Principles of Discrete Time Mechanics

A unique introduction to the chronon hypothesis, systematically building the theory up from scratch.

George Jaroszkiewicz (Author)

9781107034297, Cambridge University Press

Hardback, published 17 April 2014

360 pages, 21 b/w illus.
25.4 x 18 x 3 cm, 0.86 kg

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.

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.

Subject Areas: Mathematical physics [PHU]