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Discrete or Continuous?

Book Description

The idea of infinity plays a crucial role in our understanding of the universe, with the infinite spacetime continuum perhaps the best-known example Ð but is spacetime really continuous? Throughout the history of science, many have felt that the continuum model is an unphysical idealization, and that spacetime should be thought of as 'quantized' at the smallest of scales. Combining novel conceptual analysis, a fresh historical perspective, and concrete physical examples, this unique book tells the story of the search for the fundamental unit of length in modern physics, from early classical electrodynamics to current approaches to quantum gravity. Novel philosophical theses, with direct implications for theoretical physics research, are presented and defended in an accessible format that avoids complex mathematics. Blending history, philosophy, and theoretical physics, this refreshing outlook on the nature of spacetime sheds light on one of the most thought-provoking topics in modern physics.

Table of Contents

  1. Cover
  2. Half title
  3. Title
  4. Copyright
  5. Dedication
  6. Table of Contents
  7. Preface
  8. 1 Introduction
  9. 2 Arguments from math
    1. 2.1 Outline
    2. 2.2 Zeno’s paradox of extension
    3. 2.3 Topology and the argument against collision
    4. 2.4 Geometry and the tile argument
    5. 2.5 Richer alternatives to the real line model
    6. 2.6 The physical Church–Turing thesis
    7. 2.7 Pure versus applied mathematics
  10. 3 Arguments from philosophy
    1. 3.1 Outline
    2. 3.2 Metaphysical motivations
    3. 3.3 Epistemology and the primacy of “length”
    4. 3.4 Is discreteness transcendental?
    5. 3.5 Enough with the “isms”
  11. 4 Electrodynamics, QED, and early QFT
    1. 4.1 Outline
    2. 4.2 Classical electrodynamics
    3. 4.3 From QM to QED
    4. 4.4 The rise of renormalization
    5. 4.5 Philosophical ramifications
  12. 5 Quantum gravity: prehistory
    1. 5.1 Outline
    2. 5.2 Early steps
    3. 5.3 Gravitons, measurability, and the Planck scale
    4. 5.4 Non-commutative geometry
    5. 5.5 (Re)enters gravity
    6. 5.6 Quantizing gravity – the philosophical debate
  13. 6 Einstein on the notion of length
    1. 6.1 Outline
    2. 6.2 Constructing the principles
    3. 6.3 The Swann–Einstein correspondence
    4. 6.4 Reading Einstein
    5. 6.5 Einstein and the constructive approach to STR
    6. 6.6 Geometry and dynamics, again
  14. 7 Quantum gravity: current approaches
    1. 7.1 Outline
    2. 7.2 String theory
    3. 7.3 Background independent strategies
    4. 7.4 Emergent gravity
    5. 7.5 On the “disappearance” of spacetime
  15. 8 The proof is in the pudding
    1. 8.1 Outline
    2. 8.2 The quest for quantum gravity phenomenology
    3. 8.3 Consistency proofs
    4. 8.4 The perils of innovation
    5. 8.5 There and back again
  16. 9 Coda
  17. References
  18. Index