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Magnifying Spacetime: How Physics Changes with Scale [Minkštas viršelis]

  • Formatas: Paperback / softback, 184 pages, aukštis x plotis: 230x155 mm, weight: 266 g
  • Išleidimo metai: 10-Jul-2019
  • Leidėjas: Nova Science Publishers Inc
  • ISBN-10: 1536153192
  • ISBN-13: 9781536153194
Kitos knygos pagal šią temą:
  • Formatas: Paperback / softback, 184 pages, aukštis x plotis: 230x155 mm, weight: 266 g
  • Išleidimo metai: 10-Jul-2019
  • Leidėjas: Nova Science Publishers Inc
  • ISBN-10: 1536153192
  • ISBN-13: 9781536153194
Kitos knygos pagal šią temą:
Fundamental physics has now been stuck for almost a century. Ever since the discovery of general relativity and quantum mechanics in the early 1900s, the brightest minds in physics have been striving to combine these two paradigms into a single unified theory of quantum gravity, without success. The general consensus is that we are missing a big piece of the puzzle. Now, there are exciting new hints coming from fundamental physics research that may finally unlock the enigma of quantum gravity, the holy grail of modern physics. Recent results point toward one central idea; the importance of scale transformations in physics. Magnifying Spacetime delivers new insights into the role of scale in quantum gravity from the cutting-edge of modern research using an accessible and pedagogical style. The ideal complementary text for undergraduate and graduate students, this book also serves as an essential resource for professional physicists working on related topics. However, the scientifically literate layman should also find this work accessible due to the emphasis on conceptual understanding. Daniel Coumbe takes readers on a journey from the basics of scale transformations to the frontiers of quantum gravity research, including fractal geometry, minimum length scenarios, the renormalization group, Weinberg's asymptotic safety scenario, causal dynamical triangulations, spontaneous dimensional reduction, and Weyl's modification of Einstein's general relativity. Isaac Asimov said, "The most exciting phrase to hear in science, the one that heralds new discoveries, is not, Eureka! I've found it, but, that's odd!" The recent discovery that the world may be two-dimensional at extremely small distances, which is one of many striking results covered in this book, certainly counts as odd. There is now a small window of opportunity in which to get ahead of the curve by understanding such phenomena and developing new theoretical models and predictions, before the coming surge of experimental results.
List of Figures
ix
List of Tables
xiii
Preface xv
Units, Conventions and Common Abbreviations xviii
Acknowledgments xxi
Introduction xxiii
1 Scale Transformations
1(6)
1.1 Global Scale Transformations
1(2)
1.2 Local Scale Transformations
3(4)
2 Fractals
7(12)
2.1 The Coastline Paradox
7(1)
2.2 Fractal Dimensions
8(7)
2.2.1 The Topological Dimension
8(1)
2.2.2 The Hausdorff Dimension
9(1)
2.2.3 The Spectral Dimension
10(3)
2.2.4 The Walk Dimension
13(1)
2.2.5 Myrheim-Meyer Dimension
13(1)
2.2.6 Correlation Dimension
14(1)
2.3 Fractals Above Us and Below Us
15(4)
2.3.1 Fractals in Cosmology
15(1)
2.3.2 Fractals in Quantum Mechanics
16(3)
3 A Minimum Scale?
19(20)
3.1 Atoms of Spacetime
19(3)
3.2 Evidence for a Minimal Length
22(12)
3.2.1 A Lower Bound on Distance Measurements
22(1)
3.2.2 Black Hole Limitations
23(2)
3.2.3 Heisenberg's Microscope
25(3)
3.2.4 High-Energy Convergence
28(1)
3.2.5 Fluctuations of the Conformal Factor
29(3)
3.2.6 Modified Feynman Propagator
32(1)
3.2.7 Lattice Quantum Gravity
33(1)
3.3 Special Relativity and a Minimal Length
34(2)
3.4 Phenomenological Quantum Gravity
36(3)
4 The Renormalisation Group
39(6)
4.1 Overview
39(1)
4.2 Kadanoff's Block-Spin Model
40(1)
4.3 The Beta Function
41(2)
4.4 Renormalisation Group Operators
43(2)
5 The Asymptotic Safety Scenario
45(8)
5.1 Weinberg's Great Idea
45(4)
5.2 A Potential Problem
49(4)
6 Quantum Gravity on the Lattice
53(16)
6.1 Lattice Regularisation
53(1)
6.2 Geometric Observables
54(5)
6.3 Euclidean Dynamical Triangulations
59(6)
6.3.1 Conformal Instability
63(2)
6.4 Causal Dynamical Triangulations
65(4)
7 Is the Dimension of Spacetime Scale Dependent?
69(32)
7.1 Why 4 Dimensions?
69(2)
7.2 The Evidence for Dimensional Reduction
71(13)
7.2.1 String Theory
71(1)
7.2.2 Causal Dynamical Triangulations
71(4)
7.2.3 Euclidean Dynamical Triangulations
75(3)
7.2.4 Horava-Lifshitz Gravity
78(1)
7.2.5 Asymptotic Safety
79(2)
7.2.6 Loop Quantum Gravity
81(1)
7.2.7 The Wheeler-DeWitt Equation
82(1)
7.2.8 Causal Set Theory
83(1)
7.2.9 Non-Commutative Geometry
83(1)
7.3 A Possible Solution to an Old Problem
84(1)
7.4 Dimensional Reduction in the Sky
85(3)
7.5 Experimental Tests
88(3)
7.5.1 Cosmology
88(2)
7.5.2 GeV Scales
90(1)
7.5.3 TeV Scales
91(1)
7.6 What is Dimensional Reduction Really Telling Us?
91(10)
7.6.1 Overview
91(1)
7.6.2 Scale Dependent Length
92(5)
7.6.3 A Dual Description?
97(4)
8 Scale Dependent Spacetime
101(16)
8.1 Einstein and Weyl
101(5)
8.2 Renormalising Spacetime
106(11)
8.2.1 Motivation
106(3)
8.2.2 Estimating Ω(k)
109(1)
8.2.3 Immediate Implications
110(1)
8.2.4 Implications for Quantum Gravity
111(6)
Final Thoughts 117(2)
References 119(24)
About the Author 143(2)
Index 145(4)
Related Nova Publications 149
Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark