Book contents
- Frontmatter
- Contents
- List of papers on quantum philosophy by J. S. Bell
- Preface to the first edition
- Acknowledgements
- Introduction: John Bell and the second quantum revolution
- 1 On the problem of hidden variables in quantum mechanics
- 2 On the Einstein–Podolsky–Rosen paradox
- 3 The moral aspect of quantum mechanics
- 4 Introduction to the hidden-variable question
- 5 Subject and object
- 6 On wave packet reduction in the Coleman–Hepp model
- 7 The theory of local beables
- 8 Locality in quantum mechanics: reply to critics
- 9 How to teach special relativity
- 10 Einstein–Podolsky–Rosen experiments
- 11 The measurement theory of Everett and de Broglie's pilot wave
- 12 Free variables and local causality
- 13 Atomic-cascade photons and quantum-mechanical nonlocality
- 14 de Broglie–Bohm, delayed-choice double-slit experiment, and density matrix
- 15 Quantum mechanics for cosmologists
- 16 Bertlmann's socks and the nature of reality
- 17 On the impossible pilot wave
- 18 Speakable and unspeakable in quantum mechanics
- 19 Beables for quantum field theory
- 20 Six possible worlds of quantum mechanics
- 21 EPR correlations and EPW distributions
- 22 Are there quantum jumps?
- 23 Against ‘measurement’
- 24 La nouvelle cuisine
6 - On wave packet reduction in the Coleman–Hepp model
Published online by Cambridge University Press: 11 April 2011
- Frontmatter
- Contents
- List of papers on quantum philosophy by J. S. Bell
- Preface to the first edition
- Acknowledgements
- Introduction: John Bell and the second quantum revolution
- 1 On the problem of hidden variables in quantum mechanics
- 2 On the Einstein–Podolsky–Rosen paradox
- 3 The moral aspect of quantum mechanics
- 4 Introduction to the hidden-variable question
- 5 Subject and object
- 6 On wave packet reduction in the Coleman–Hepp model
- 7 The theory of local beables
- 8 Locality in quantum mechanics: reply to critics
- 9 How to teach special relativity
- 10 Einstein–Podolsky–Rosen experiments
- 11 The measurement theory of Everett and de Broglie's pilot wave
- 12 Free variables and local causality
- 13 Atomic-cascade photons and quantum-mechanical nonlocality
- 14 de Broglie–Bohm, delayed-choice double-slit experiment, and density matrix
- 15 Quantum mechanics for cosmologists
- 16 Bertlmann's socks and the nature of reality
- 17 On the impossible pilot wave
- 18 Speakable and unspeakable in quantum mechanics
- 19 Beables for quantum field theory
- 20 Six possible worlds of quantum mechanics
- 21 EPR correlations and EPW distributions
- 22 Are there quantum jumps?
- 23 Against ‘measurement’
- 24 La nouvelle cuisine
Summary
Introduction
In a very elegant and rigorous paper, K. Hepp has discussed quantum measurement theory. He uses the C* algebra description of infinite quantum systems. Here an attempt is made to give a more popular account of some of his reasoning. Such an attempt seems worthwhile because many people not familiar with the C* algebra approach, and even somewhat intimidated by it, have been intrigued by the following statement in Hepp's abstract:
In several explicitly soluble models, the measurement leads to macroscopically different ‘pointer positions’ and to a rigorous ‘reduction of the wave packet’ with respect to all local observables.
This could look like a clean solution at last to the infamous measurement problem. But it is not so, nor thought by Hepp to be so. Here we will take one of his models and analyse it in elementary text-book terms. It will be insisted that the ‘rigorous reduction’ does not occur in physical time but only in an unattainable mathematical limit. It will be argued that the distinction is an important one.
We will work at first in the Schrödinger picture, but later, with the extension to relativistic systems in mind, it will be argued that such considerations become particularly clear in the Heisenberg picture.
- Type
- Chapter
- Information
- Speakable and Unspeakable in Quantum MechanicsCollected Papers on Quantum Philosophy, pp. 45 - 51Publisher: Cambridge University PressPrint publication year: 2004