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Science from Fisher Information: A Unification

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This is a compilation of Roy Frieden's work in major physics journals over the last decade deriving the basic laws of physics - relativistic quantum mechanics, electromagnetism, gravitation, statistical thermodynamics - from a quantity (used by mathematical statisticians and by hardly anyone else) called Fisher Information. He derives the Klein-Gordon equation, Schroedinger wave equations, Maxwell's equations, DeWitt-Wheeler law of quantum gravity, and various statistical thermodynamics laws. Whew. Basically, while folks have focused in the past on Shannon information and entropy (all global measures), Frieden's worked on Fisher information which is a local measure (e.g. based on a derivative). Optimization of functionals of Fisher information gives differential equations as results, which become laws of physics. Cute.

Anyone with a Bachelors in Engineering would have been exposed to enough physics to understand what Frieden has done. The mathematics is at senior-level math/grad level engineering level. Well-written and not at all cryptic, Frieden goes out of his way to motivate his arguments. In fact, Roy spends 100 pages in preparation and discussion before he even gets to his first real derivation.

Operations Researchers (like me), Applied Mathematicians, EE Control Theory types and Statisticians will find the mathematics pretty comfortable...even if we don't understand all the physics implications. Philosophical types with strong math backgrounds can profitably wade through the text just to get a flavor of his arguments.

Cambridge *really* wanted to publish this textbook. They even included Frieden's umm..errr...interesting pencil sketches of himself and other luminaries. Check out the New Scientist archives for an article in January 1999 on Frieden's work.

One warning. This is *not* light reading. Those looking for the "Tao of Fisher Information" will have to wait for some of us to write a pop sci version of his work. If you want to get a feeling for Frieden's work before you buy the book, read the articles "Estimation of distribution laws, and physical laws, by a principle of extremized physical information", Physica A, 198 (1993) 262-338 or "Lagrangians of physics and the game of Fisher-information transfer", Phys Rev E, 52(3), Sept 1995, 2274-2286.

If, like me, you're fed up with popular science books which are too scared to include equations, I expect you'll find this as enormously challenging, stimulating and satisfying as I did.

The author interprets all physical measurement as extraction of Fisher information from the object being measured. From this he derives, for example, the Heisenberg uncertainty principle as a special case of the Cramer-Rao lower bound. By assuming, in addition, conservation of charge he derives Maxwell's equations and, similarly, from conservation of momentum he derives general relativity. He also derives - - amongst others! - - classical thermodynamics, and the Klein-Gordon equation (relativistic generalization of Schrodinger equation).

He also uses his theory to make predictions, such as that the neutrino has mass >0, and that the rate of change of entropy has a finite upper bound (as well as the lower bound of zero). Towards the end of the book are chapters on less physical topics including financial markets and cancer growth.

It wasn't easy going, even with a degree in maths (more knowledge of tensors would've helped), but the way he derives such a frankly amazing amount from so few premises convinces me that he is on to something important.

"Physics from Fisher Information" is a unification, indeed. The author derives the physical laws for such different fields as quantum mechanics, classical electromechanics, general relativity and statistical mechanics from the single powerful principle of Extreme Physical Information (EPI). This principle probably goes deeper than merely a mathematical similarity between the laws, which as such already helps to grasp the full picture of physics. Personally, I think it's a pity this clarifying book was not written yet when I was a student of physics. To miss this book, is to miss something essential.

"Physics from Fisher Information" is a unification, indeed. The author derives the physical laws for such different fields as quantum mechanics, classical electromechanics, general relativity and statistical mechanics from the single powerful principle of Extreme Physical Information (EPI). This principle probably goes deeper than merely a mathematical similarity between the laws, which as such already helps to grasp the full picture of physics. Personally, I think it's a pity this clarifying book was not written yet when I was a student of physics. To miss this book, is to miss something essential.

I was very excited at the first eyedrop in this book.

But having read half of it, I asked myself: what did I learn and is it worth to continue the reading.
What I learned is the definition of the Fisher information matrix and the eventuality that the laws of physics are woven with the thread of information. But I stopped reading further.

I had the bad feeling that the author greatly overstates his case.
It was nearly clear for me that all applications of the supposed theory where built on a simple canvas:

- rename the two terms of the Lagrangian as 'Fisher information' and 'physical information'
- and rename further the least-action-principle as 'EPI' (Extreme Physical Information)

Still, I think the subject is interresting and I may myself give it a second chance.
Therefore it is a good buy only if you can accept some disappointement and if you hope to go further by yourself.

R. F. Streater has a website listing "Lost Causes in Theoretical Physics." Physics from Fisher Information is number 7 on the list.

This review refers to the 1998 edition of the book, ISBN 0 521 63167 X hardback.

I had originally gotten excited when I found this book. However:

The author sums it best in the last sentence of the book (P282). I quote him thanking "E.M.Wright, for bringing to my attention many aspects of modern quantum theory, especially its wonderful mysteries and paradoxes, bringing me up to date on the subject of measurement theory, and (hopefully) constraining my enthusiastic forays of theory to stay within physical bounds".

I cant help wonder at attempting to associate with fame: J.A. Wheeler (P2), R.A. Fisher (P23), L. Brillouin (P66). Are the photos a lead up to justify the inclusion of the author's portrait (P73) ?

I started getting concerned for the veracity of the author's "science" with the use an anthropic argument (P218). For example, stating "Thus, the values of (universal) constants are somehow scaled to accommodate the presence of human beings. This is flattering if true: it means that our presence has a profound - if indirect - effect upon physical laws and, hence, the Universe!", (his exclamation mark, not mine).

On a more basic level, there was no nomenclature list for variables used in equations throughout the text. However the maths was presented at a good level.

Readers interested in B. Roy Frieden may like to search out more information using Wikipedia

The essence of really great theoretical physics is that it creates new insights and makes novel, experimentally verifiable predictions that take us in new directions, capabilities and understanding.

And that is what is missing from Frieden's work, thoroughly reviewed here - it just re-derives well-established standard-physics results from a different angle, but doesn't lead into new pastures - or at least, not yet... So what?

Must try harder; 'me too' is simply not good enough.

With my advanced copy of this wonderful book, I can truly say that all physics ends here. I foresee every field of science laying down their texts and proclaiming this one as the end all be all. A must read for anyone.