Discrete or Continuous?

The idea of infinity plays a crucial role in our understanding of the universe, with the infinite spacetime continuum perhaps the best-known example - 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. 'Amit Hagar's Discrete or Continuous?: The Quest for Fundamental Length in Modern Physics takes the reader on an enjoyable journey - by turns historical, philosophical, and physical - in a quest to unravel many of the subtleties that underlie the concept of a minimum length in physics.' Luis J. Garay, Physics Today 'The author's discourse is not centered in philosophy or physics, but rather in the attempts to resolve quantum mechanics and general relativity. Throughout the work, Hagar does a good job of showing how complicated this issue is without burying the reader in technical points.' E. Kincanon, Choice '... this book is a comprehensive and even-handed exposition of the mathematical and philosophical formulations of theoretical physics in terms of discrete or continuous space-time structures. It spans the analyses of the subject from the ancient Greeks thought to the present day: from Zeno (450BC) to several discussions published as late as 2013. The monograph is extremely well referenced and cites some 550 articles and books.' Richard Keesing, Contemporary Physics1. Introduction; 2. Arguments from mathematics; 3. Arguments from philosophy; 4. Electrodynamics, QED, and early QFT; 5. Quantum gravity: prehistory; 6. Einstein on the notion of length; 7. Quantum gravity: current approaches; 8. The proof is in the pudding; 9. Coda.