Principles of Discrete Time Mechanics
Principles of Discrete Time Mechanics
George Jaroszkiewicz, University of Nottingham
April 2014
Temporarily unavailable - available from March 2025
Hardback
9781107034297
£104.00
GBPHardback
USD
eBook
Could time be discrete on some unimaginably small scale? Exploring the idea in depth, this unique introduction to discrete time mechanics systematically builds the theory up from scratch, beginning with the historical, physical and mathematical background to the chronon hypothesis. Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, including spreadsheet mechanics, classical and quantum register mechanics, and classical and quantum mechanics and field theories. A consistent emphasis on contextuality and the observer-system relationship is maintained throughout.
- Demonstrates the feasibility of discrete time mechanics, and intended to stimulate further developments in this approach to physics
- Includes an accessible exploration of spreadsheet mechanics, allowing exploration of a limitless variety of cellular dynamical models, giving insight into relativistic lightcones and time dilation
- Written such that the discrete time hypothesis is the only new concept readers need to take on board: all other familiar concepts are retained
Product details
April 2014Hardback
9781107034297
360 pages
254 × 180 × 30 mm
0.86kg
21 b/w illus.
Temporarily unavailable - available from March 2025
Table of Contents
- 1. Introduction
- 2. The physics of discreteness
- 3. The road to calculus
- 4. Temporal discretization
- 5. Discrete time dynamics architecture
- 6. Some models
- 7. Classical cellular automata
- 8. The action sum
- 9. Worked examples
- 10. Lee's approach to discrete time mechanics
- 11. Elliptic billiards
- 12. The construction of system functions
- 13. The classical discrete time oscillator
- 14. Type 2 temporal discretization
- 15. Intermission
- 16. Discrete time quantum mechanics
- 17. The quantized discrete time oscillator
- 18. Path integrals
- 19. Quantum encoding
- 20. Discrete time classical field equations
- 21. The discrete time Schrodinger equation
- 22. The discrete time Klein–Gordon equation
- 23. The discrete time Dirac equation
- 24. Discrete time Maxwell's equations
- 25. The discrete time Skyrme model
- 26. Discrete time quantum field theory
- 27. Interacting discrete time scalar fields
- 28. Space, time and gravitation
- 29. Causality and observation
- 30. Concluding remarks
- Appendix A. Coherent states
- Appendix B. The time-dependent oscillator
- Appendix C. Quaternions
- Appendix D. Quantum registers
- References
- Index.
