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

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218 C. M. WillFig. 3. Measurements of the coefficient (1 + γ)/2 from observations of the deflectionof light and of the Shapiro delay in propagation of radio signals near the Sun. Thegeneral relativity prediction is unity. “Optical” denotes measurements of stellar deflectionmade during solar eclipes, “Radio” denotes interferometric measurements of radio-wavedeflection, and “VLBI” denotes Very Long Baseline Radio Interferometry. “Hipparcos”denotes the European optical astrometry satellite. Arrows denote values well off thechart from one of the 1919 eclipse expeditions and from others through 1947. Shapirodelay measurements using the Cassini spacecraft on its way to Saturn yielded tests atthe 0.001 percent level, and light deflection measurements using VLBI have reached 0.02percent.
Was Einstein Right? 219milliarcsecond per year frame dragging or Lense-Thirring effect caused bythe rotation of the Earth; its secondary goal was to measure to six parts in10 5 the larger 6.6 arcsecond per year geodetic precession caused by spacecurvature [Eq. (8)].A complementary test of the Lense-Thirring precession, albeit withabout 10 times lower accuracy than the GPB goal, was reported by Ciufoliniand Pavlis 53 . This experiment measured the precession of the orbitalplanes of two Earth-orbiting laser-ranged satellites called LAGEOS, usingup-to-date models of the gravitational field of the Earth in an attempt tosubtract the dominant Newtonian precession with sufficient accuracy toyield a measurement of the relativistic effect.4. The Binary PulsarThe binary pulsar PSR 1913+16, discovered in 1974 by Joseph Taylor andRussell Hulse, provided important new tests of general relativity, specificallyof gravitational radiation and of strong-field gravity. Through precisetiming of the pulsar “clock”, the important orbital parameters of the systemcould be measured with exquisite precision. These included non-relativistic“Keplerian” parameters, such as the eccentricity e, and the orbital period(at a chosen epoch) P b , as well as a set of relativistic “post-Keplerian” parameters.The first PK parameter, 〈 ˙ω〉, is the mean rate of advance of periastron,the analogue of Mercury’s perihelion shift. The second, denoted γ ′ isthe effect of special relativistic time-dilation and the gravitational redshifton the observed phase or arrival time of pulses, resulting from the pulsar’sorbital motion and the gravitational potential of its companion. The third,P˙b , is the rate of decrease of the orbital period; this is taken to be the resultof gravitational radiation damping (apart from a small correction due togalactic differential rotation). Two other parameters, s and r, are relatedto the Shapiro time delay of the pulsar signal if the orbital inclination issuch that the signal passes in the vicinity of the companion; s is a directmeasure of the orbital inclination sin i. According to GR, the first threepost-Keplerian effects depend only on e and P b , which are known, and onthe two stellar masses which are unknown. By combining the observationsof PSR 1913+16 with the GR predictions, one obtains both a measurementof the two masses, and a test of GR, since the system is overdetermined.The results are 54m 1 = 1.4414 ± 0.0002M ⊙ , m 2 = 1.3867 ± 0.0002M ⊙ ,P˙bGR / P ˙ b OBS = 1.0013 ± 0.0021 . (9)
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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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Page 185 and 186: Probing Space-Time Through Numerica
Page 193 and 194: CHAPTER 7UNDERSTANDING OUR UNIVERSE
Page 195 and 196: Understanding Our Universe: Current
Page 223 and 224: CHAPTER 8WAS EINSTEIN RIGHT? TESTIN
Page 225 and 226: Was Einstein Right? 207We begin in
Page 227 and 228: Was Einstein Right? 20910 -810 -9E
Page 229 and 230: Was Einstein Right? 211On this 100t
Page 231 and 232: Was Einstein Right? 213The SME and
Page 233 and 234: Was Einstein Right? 215where d is t
Page 235: Was Einstein Right? 217of VLBI data
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Page 241 and 242: Was Einstein Right? 223be measured
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
Page 249 and 250: Receiving Gravitational Waves 231gr
Page 251 and 252: Receiving Gravitational Waves 233Th
Page 253 and 254: Receiving Gravitational Waves 235We
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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
Page 271 and 272: Receiving Gravitational Waves 253Eq
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Page 275 and 276: CHAPTER 10RELATIVITY IN THE GLOBAL
Page 277 and 278: Relativity in the Global Positionin
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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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