Approaches to Quantum Gravity

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viii Contents 11 String theory, holography and Quantum Gravity 187 T. Banks 12 String field theory 210 W. Taylor Questions and answers 229 Part III Loop quantum gravity and spin foam models 233 13 Loop quantum gravity 235 T. Thiemann 14 Covariant loop quantum gravity? 253 E. Livine 15 The spin foam representation of loop quantum gravity 272 A. Perez 16 Three-dimensional spin foam Quantum Gravity 290 L. Freidel 17 The group field theory approach to Quantum Gravity 310 D. Oriti Questions and answers 332 Part IV Discrete Quantum Gravity 339 18 Quantum Gravity: the art of building spacetime 341 J. Ambjørn, J. Jurkiewicz and R. Loll 19 Quantum Regge calculus 360 R. Williams 20 Consistent discretizations as a road to Quantum Gravity 378 R. Gambini and J. Pullin 21 The causal set approach to Quantum Gravity 393 J. Henson Questions and answers 414 Part V Effective models and Quantum Gravity phenomenology 425 22 Quantum Gravity phenomenology 427 G. Amelino-Camelia 23 Quantum Gravity and precision tests 450 C. Burgess 24 Algebraic approach to Quantum Gravity II: noncommutative spacetime 466 S. Majid
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Page 8: APPROACHES TO QUANTUM GRAVITY Towar
Page 12: A Sandra
Page 20: Contents ix 25 Doubly special relat
Page 24: List of contributors xi O. Dreyer T
Page 28: List of contributors xiii W. Taylor
Page 34: xvi Preface new mathematics as well
Page 38: xviii Preface as the current tentat
Page 44: Part I Fundamental ideas and genera
Page 50: 4 C. Rovelli QFT relies heavily on
Page 54: 6 C. Rovelli For instance, the Heis
Page 58: 8 C. Rovelli Conceptually, the key
Page 62: 10 C. Rovelli In addition, a number
Page 66: 12 C. Rovelli [20] S. W. Hawking,
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14 G. ’t Hooft of time, of Cauchy
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16 G. ’t Hooft generally, in 2 +
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18 G. ’t Hooft of the small-dista
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20 G. ’t Hooft that a theory exis
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22 G. ’t Hooft This means that th
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24 G. ’t Hooft 2.7 Gauge- and dif
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3 Does locality fail at intermediat
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28 R. D. Sorkin a little thought in
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30 R. D. Sorkin this approach one n
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32 R. D. Sorkin The suggestion of o
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34 R. D. Sorkin But is our “discr
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36 R. D. Sorkin (as one might have
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38 R. D. Sorkin It seems likely tha
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40 R. D. Sorkin in particular, woul
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42 R. D. Sorkin small, as discussed
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4 Prolegomena to any future Quantum
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46 J. Stachel breakups, it is impor
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48 J. Stachel gauge fields and GR,
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50 J. Stachel where S is any 2-surf
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52 J. Stachel connection (see, e.g.
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54 J. Stachel of a projective struc
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56 J. Stachel problem on a spacelik
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58 J. Stachel (3) a break-up of the
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60 J. Stachel simplification of the
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62 J. Stachel investigate (3 + 1) a
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64 J. Stachel partitioned into slic
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66 J. Stachel [13] S. Frittelli, C.
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5 Spacetime symmetries in histories
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70 N. Savvidou of time. The develop
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72 N. Savvidou In order to define c
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74 N. Savvidou The novel feature in
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76 N. Savvidou We start instead fro
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78 N. Savvidou Relation between the
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80 N. Savvidou 5.4 A spacetime appr
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82 N. Savvidou the T 0 variables -
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Categorical geometry and the mathem
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86 L. Crane called morphisms [1]. A
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88 L. Crane are defined combinatori
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90 L. Crane 6.3.1 The BC categorica
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92 L. Crane Classical behavior occu
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94 L. Crane One could then apply th
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96 L. Crane This model also has a n
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98 L. Crane [13] J. Barrett and L.
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100 O. Dreyer Is spacetime fundamen
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102 O. Dreyer Since the inverse pro
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104 O. Dreyer where we have denoted
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106 O. Dreyer and the points are th
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108 O. Dreyer m 1 m 2 =− v 2 v 1
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110 O. Dreyer In addition to the pr
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112 R. Percacci In section 8.2 I in
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114 R. Percacci this case the theor
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116 R. Percacci The requirement of
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118 R. Percacci be bounded. This is
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120 R. Percacci where the heat kern
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122 R. Percacci ~ G 1 0.8 0.6 0.4 0
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124 R. Percacci will still be possi
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126 R. Percacci Einstein-Hilbert ac
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128 R. Percacci [24] O. Lauscher an
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130 F. Markopoulou has been claimed
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132 F. Markopoulou vertex x ∈ V (
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134 F. Markopoulou Note that comple
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136 F. Markopoulou 9.2.2 The meanin
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138 F. Markopoulou Fock space for t
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140 F. Markopoulou A = 1 A 2 A 3 A
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142 F. Markopoulou effective theori
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144 F. Markopoulou Quantum Field Th
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146 F. Markopoulou is concerned wit
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148 F. Markopoulou The dynamics is
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Questions and answers • Q - L. Cr
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152 Questions and answers Hausdorff
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154 Questions and answers - A-R.Sor
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156 Questions and answers Now a goo
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158 Questions and answers would see
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160 Questions and answers 3. You me
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162 Questions and answers - A - R.
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164 Questions and answers notion of
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Part II String/M-theory
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170 G. Horowitz and J. Polchinski a
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172 G. Horowitz and J. Polchinski w
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178 G. Horowitz and J. Polchinski T
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180 G. Horowitz and J. Polchinski m
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182 G. Horowitz and J. Polchinski N
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184 G. Horowitz and J. Polchinski c
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186 G. Horowitz and J. Polchinski [
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188 T. Banks This looks peculiar to
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190 T. Banks This lightning review
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192 T. Banks Since the holographic
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194 T. Banks definition of local ev
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196 T. Banks we have postulated are
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198 T. Banks with observerphilic de
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200 T. Banks de Sitter horizon is t
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202 T. Banks of the dS-Schwarzschil
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204 T. Banks Thus, there are of ord
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206 T. Banks it has given us a cons
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208 T. Banks [3] G. T. Horowitz, Th
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12 String field theory W. TAYLOR 12
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212 W. Taylor possible configuratio
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214 W. Taylor raising operators α
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216 W. Taylor ❍❨ 1 ❍❍✟
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218 W. Taylor level truncation is t
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220 W. Taylor different description
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222 W. Taylor In closed string fiel
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224 W. Taylor closed string field t
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226 W. Taylor or other 6D manifold.
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228 W. Taylor [37] W. Taylor, & B.
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230 Questions and answers 3. You st
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232 Questions and answers (proving
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13 Loop quantum gravity T. THIEMANN
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Loop quantum gravity 237 13.2 Canon
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Loop quantum gravity 239 In what fo
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Loop quantum gravity 241 equivalenc
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Loop quantum gravity 243 ∂ F τ f
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Loop quantum gravity 245 will play
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Loop quantum gravity 247 U(ϕ)T n =
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Loop quantum gravity 249 a definite
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Loop quantum gravity 251 [28] T. Th
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14 Covariant loop quantum gravity?
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Covariant loop quantum gravity? 255
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The spin foam representation of loo
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Three-dimensional spin foam Quantum
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The group field theory approach to
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Questions and answers 333 the holes
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Questions and answers 335 their vac
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Questions and answers 337 of some s
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18 Quantum Gravity: the art of buil
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Quantum Gravity: the art of buildin
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Quantum Regge calculus 361 is given
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Quantum Regge calculus 363 group. W
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Quantum Regge calculus 365 emanatin
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Quantum Regge calculus 367 We will
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Quantum Regge calculus 369 reason,
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Quantum Regge calculus 371 gravitat
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Quantum Regge calculus 373 where ξ
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Quantum Regge calculus 375 [4] J. W
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Quantum Regge calculus 377 [52] M.
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Consistent discretizations as a roa
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21 The causal set approach to Quant
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The causal set approach to Quantum
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22 Quantum Gravity phenomenology G.
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Quantum Gravity phenomenology 429 T
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Quantum Gravity phenomenology 431 t
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Quantum Gravity phenomenology 433 c
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Quantum Gravity phenomenology 435 p
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Quantum Gravity phenomenology 437 F
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Quantum Gravity phenomenology 439 l
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Quantum Gravity phenomenology 441 p
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Quantum Gravity phenomenology 443 w
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Quantum Gravity phenomenology 445 i
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Quantum Gravity phenomenology 447 s
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Quantum Gravity phenomenology 449 [
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Quantum Gravity and precision tests
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Algebraic approach to Quantum Gravi
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25 Doubly special relativity J. KOW
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Doubly special relativity 495 DSR t
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Doubly special relativity 497 On th
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Doubly special relativity 499 some
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Doubly special relativity 501 [x 0
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Doubly special relativity 503 that
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Doubly special relativity 505 can b
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Doubly special relativity 507 scale
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26 From quantum reference frames to
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From quantum reference frames to de
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Lorentz invariance violation & its
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Generic predictions of quantum theo
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Questions and answers • Q - L. Cr
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Questions and answers 573 frame. Ju
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Questions and answers 575 - A - J.
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Questions and answers 577 where thi
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Questions and answers 579 would all
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Index 581 cosmology, 26, 155, 184,
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Index 583 emergent, 99, 109, 163, 1
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Approaches to Quantum Gravity

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