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D. Giulini C. Kiefer C. La¨mmerzahl (Eds.)
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
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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 H´aj´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
