Abstract
Consider a statistically-repeatable, shift-invariant system obeying an unknown probability law p(x) ≡ q2(x): Amplitude q(x) defines a source effect that is to be found. We show that q(x) may be found by considering the flow of Fisher information J → I from source effect to observer that occurs during macroscopic observation of the system. Such an observation is irreversible and, hence, incurs a general loss I - J of the information. By requiring stability of the law q(x), as well, it is found to obey a principle I − J = min. of “extreme physical information” (EPI). Information I is the same functional of q(x) for any shift-invariant system, and J is a functional defining a physical source effect that must be known at least approximately. The minimum of EPI implies that I ≈ J or received information tends to well-approximate reality. Past applications of EPI to predicting laws of statistical physics, chemistry, biology, economics and social organization are briefly described.
Highlights
Consider the epistemological question: How much can be learned about a scientific phenomenon by observing it one or, at most, a finite number of times? In particular, can it be so derived? Again, this is without necessarily using knowledge of its energy aspects T or V
An alternative variational approach to least action that does have prior significance and, in particular, does not necessarily require knowledge of energies? we find that generally disregarding energy considerations and, instead, taking an epistemological viewpoint results in the principle of extreme physical information (EPI)
In describing: (1) quantum observation of the position of a particle [6,12], J is proportional to the square of the particle’s mass; (2) cell growth, J increases with reproductive fitness [6,8,18]; (3) the growth of investment capital in econophysics, J increases as the expected value of the production function [11]; (4) cancer growth, J increases with cancer mass [6,13]; (5) the growth of competing populations, J is proportional to the mean-squared fitness over the populations [6,18]
Summary
It is often asserted that all physically-observable effects are expressions of information; or, more precisely, all observed effects are defined by flows of information to the observer. We consider any such effect that is repeatable statistically, i.e., is consistent. How is the mathematical form of the effect defined by its observation?
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