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.
Author(s): Daniel Nathan Coumbe
Series: Physics Research and Technology
Publisher: Nova Science Publishers
Year: 2019
Language: English
Pages: 184
City: Hauppauge
MAGNIFYING SPACETIMEHOW PHYSICS CHANGES WITH SCALE
MAGNIFYING SPACETIMEHOW PHYSICS CHANGES WITH SCALE
Contents
List of Figures
List of Tables
Preface
Units, Conventions and Common Abbreviations
Acknowledgments
Introduction
Chapter 1Scale Transformations
1.1. Global Scale Transformations
1.2. Local Scale Transformations
Chapter 2Fractals
2.1. The Coastline Paradox
2.2. Fractal Dimensions
2.2.1. The Topological Dimension
2.2.2. The Hausdorff Dimension
2.2.3. The Spectral Dimension
2.2.4. TheWalk Dimension
2.2.5. Myrheim-Meyer Dimension
2.2.6. Correlation Dimension
2.3. Fractals Above Us and Below Us
2.3.1. Fractals in Cosmology
2.3.2. Fractals in QuantumMechanics
Chapter 3A Minimum Scale?
3.1. Atoms of Spacetime
3.2. Evidence for a Minimal Length
3.2.1. A Lower Bound on Distance Measurements
3.2.2. Black Hole Limitations
3.2.3. Heisenberg’sMicroscope
3.2.4. High-Energy Convergence
3.2.5. Fluctuations of the Conformal Factor
3.2.6. Modified Feynman Propagator
3.2.7. Lattice Quantum Gravity
3.3. Special Relativity and a Minimal Length
3.4. Phenomenological Quantum Gravity
Chapter 4The Renormalisation Group
4.1. Overview
4.2. Kadanoff’s Block-SpinModel
4.3. The Beta Function
4.4. Renormalisation Group Operators
Chapter 5The Asymptotic Safety Scenario
5.1. Weinberg’s Great Idea
5.2. A Potential Problem
Chapter 6Quantum Gravity on the Lattice
6.1. Lattice Regularisation
6.2. Geometric Observables
6.3. Euclidean Dynamical Triangulations
6.3.1. Conformal Instability
6.4. Causal Dynamical Triangulations
Chapter 7Is the Dimension of SpacetimeScale Dependent?
7.1. Why 4 Dimensions?
7.2. The Evidence for Dimensional Reduction
7.2.1. String Theory
7.2.2. Causal Dynamical Triangulations
7.2.3. Euclidean Dynamical Triangulations
7.2.4. Horava-Lifshitz Gravity
7.2.5. Asymptotic Safety
7.2.6. Loop Quantum Gravity
7.2.7. TheWheeler-DeWitt Equation
7.2.8. Causal Set Theory
7.2.9. Non-Commutative Geometry
7.3. A Possible Solution to an Old Problem
7.4. Dimensional Reduction in the Sky
7.5. Experimental ests
7.5.1. Cosmology
7.5.2. GeV Scales
7.5.3. TeV Scales
7.6. What is Dimensional Reduction Really Telling Us?
7.6.1. Overview
7.6.2. Scale Dependent Length
7.6.3. A Dual Description?
Chapter 8Scale Dependent Spacetime
8.1. Einstein andWeyl
8.2. Renormalising Spacetime
8.2.1. Motivation
8.2.2. Estimating W(k)
8.2.3. Immediate Implications
8.2.4. Implications for Quantum Gravity
Final Thoughts
References
About the Author
Index
Blank Page
