Book contents
- Frontmatter
- Contents
- A MEASUREMENT IN QUANTUM MECHANICS
- 1 Role of the observer in quantum theory
- 2 Approximate measurement in quantum mechanics
- 3 Proposed neutron interferometer test of some nonlinear variants of wave mechanics
- 4 Desiderata for a modified quantum dynamics
- 5 Filters with infinitely many components
- 6 Proposed neutron interferometer observation of the sign change of a spinor due to 2π precession
- B QUANTUM ENTANGLEMENT AND NONLOCALITY
- C COMPLEX SYSTEMS
- D TIME
- E THE MENTAL AND THE PHYSICAL
- Index
2 - Approximate measurement in quantum mechanics
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- A MEASUREMENT IN QUANTUM MECHANICS
- 1 Role of the observer in quantum theory
- 2 Approximate measurement in quantum mechanics
- 3 Proposed neutron interferometer test of some nonlinear variants of wave mechanics
- 4 Desiderata for a modified quantum dynamics
- 5 Filters with infinitely many components
- 6 Proposed neutron interferometer observation of the sign change of a spinor due to 2π precession
- B QUANTUM ENTANGLEMENT AND NONLOCALITY
- C COMPLEX SYSTEMS
- D TIME
- E THE MENTAL AND THE PHYSICAL
- Index
Summary
This is the first of two papers showing that the quantum problem of measurement remains unsolved even when the initial state of the apparatus is described by a statistical operator and when the results of measurement have a small probability of being erroneous. A realistic treatment of the measurement of observables of microscopic objects (e.g., the position or the spin of an electron) by means of observables of macroscopic apparatus (e.g., the position of a spot on a photographic plate) requires the consideration of errors. The first paper considers measurement procedures of the following type: An initial eigenstate of the object observable leads to a final statistical operator of the object plus apparatus which describes a mixture of “approximate” eigenstates of the apparatus observable. It is proved that each of a large class of initial states leads to a final statistical operator which does not describe any mixture containing even one “approximate” eigenstate of the apparatus observable.
INTRODUCTION
Several writers have tried to solve the quantum-mechanical problem of measurement through one or both of the following proposals: (a) describthe initial state of the measuring apparatus by a projection onto a subspace of the associated Hilbert space or by a statistical operator, thus taking into account the practical impossibility of knowing the exact quantum state of a macroscopic object; (b) recognizing that there may be some physical inaccuracy, such as a small error in the position of a pointer needle, in the final registration of the outcome of the measurement by the apparatus.
- Type
- Chapter
- Information
- The Search for a Naturalistic World View , pp. 34 - 47Publisher: Cambridge University PressPrint publication year: 1993