Book contents
- Frontmatter
- Contents
- Preface
- Part I Discrete time concepts
- Part II Classical discrete time mechanics
- Part III Discrete time quantum mechanics
- Part IV Discrete time classical field theory
- Part V Discrete time quantum field theory
- Part VI Further developments
- 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
28 - Space, time and gravitation
from Part VI - Further developments
Published online by Cambridge University Press: 05 May 2014
- Frontmatter
- Contents
- Preface
- Part I Discrete time concepts
- Part II Classical discrete time mechanics
- Part III Discrete time quantum mechanics
- Part IV Discrete time classical field theory
- Part V Discrete time quantum field theory
- Part VI Further developments
- 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
Summary
In this chapter we are going to discuss some aspects touching upon the discretization of time in the context of Einstein's theories of special relativity (SR) and general relativity (GR).
Snyder's quantized spacetime
At first sight SR seems the wrong theory for temporal discretization. In Newtonian mechanics, time is absolute, which means that simultaneity is absolute: it is the same for all inertial observers. Therefore, if absolute time is discretized for one inertial observer, it is discretized in exactly the same way for all other inertial observers. In that respect, Newtonian discrete time mechanics does not require a preferred inertial frame. Simultaneity is not absolute in SR, however, which suggests that discretizing time will break Lorentz covariance: the use of a preferred inertial frame in which to temporally discretize seems inevitable.
This conclusion is based on classical thinking. The example of quantized angular momentum demonstrates that it is possible to reconcile having a continuous parameter space with a discrete spectrum of observable values. Suppose that an observer is conducting a Stern–Gerlach (SG) experiment, firing a beam of electrons through an apparatus containing a strong inhomogeneous magnetic field (Gerlach and Stern, 1922a). In such an experiment, the observer will first fix the orientation of the apparatus relative to the source. Then it will be found that an electron passing through the apparatus will be detected finally in only one of two possible angular momentum states.
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- Information
- Principles of Discrete Time Mechanics , pp. 323 - 332Publisher: Cambridge University PressPrint publication year: 2014