The Problem of Time

Quantum Mechanics Versus General Relativity

  • Edward Anderson

Part of the Fundamental Theories of Physics book series (FTPH, volume 190)

Table of contents

  1. Front Matter
    Pages I-XXXVIII
  2. Time in Fundamental Physics

  3. Classical Problem of Time

    1. Front Matter
      Pages 203-203
    2. Edward Anderson
      Pages 205-208
    3. Edward Anderson
      Pages 217-229
    4. Edward Anderson
      Pages 243-246
    5. Edward Anderson
      Pages 261-270
    6. Edward Anderson
      Pages 271-275
    7. Edward Anderson
      Pages 277-286
    8. Edward Anderson
      Pages 287-288
    9. Edward Anderson
      Pages 289-296
    10. Edward Anderson
      Pages 297-319
    11. Edward Anderson
      Pages 337-346
    12. Edward Anderson
      Pages 347-353
    13. Edward Anderson
      Pages 355-357
    14. Edward Anderson
      Pages 359-364
    15. Edward Anderson
      Pages 365-378
    16. Edward Anderson
      Pages 379-390
    17. Edward Anderson
      Pages 419-429
    18. Edward Anderson
      Pages 431-437
    19. Edward Anderson
      Pages 439-441
  4. Quantum Problem of Time

    1. Front Matter
      Pages 475-475
    2. Edward Anderson
      Pages 501-510
    3. Edward Anderson
      Pages 511-520
    4. Edward Anderson
      Pages 521-525
    5. Edward Anderson
      Pages 527-529

About this book


This book is a treatise on time and on background independence in physics. It first considers how time is conceived of in each accepted paradigm of physics: Newtonian, special relativity, quantum mechanics (QM) and general relativity (GR).  Substantial differences are moreover uncovered between what is meant by time in QM and in GR. These differences jointly source the Problem of Time: Nine interlinked facets which arise upon attempting concurrent treatment of the QM and GR paradigms, as is required in particular for a background independent theory of quantum gravity.  A sizeable proportion of current quantum gravity programs - e.g. geometrodynamical and loop quantum gravity approaches to quantum GR, quantum cosmology, supergravity and M-theory - are background independent in this sense. This book's foundational topic is thus furthermore of practical relevance in the ongoing development of quantum gravity programs. 

    This book shows moreover that eight of the nine facets of the Problem of Time already occur upon entertaining background independence in classical (rather than quantum) physics. By this development, and interpreting shape theory as modelling background independence, this book further establishes background independence as a field of study.  Background independent mechanics, as well as minisuperspace (spatially homogeneous) models of GR and perturbations thereabout are used to illustrate these points. As hitherto formulated, the different facets of the Problem of Time greatly interfere with each others' attempted resolutions. This book explains how, none the less, a local resolution of the Problem of Time can be arrived at after various reconceptualizations of the facets and reformulations of their mathematical implementation.  Self-contained appendices on mathematical methods for basic and foundational quantum gravity are included. Finally, this book outlines how supergravity is refreshingly different from GR as a realization of background independence, and what background independence entails at the topological level and beyond. 


Emergent Semiclassical Time Foundational Theories of Physics General Relativity and Spacetime Halliwell-Hawking Model Hidden Time Loop Quantum Gravity Philosophy of Time and Space Principles of Dynamics Quantum Mechanics and Gravity

Authors and affiliations

  • Edward Anderson
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of Cambridge Centre for Mathematical SciencesCambridgeUnited Kingdom

Bibliographic information