent Discrete Space-Time 431a
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Consistent Discrete Space-Time 433n
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Consistent Discrete Space-Time 435t
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Consistent Discrete Space-Time 437w
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Consistent Discrete Space-Time 439f
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Consistent Discrete Space-Time 441(
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Consistent Discrete Space-Time 443R
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CHAPTER 16CAUSAL SETS ANDTHE DEEP S
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Causal Sets and the Deep Structure
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CHAPTER 17THE TWISTOR APPROACH TOSP
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The Twistor Approach to Space-Time
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INDEXσ models, 57, 65, 693+1 formu
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Index 509inflation, 383, 385-387, 4
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