Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Wave functions
- 3 Linear algebra in Dirac notation
- 4 Physical properties
- 5 Probabilities and physical variables
- 6 Composite systems and tensor products
- 7 Unitary dynamics
- 8 Stochastic histories
- 9 The Born rule
- 10 Consistent histories
- 11 Checking consistency
- 12 Examples of consistent families
- 13 Quantum interference
- 14 Dependent (contextual) events
- 15 Density matrices
- 16 Quantum reasoning
- 17 Measurements I
- 18 Measurements II
- 19 Coins and counterfactuals
- 20 Delayed choice paradox
- 21 Indirect measurement paradox
- 22 Incompatibility paradoxes
- 23 Singlet state correlations
- 24 EPR paradox and Bell inequalities
- 25 Hardy's paradox
- 26 Decoherence and the classical limit
- 27 Quantum theory and reality
- Bibliography
- References
- Index
17 - Measurements I
Published online by Cambridge University Press: 10 December 2009
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Wave functions
- 3 Linear algebra in Dirac notation
- 4 Physical properties
- 5 Probabilities and physical variables
- 6 Composite systems and tensor products
- 7 Unitary dynamics
- 8 Stochastic histories
- 9 The Born rule
- 10 Consistent histories
- 11 Checking consistency
- 12 Examples of consistent families
- 13 Quantum interference
- 14 Dependent (contextual) events
- 15 Density matrices
- 16 Quantum reasoning
- 17 Measurements I
- 18 Measurements II
- 19 Coins and counterfactuals
- 20 Delayed choice paradox
- 21 Indirect measurement paradox
- 22 Incompatibility paradoxes
- 23 Singlet state correlations
- 24 EPR paradox and Bell inequalities
- 25 Hardy's paradox
- 26 Decoherence and the classical limit
- 27 Quantum theory and reality
- Bibliography
- References
- Index
Summary
Introduction
I place a tape measure with one end on the floor next to a table, read the height of the table from the tape, and record the result in a notebook. What are the essential features of this measurement process? The key point is the establishment of a correlation between a physical property (the height) of a measured system (the table) and a suitable record (in the notebook), which is itself a physical property of some other system. It will be convenient in what follows to think of this record as part of the measuring apparatus, which consists of everything essential to the measuring process apart from the measured system. Human beings are not essential to the measuring process. The height of a table could be measured by a robot. In the modern laboratory, measurements are often carried out by automated equipment, and the results stored in a computer memory or on magnetic tape, etc. While scientific progress requires that human beings pay attention to the resulting data, this may occur a long time after the measurements are completed.
In this and the next chapter we consider measurements as physical processes in which a property of some quantum system, which we shall usually think of as some sort of “particle”, becomes correlated with the outcome of the measurement, itself a property of another quantum system, the “apparatus”. Both the measured system and the apparatus which carries out the measurement are to be thought of as parts of a single closed quantum mechanical system. This makes it possible to apply the principles of quantum theory developed in earlier chapters.
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- Chapter
- Information
- Consistent Quantum Theory , pp. 228 - 242Publisher: Cambridge University PressPrint publication year: 2001