Damien Broderick <email@example.com> writes:
> Truly mindboggling article about the work of Roy Frieden on Fisher
> information and the basic laws of physics (there's not much abt him on the
> Web), at
> I'd like to see some informed discussion from the mathematics and
> physicists on this topic.
Interesting. The article seems severely dumbed down in places and I'm not familiar with Fisher information, but the idea sounds neat (and quite similar to what happens in the Bayesian Confidence Propagation Neural Networks I'm working with; there the network tries to minimize an "energy" based on the mutual information and entropy of the data). I'm not sure it will work out in the end, but it is a fresh way of looking at things.
Shades of Egan's _Distress_? :-)
I have not found that much of his articles on the net, but one is
Fisher's arrow of `time' in cosmological coherent phase space
Authors: B. Roy Frieden, H.C. Rosu
Comments: 10 pages, LaTex, Honorable Mention at GRF-1997 Journal-ref: Mod.Phys.Lett. A13 (1998) 39-46
Fisher's arrow of `time' in a cosmological phase space defined as in quantum optics (i.e., whose points are coherent states) is introduced as follows. Assuming that the phase space evolution of the universe starts from an initial squeezed cosmological state towards a final thermal one, a Fokker-Planck equation for the time-dependent, cosmological Q phase space probability distribution can be written down. Next, using some recent results in the literature, we derive an information arrow of time for the Fisher phase space cosmological entropy based on the Q function. We also mention the application of Fisher's arrow of time to stochastic inflation models
Here is something from the Optical Sciences Center own pages (http://www.optics.arizona.edu/News/Oscillations.asp/July.htm):
Fisher Information. A New Concept for Physics
In early April, the Center hosted the first international meeting of scientists who work with Fisher information in application to physics. Professor B. Roy Frieden, who founded the group, said the goal of the meeting was to promote research on the connection between Fisher information and basic physics.
The charter members of the Fisher Information Interest Group are (standing) Optical Sciences Center Professors Arvind Marathay and B. Roy Frieden with Bernard Soffer of Hughes, Malibu and (seated) Roy Hughes of DoD, Australia. Many members of the group believe that all of thermodynamics can be derived from the standpoint of minimum Fisher information. Roy and his colleagues will be seriously attacking this problem in the fall when another group member, Professor Angelo Plastino of the Department of Physics of the University of La Plata in Argentina, visits the Center. He will also work with Roy on Fisher temperature-and time concepts.
Fisher information is an old concept. It has been used since about 1922 to judge the quality of statistical estimates. Now it is the central concept in a new theory of measurement. This predicts that each physical phenomenon arises in response to a request for data about it. Roy explained, "The probe particle that initiates a measurement perturbs the measured particle's wave function. This perturbs the particle's Fisher information level, and initiates a variational principle whose solution and output is the probability law that produces the requested measurement. For example, the Schroedinger wave equation arises out of a request for the position of a particle. In this way, the phenomenon that is to be measured is produced `on the spot.' The result is a kind of local creation of reality. This appears to be an effect that is new to both physics and metaphysics, resembling the 'participatory universe' of Professor J.A. Wheeler."
Roy continued, "Virtually all of known physics, from relativistic quantum mechanics to statistical mechanics to quantum gravity, has been derived by this measurement approach. The local creation of reality is a microscopic effect. It arises in measuring and interacting with single elementary particles. It's reminiscent of the microscopic reversibility to time of the laws of physics. As with the latter, we don't yet know how and if `reality on demand' translates into a macroscopic effect."
A traditional measure of disorder, entropy, has provided the usual definitions of time and temperature. Said Roy, "Fisher information provides us with new definitions. They arise out of a newly discovered `H-theorem' for the information: It can only decrease with time. This makes Fisher information a measure of disorder and means that Fisher information must provide its own definitions of time and temperature. Time is defined to increase when Fisher information decreases. Intriguingly, we find that Fisher time and entropy time do not agree about 1% `of the time.' Temperature is defined as the resistance to a change in energy of the Fisher information of a system. The relationship of the Fisher temperature scale to the entropic, or conventional, temperature scale is currently not known."
B. Roy Frieden's fall 1998 course offering, Opti 529, crosslisted as Phys 529, is titled "Physics from Fisher Information, a Unification." It will show that Fisher information provides a basis for nearly all physical laws, including quantum mechanics, classical e&m theory, special and general relativity, diffraction optics, the statistical gas laws, quantum gravity, and the ubiquitous 1/f-noise power law. The textbook for the course, Physics from Fisher Information, a Unification by B. Roy Frieden will be published in December 1998 by Cambridge University Press.
B. Roy Frieden has been with the Center since 1966 and has worked with Fisher information since 1987. His research interests include digital methods of enhancing or restoring images, blind deconvolution, and the synthesis of physics using Fisher information.
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