This book defines and develops a unifying principle of physics, that of 'extreme physical information'. The information in question is, perhaps surprisingly, not Shannon or Boltzmann entropy but, rather, Fisher information, a simple concept little known to physicists. Both statistical and physical properties of Fisher information are developed. This information is shown to be a physical measure of disorder, sharing with entropy the property of monotonic change with time. The information concept is applied 'phenomenally' to derive most known physics, from statistical mechanics and thermodynamics to quantum mechanics, the Einstein field equations, and quantum gravity. Many new physical relations and concepts are developed, including new definitions of disorder, time and temperature. The information principle is based upon a new theory of measurement, one which incorporates the observer into the phenomenon that he/she observes. The 'request' for data creates the law that, ultimately, gives rise to the data. The observer creates his or her local reality.
This book defines and develops a unifying principle of physics, that of 'extreme physical information'. The information in question is, perhaps surprisingly, not Shannon or Boltzmann entropy but, rather, Fisher information, a simple concept little known to physicists. Both statistical and physical properties of Fisher information are developed. This information is shown to be a physical measure of disorder, sharing with entropy the property of monotonic change with time. The information concept is applied 'phenomenally' to derive most known physics, from statistical mechanics and thermodynamics to quantum mechanics, the Einstein field equations, and quantum gravity. Many new physical relations and concepts are developed, including new definitions of disorder, time and temperature. The information principle is based upon a new theory of measurement, one which incorporates the observer into the phenomenon that he/she observes. The 'request' for data creates the law that, ultimately, gives rise to the data. The observer creates his or her local reality.
This book defines and develops a unifying principle of physics, that of 'extreme physical information'. The information in question is, perhaps surprisingly, not Shannon or Boltzmann entropy but, rather, Fisher information, a simple concept little known to physicists. Both statistical and physical properties of Fisher information are developed. This information is shown to be a physical measure of disorder, sharing with entropy the property of monotonic change with time. The information concept is applied 'phenomenally' to derive most known physics, from statistical mechanics and thermodynamics to quantum mechanics, the Einstein field equations, and quantum gravity. Many new physical relations and concepts are developed, including new definitions of disorder, time and temperature. The information principle is based upon a new theory of measurement, one which incorporates the observer into the phenomenon that he/she observes. The 'request' for data creates the law that, ultimately, gives rise to the data. The observer creates his or her local reality.
Knowledge of Fisher information is not part of the educational background of most physicists. Why should a physicist bother to learn about this concept? Surely the (related) concept of entropy is sufficient to describe the degree of disorder of a given phenomenon. These important questions may be answered as follows. (a) The point made about entropy is true, but does not go far enough. Why not seek a measure of disorder whose variation derives the phenomenon? The concept of entropy cannot do this, for reasons discussed in Sec. 1.3. Fisher information will turn out to be the appropriate measure of disorder for this purpose. (b) Why should a physicist bother to learn this concept? Aside from the partial answer in (a): (i) Fisher information is a simple and intuitive concept. As theories go, it is quite elementary. To understand it does not require mathematics beyond differential equations. Even no prior knowledge of statistics is needed: this is easy enough to learn ‘on the fly’. The derivation of the defining property of Fisher information, in Sec. 1.2.3, is readily understood. (ii) The subject has very little specialized jargon or notation. The beginner does not need a glossary of terms and symbols to aid in its understanding. (iii) Most importantly, once understood, the concept gives strong payoff – one might call it ‘phenomen-all’ – in scope of application. It's simply worth learning.
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.
Aims of the book The primary 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 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. The measurement theory is simply a description of how Fisher information flows from a physical source effect to a data space. It therefore applies to all scenarios where quantitative data from repeatable experiments may be collected. This describes measurement scenarios of physics but, also, of science in general. The theory of measurement is found to define an analytical procedure for deriving all laws of science. The approach is called EPI, for “extreme physical information.” The secondary aim of the book is to show, by example, that most existing laws of science fit within the EPI framework. That is, they can be derived by its use. (Many can of course be derived by other approaches, but, apparently, no other single approach can derive all of them.) In this way the EPI approach unifies science under an umbrella of measurement and information.
Consider an isolated statistical system specified by a coordinate x and its probability density p(x). A functional of p(x) called ``Fisher information'' can be used to measure the degree of disorder of the system due to the spread in p(x). Fisher information may be minimized, subject to a physical constraint, to attain a temporal equilibrium solution p(x). When the constraint is linear in the mean kinetic energy of the system, the equilibrium solution p(x) often obeys the correct differential equation for the system. In this way, the Schr\"odinger (energy) wave equation, Klein-Gordon equation, Helmholtz wave equation, diffusion equation, Boltzmann law, and Maxwell-Boltzmann law may be derived from one classical principle of disorder. The convergence rate for Fisher information is about that for alternative use of maximum entropy (in problems where both have the same equilibrium solution). This suggests that Fisher information defines an arrow of time. The arrow points in the direction of decreasing accuracy for the determination of the mean, or ideal, value of a parameter.
Consider a finite-sized, multidimensional system in parameter state a. The system is either at statistical equilibrium or general nonequilibrium, and may obey either classical or quantum physics. L. Hardy's mathematical axioms provide a basis for the physics obeyed by any such system. One axiom is that the number N of distinguishable states a in the system obeys N=max. This assumes that N is known as deterministic prior knowledge. However, most observed systems suffer statistical fluctuations, for which N is therefore only known approximately. Then what happens if the scope of the axiom N=max is extended to include such observed systems? It is found that the state a of the system must obey a principle of maximum Fisher information, I=I(max). This is important because many physical laws have been derived, assuming as a working hypothesis that I=I(max). These derivations include uses of the principle of extreme physical information (EPI). Examples of such derivations were of the De Broglie wave hypothesis, quantum wave equations, Maxwell's equations, new laws of biology (e.g., of Coulomb force-directed cell development and of in situ cancer growth), and new laws of economic fluctuation and investment. That the principle I=I(max) itself derives from suitably extended Hardy axioms thereby eliminates its need to be assumed in these derivations. Thus, uses of I=I(max) and EPI express physics at its most fundamental level, its axiomatic basis in math.