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Bernard Roy Frieden (born September 10, 1936) is an American mathematical physicist.
Frieden obtained a Ph.D. in optics from The Institute of Optics at the University of Rochester. His doctoral thesis advisor was Robert E. Hopkins. Frieden is now an emeritus professor of optical sciences at the University of Arizona.
Frieden is best known for his extensive work on Fisher information as a grounding principle for deriving and elaborating physical theory. (Examples are the Schrödinger wave equation of quantum mechanics and the Maxwell–Boltzmann distribution of statistical mechanics.) Such theories take the form of differential equations or probability distribution functions.
Central to Frieden's derivations is the mathematical variational principle of extreme physical information (EPI). This principle builds on the well-known idea that the observation of a "source" phenomenon is never completely accurate. That is, information is inevitably lost in transit from source to observation. Furthermore, the random errors that creep in are presumed to define the distribution function of the source phenomenon. As Frieden puts it, "the physics lies in the fluctuations." Finally, the information loss may be shown to be an extreme value. Thus if the observed level of Fisher information in the data has value I, and the level of Fisher information that existed at the source has value J, the EPI principle states that I − J = extremum. In most situations, the extremum is a minimum, meaning that there is a tendency for any observation to faithfully match up with its source.
Applications
Frieden has used Fisher information and the EPI principle to derive most existing fundamental laws of physics, and some new and existing laws of biology, cancer growth, chemistry, and economics. Frieden argues that Fisher information, especially its loss I − J during observation, and EPI make up a general method for deriving scientific laws.
Criticism
There is a view that puts into doubt the physical and mathematical correctness of Frieden's ideas, this coming from Raymond F. Streater's Lost Causes in Theoretical Physics: Physics from Fisher Information (2003), and Cosma Shalizi's review (2000) of Physics from Fisher Information.
D.A. Lavis and R.F. Streater in their review[1] write:
In trying to evaluate the success of this project it is reasonable, as in the case of Jaynes, to distinguish questions of philosophical predilection from those of method. We shall mainly concentrate on the latter, and within this brief we try to answer two questions:
- Does the method of extreme physical information appear to be a promising approach to physics?
- Has Frieden provided a persuasive account of its use?
If we were convinced that the answer to (1) were clearly negative, we should be wasting our time writing this review. However, it seems to us that there may be something interesting here.
— Lavis and Streater, ESSAY REVIEW: Physics from Fisher Information (2002)
They also write:
The application of the ideas of information theory to physics is interesting; and the use of Fisher information to provide the gradient terms in the Lagrangian for a variational procedure is of some importance. The crucial step, however, is to provide in some rational and widely-applicable manner the remaining terms of the Lagrangian. Frieden believes he is able to do this by using the idea of bound information.
We have shown, however, that there are errors in his procedure, both at the level of the derivation of the defining equations (14) and (16) and also in particular applications. In the case of the latter we have not discussed all the systems contained in the book. We thought it was more useful to deal in greater depth with some particular cases; similar difficulties can be uncovered in the other chapters. We regret to say that we find this book to be fundamentally flawed in both its overall concept and mathematical detail. It cannot be read as a textbook providing a valid approach to physics.
It could, perhaps, however, be a source of stimulation for some new and interesting work.
— Lavis and Streater, ESSAY REVIEW: Physics from Fisher Information (2002)
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