Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Irreversibility
- 3 Arrows of time
- 4 Correlating arrows of time
- 5 Two-time boundary value problems
- 6 Quantum measurements: cats, clouds and everything else
- 7 Existence of special states
- 8 Selection of special states
- 9 Abundance of special states
- 10 Experimental tests
- 11 Conclusions and outlook
- Author index
- Index
9 - Abundance of special states
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Irreversibility
- 3 Arrows of time
- 4 Correlating arrows of time
- 5 Two-time boundary value problems
- 6 Quantum measurements: cats, clouds and everything else
- 7 Existence of special states
- 8 Selection of special states
- 9 Abundance of special states
- 10 Experimental tests
- 11 Conclusions and outlook
- Author index
- Index
Summary
Pure quantum evolution is deterministic, ψ → exp(—iHt/ħ)ψ, but as for classical mechanics probability enters because a given macroscopic initial condition contains microscopic states that lead to different outcomes; the relative probability of those outcomes equals the relative abundance of the microscopic states for each outcome. This is the postulated basis for the recovery of the usual quantum probabilities, as discussed in Chapter 6. In this chapter we take up the question of whether the allowable microstates (the ‘special’ states) do indeed come with the correct abundance. To recap: ‘special’ states are microstates not leading to superpositions of macroscopically different states (‘grotesque’ states). For a given experiment and for each macroscopically distinct outcome of that experiment these states form a subspace. We wish to show that the dimension of that subspace is the relative probability of that outcome.
This is an ambitious goal, especially considering the effort needed to establish that there are any special states—the subject of Chapter 7. As remarked there, the special states exhibited are likely to be only a small and atypical fraction of all special states in the physical apparatus being modeled (e.g., the cloud chamber). In one example (the decay model) there is a remarkable matching of dimension and conventional probability, but I would not make too much of that. What is especially challenging about the present task is that we seek a universal distribution.
- Type
- Chapter
- Information
- Time's Arrows and Quantum Measurement , pp. 268 - 298Publisher: Cambridge University PressPrint publication year: 1997