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
11 - Research topics
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
Scope
Preceding chapters have dealt with relatively elementary applications of the EPI principle. These are problems whose answers are well-established within known experimental limits. Historically, such problems constituted ‘first tests’ of the principle. As we found, EPI agreed with the established answers, albeit with several extensions and refinements. The next step in the evolution of the theory is to apply it ‘in the large’, i.e., to more difficult problem areas, those of active, current research by the physics and engineering communities.
Two such are the phenomena of (i) quantum gravity and (ii) turbulence at low Mach number. We show, next, the current status of EPI work on these problems. Aspects of the approaches that are, as yet, uncertain are pointed out in the developments. It is hoped that, with time, rigorously correct EPI approaches to the problems will ensue. It is expected that final versions of the theory will closely resemble the first ‘tries’ given below.
Quantum gravity
Introduction
The central concept of gravitational theory is the metric tensor gμν(x). (For a review, see Exercise 6.2.5 and the material preceding it.) This defines the local distortion of space at a four-coordinate x. The Einstein field Eq. (6.68) permits the metric tensor to be computed from knowledge of the gravitational source ― the stress energy tensor Tμν(Sec. 6.3.4). This is a deterministic view of gravity. That is, for a given stress energy tensor and initial conditions, a given metric tensor results. This view holds over macroscopic distances x.
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- Information
- Physics from Fisher InformationA Unification, pp. 254 - 272Publisher: Cambridge University PressPrint publication year: 1998