Book contents
- Frontmatter
- Contents
- 0 Introduction
- 1 What is Fisher information?
- 2 Fisher information in a vector world
- 3 Extreme physical information
- 4 Derivation of relativistic quantum mechanics
- 5 Classical electrodynamics
- 6 The Einstein field equation of general relativity
- 7 Classical statistical physics
- 8 Power spectral 1/f noise
- 9 Physical constants and the 1/x probability law
- 10 Constrained-likelihood quantum measurement theory
- 11 Research topics
- 12 Summing up
- Appendix A Solutions common to entropy and Fisher I-extremization
- Appendix B Cramer–Rao inequalities for vector data
- Appendix C Cramer–Rao inequality for an imaginary parameter
- Appendix D Simplified derivation of the Schroedinger wave equation
- Appendix E Factorization of the Klein–Gordon information
- Appendix F Evaluation of certain integrals
- Appendix G Schroedinger wave equation as a non-relativistic limit
- Appendix H Non-uniqueness of potential A for finite boundaries
- References
- Index
0 - Introduction
Published online by Cambridge University Press: 30 January 2010
- Frontmatter
- Contents
- 0 Introduction
- 1 What is Fisher information?
- 2 Fisher information in a vector world
- 3 Extreme physical information
- 4 Derivation of relativistic quantum mechanics
- 5 Classical electrodynamics
- 6 The Einstein field equation of general relativity
- 7 Classical statistical physics
- 8 Power spectral 1/f noise
- 9 Physical constants and the 1/x probability law
- 10 Constrained-likelihood quantum measurement theory
- 11 Research topics
- 12 Summing up
- Appendix A Solutions common to entropy and Fisher I-extremization
- Appendix B Cramer–Rao inequalities for vector data
- Appendix C Cramer–Rao inequality for an imaginary parameter
- Appendix D Simplified derivation of the Schroedinger wave equation
- Appendix E Factorization of the Klein–Gordon information
- Appendix F Evaluation of certain integrals
- Appendix G Schroedinger wave equation as a non-relativistic limit
- Appendix H Non-uniqueness of potential A for finite boundaries
- References
- Index
Summary
Aim of the book
The overall aim of this book is to develop a theory of measurement that incorporates the observer into the phenomenon under measurement. By this theory, the observer becomes both a collector of data and an activator of the physical phenomenon that gives rise to the data. These ideas have probably been best stated by J. A. Wheeler (1990), (1994):
All things physical are information-theoretic in origin and this is a participatory universe … Observer participancy gives rise to information; and information gives rise to physics.
The measurement theory that will be presented is largely, in fact, a quantification of these ideas. However, the reader might be surprised to find that the ‘information’ that is used is not the usual Shannon or Boltzmann entropy measures, but one that is relatively unknown to physicists, that of R. A. Fisher.
During the same years that quantum mechanics was being developed by Schroedinger (1926) and others, the field of classical measurement theory was being developed by R. A. Fisher (1922) and co-workers (see Fisher Box, 1978, for a personal view of his professional life). According to classical measurement theory, the quality of any measurement(s) may be specified by a form of information that has come to be called Fisher information.Since these formative years, the two fields - quantum mechanics and classical measurement theory - have enjoyed huge success in their respective domains of application. And until recent times it has been presumed that the two fields are distinct and independent.
- Type
- Chapter
- Information
- Physics from Fisher InformationA Unification, pp. 1 - 21Publisher: Cambridge University PressPrint publication year: 1998