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Quantum Gravity From Theory to Experimental Search 1 3 Editors DomenicoJ.W.Giulini ClausLa¨mmerzahl Universita¨tFreiburg Universita¨tBremen Fakulta¨tPhysikundMathematik ZARM Hermann-HerderStr.3 AmFallturm 79104Freiburg,Germany 28359Bremen,Germany ClausKiefer Universita¨tzuKo¨ln InstitutTheoretischenPhysik Zu¨lpicherStr.77 50937Ko¨ln,Germany Cataloging-in-PublicationDataappliedfor AcatalogrecordforthisbookisavailablefromtheLibraryofCongress. 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Preface The relation between quantum theory and the theory of gravitation is certainly one of the most outstanding unresolved issues of modern physics. On one side, quantum theory, in its usual formulation and orthodox interpretation, requires anambientnon-dynamicalspacetime.Ontheotherside,gravity,asdescribedby general relativity, requires a dynamical geometry of spacetime which is coupled to all material processes within. This implies that at least one of these theories cannotbefundamentallycorrect.Hence,accordingtogeneralexpectation,there should exist a theory of quantum gravity comprising both previous theories. Such a theory should make definite predictions where previous theories failed to do so, like close to the Big Bang or during the radiational decay of Black Holes. Moreover, a theory of quantum gravity should also clarify the structure of spacetime at smallest scales. Up to now, no finally worked out theory of quantum gravity exists. Currently the most promising approaches to such a theory go under the names of Canonical Quantum Gravity and String Theory. The purpose of the 271st WE-Heraeus Seminar “Aspects of Quantum Gravity – From Theory to Experimental Search”, which took place in Bad Honnef from February 24th to March 1st, 2002, was to discuss issues surrounding quantum gravity on a level accessible to graduate students. The range of topics spanned an arc from fundamental questions concerning the notion of “quantisation”, over the presentation of definite approaches, to the possibility of astrophysical observations as well as laboratory experiments. We sincerely thank all speakers for their presentations and especially those who were moreover willing to write them up for the present volume. Last but not least we thank the Wilhelm and Else Heraeus Foundation for its generous support, without which this seminar could not have been realized, and the Physikzentrum for its kind hospitality. Freiburg, Ko¨ln, and Bremen Domenico Giulini April 2003 Claus Kiefer Claus La¨mmerzahl Contents Overview Quantum Gravity – A General Introduction Claus Kiefer ...................................................... 3 1 Quantum Theory and the Gravitational Field ...................... 3 2 Approaches to Quantum Gravity ................................. 6 3 Quantum Black Holes and Quantum Cosmology.................... 9 4 Semiclassical Approximation and Decoherence ..................... 11 References ........................................................ 13 Part I General Formalism and Specific Approaches That Strange Procedure Called Quantisation Domenico Giulini .................................................. 17 1 Introduction and Motivation..................................... 17 2 Canonical Quantisation ......................................... 18 3 Constrained Systems............................................ 32 References ........................................................ 39 Lectures on Loop Quantum Gravity Thomas Thiemann ................................................. 41 1 Motivation and Introduction..................................... 43 2 Mathematical and Physical Foundations of Quantum General Relativity................................... 67 3 Selected Areas of Current Research ............................... 85 4 Selection of Open Research Problems ............................. 124 References ........................................................ 127 A Discrete History of the Lorentzian Path Integral Renate Loll ....................................................... 137 1 Introduction ................................................... 137 2 Quantum Gravity from Dynamical Triangulations .................. 139 3 Brief Summary of Discrete Gravitational Path Integrals ............. 141 4 Geometry from Simplices........................................ 143 5 Lorentzian Nature of the Path Integral............................ 146 6 Brief Conclusion ............................................... 167 References ........................................................ 169 VIII Contents Introduction to String Theory Thomas Mohaupt .................................................. 173 1 Introductory Remarks .......................................... 173 2 Free Bosonic Strings ............................................ 175 3 Interacting Bosonic Strings ...................................... 192 4 Supersymmetric Strings ......................................... 213 5 p-Branes in Type II String Theories .............................. 227 6 Outlook....................................................... 236 References ........................................................ 247 Part II Black Holes and Cosmology Quantum Theory of Gravitational Collapse (Lecture Notes on Quantum Conchology) Petr Háj´ıˇcek ...................................................... 255 1 Introduction ................................................... 255 2 Gauge-Invariant Method in the Canonical Theory of Generally Covariant Systems .................................. 257 3 A Model: Gravitating Shell ...................................... 267 4 Quantum Theory............................................... 284 References ........................................................ 298 Primordial Black Holes as a Probe of the Early Universe, Gravitational Collapse, High Energy Physics and Quantum Gravity Bernard J. Carr ................................................... 301 1 Introduction ................................................... 301 2 Historical Overview............................................. 302 3 PBHs as a Probe of Primordial Inhomogeneities.................... 304 4 PBHs as Probe of Cosmological Phase Transitions.................. 307 5 PBHs as a Probe of a Varying Gravitational Constant .............. 310 6 PBHs as a Probe of Gravitational Collapse ........................ 311 7 PBHs as a Probe of High Energy Physics.......................... 312 8 PBHs as a Probe of Quantum Gravity ............................ 317 9 Conclusions.................................................... 319 References ........................................................ 319 On the Assignment of Entropy to Black Holes Daniel Sudarsky ................................................... 323 1 Introduction ................................................... 323 2 The Assignment of Entropy...................................... 324 3 The Schro¨dinger Black Hole ..................................... 326 4 The Problem and the Lessons.................................... 329 References ........................................................ 333 Contents IX Part III Experimental Search Physics with Large Extra Dimensions and Non-Newtonian Gravity at Sub-mm Distances Ignatios Antoniadis ................................................ 337 1 Introduction ................................................... 337 2 Hiding Extra Dimensions........................................ 346 3 Low-Scale Strings .............................................. 348 4 Gravity Modification and Sub-millimeter Forces .................... 350 5 Conclusions.................................................... 352 References ........................................................ 353 Quantum States of Neutrons in the Gravitational Field and Limits for Non-Newtonian Interaction in the Range between 1 µm and 10 µm Hartmut Abele, Stefan Baeßler, Alexander Westphal.................... 355 1 A Quantum System ............................................ 355 2 Limits for Non-Newtonian Interaction Below 10 µm................. 356 3 The Experiment at the Institut Laue-Langevin..................... 358 4 Gravity and Quantum Mechanics Work Together ................... 361 5 Summary...................................................... 365 References ........................................................ 365 The Einstein Equivalence Principle and the Search for New Physics Claus La¨mmerzahl ................................................. 367 1 Introduction ................................................... 367 2 The Einstein Equivalence Principle ............................... 369 3 Implications of the Einstein Equivalence Principle .................. 373 4 Models Which Violate the Einstein Equivalence Principle............ 375 5 Experimental Tests of the Einstein Equivalence Principle ............ 381 6 New Experimental Devices and Developments...................... 386 7 EEP and Modern Metrology ..................................... 388 8 Conclusion .................................................... 393 References ........................................................ 394