Quantum Gravity

by Mark A. Martin, Ph.D.

Abstract | Mark's Bio | History | Terms of Use | Table of Contents


In this presentation, I will discuss recent efforts to understand the nature of spacetime on the smallest scales and reconcile the incompatible ways that space and time are treated in quantum mechanics and relativity. Most (but not all) physicists believe that a quantum theory of gravity is needed to accomplish these goals. Understanding the nature of spacetime on the smallest scales is important for understanding environments where quantum and gravitational effects are close to the same magnitudes, such as regions near black holes and the very early universe. Conversely, consideration of such extreme environments and of the thermodynamics of black holes, in particular, has provided critical insights into the fundamental nature of spacetime and has guided the development of general theories of quantum gravity. In this talk, I will describe features that one would like a quantum theory of gravity to have, explore some of the results derived from the study of black holes, and consider two candidate theories that describe quantum gravity. The theories that I will discuss are loop quantum gravity and string theories. There are currently no experimental or observational data that suggest the need for such a theory or that indicate that our current physical theories are flawed. As a result, everything that I discuss must be considered purely speculative.

My presentation will mostly follow the book "Three Roads to Quantum Gravity" by Lee Smolin. Smolin identifies the three roads as black hole thermodynamics, loop quantum gravity, and string theories. The roads are not necessarily theories of quantum gravity but are approaches to understanding the nature of spacetime on the smallest scales. All three approaches lead to the conclusion that space and time are comprised of discrete quanta and exhibit quantum behavior.

Mark's Bio

I have a Ph.D. and a Master's degree in applied mathematics from the University of Washington, a Master's degree in pure mathematics from the University of Arizona, and a Bachelor's degree in mathematics from the University of Colorado in Boulder. At UW, I focused on numerical analysis, dynamical systems, and mathematical biology, and applied my skills toward understanding meteorological and oceanographic systems. The topic of my dissertation was how climatic and seasonal environmental changes influence plankton populations in the oceans. This is important because plankton comprise the base of almost all aquatic food webs; play crucial roles in the environmental cycling of many elements and in maintaining atmospheric oxygen, in particular; and produce chemicals that have a significant influence on the climate. I have mostly worked in the field of biotechnology since completing my Ph.D. I am a Linux/UNIX enthusiast, a programmer, and a web developer. My interests extend to a large number of scientific and technical fields, including physics, astronomy, cosmology, space travel and exploration, oceanography, climatology, alternative energy, biology, ecology, physiology, biomechanics, and computing.

I have had an almost life-long interest in theoretical physics, astronomy, and cosmology. As a result, I began my college career as a physics major but realized at the end of my junior year that I thought more like a mathematician than a physicist. So, although I had already taken nearly all of the undergraduate physics courses offered at the university, I changed my major to mathematics. I am not a professional physicist or astronomer and not an expert in quantum gravity. But I have avidly read popular and semi-technical accounts of developments in these areas and my mathematical background has helped me understand some of these developments in a little more depth than one typically gets from popular accounts.

You can read more about me on my web site and in my C.V. and résumé, which are available from the Résumé section of my web site.


I first gave this talk in two parts on January 19, 2006 and February 23, 2006 to the Astrophysics/Cosmology Special Interest Group of the Rose City Astronomers.

I gave it a second time to the Wanderers on April 12, 2006 and April 26, 2006.

Terms of Use

I am the author of the images and text except where otherwise indicated. Please contact me for permission if you wish to use any of my images or text.

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Table of Contents

  1. Quantum Gravity — Part I
  2. Introduction
  3. Outline
  4. I. Foundations
  5. a. Relativistic Foundations
  6. Relativistic Fundamentals
  7. There are No Objects, Only Processes
  8. Causal Relationships
  9. Light Cones
  10. b. Cosmological Foundations
  11. Cosmological Fundamentals
  12. Logical Consequences
  13. c. Quantum Mechanical Foundations
  14. The Uncertainty Principle
  15. Quantum States
  16. A Quantum System
  17. Superposition
  18. Conventional Quantum Cosmology
  19. Relativized Quantum Cosmology
  20. The Planck Scale
  21. II. Approaches to Quantum Gravity
  22. a. Road 1 — Starting from Scratch: Black Hole Thermodynamics
  23. Black Holes
  24. Horizons & Hidden Regions
  25. Accelerating in Empty Space
  26. Accelerating in Empty Space
  27. Accelerating in Empty Space
  28. Entropy & Hidden Regions
  29. Entropy of a Black Hole
  30. Temperature of a Black Hole
  31. Area & Information
  32. Conclusions
  33. References
  34. Quantum Gravity — Part II
  35. Introduction
  36. Outline
  37. Key Ideas from Part 1
  38. b. Road 2 — Loop Quantum Gravity
  39. Magnetic Field Lines
  40. Magnetic Field Lines in a Superconductor
  41. Color Force Field Lines Act Like Magnetic Field Lines in a Superconductor
  42. The Gravitational Field is Like the Electric Field
  43. Space is Composed of Loops of Gravitational (Geometric) Flux
  44. Different States of Space are Distinguished by How Loops Knot, Link, and Kink
  45. Evolution of Spacetime is Determined by Evolution of Relationships Between Loops
  46. Spin Networks & Spin Foam
  47. Simulations of Lorentzian 2d Quantum Gravity
  48. Virtues of Loop Quantum Gravity
  49. Shortcomings of Loop Quantum Gravity
  50. Issues that Loop Quantum Gravity Doesn't Resolve
  51. c. Road 3 — String Theories
  52. The Mathematics of String Theories
  53. The Nature of Strings
  54. Compactified Dimensions & Discrete Space in String Theories
  55. Virtues of String Theories
  56. Shortcomings of String Theories
  57. M-Theory
  58. d. Other Roads
  59. III. Merging the Streams
  60. a. The Holographic Principle
  61. b. Constructing a More General Theory
  62. IV. Conclusions
  63. References

Top of Page | Abstract | Mark's Bio | History | Terms of Use | Table of Contents

I am the author of the images and text except where otherwise indicated. Please contact me for permission if you wish to use any of my images or text.

Created on Wednesday 03 May 2006 by Mark A. Martin with KPresenter and a lot of manual modifications.