Art Hobson

A new theorem of information theory

Consider a random experiment whose possible outcomes arez1,z2,...,zn. Let the prior probabilities be p10, ...,pn0, and let the posterior probabilities bep1,...,pn. It is shown that, subject to certain prescribed and intuitively reasonable conditions, the expressionI =k ⌆ pi In (pi/pi0), wherek is a positive constant, is the unique expression for the information contained in a message which alters the probabilities from thepi0 to thepi.

A Comparison of the Shannon and Kullback Information Measures

Two widely used information measures are compared. It is shown that the Kullback measure, unlike the Shannon measure, provides the basis for a consistent theory of information which extends to continuous sample spaces and to nonconstant prior distributions. It is shown that the Kullback measure is a generalization of the Shannon measure, and that the Kullback measure has more reasonable additivity properties than does the Shannon measure. The results lend support to Jayness entropy maximization procedure.

There are no particles, there are only fields

Quantum foundations are still unsettled, with mixed effects on science and society. By now it should be possible to obtain consensus on at least one issue: Are the fundamental constituents fields or particles? As this paper shows, experiment and theory imply that unbounded fields, not bounded particles, are fundamental. This is especially clear for relativistic systems, implying that its also true of nonrelativistic systems. Particles are epiphenomena arising from fields. Thus, the Schrodinger field is a space-filling physical field whose value at any spatial point is the probability amplitude for an interaction to occur at that point. The field for an electron is the electron; each electron extends over both slits in the two-slit experiment and spreads over the entire pattern; and quantum physics is about interactions of microscopic systems with the macroscopic world rather than just about measurements. Its important to clarify this issue because textbooks still teach a particles- and measurement-orien...

Irreversibility and Information in Mechanical Systems

Concepts from information theory are used to investigate the relation between measurement and irreversibility in finite, closed classical systems having known Hamiltonians. The effects of measurement upon the predictions of the observer are found for the cases of a single measurement, two simultaneous measurements, and two measurements at different times. The physical basis of coarse graining and the significance of the increase in the coarse‐grained entropy are discussed. An evolution equation is obtained describing the probability distribution of the measured quantities, and it is shown that this equation is non‐Markoffian. Despite this non‐Markoffian behavior, the distribution may behave irreversibly and may approach equilibrium. Thus, irreversible behavior is obtained without continual coarse graining. The condition for irreversible behavior is given for the case of a single measurement. The thermodynamic entropy is defined for general nonequilibrium situations.

Electrons as field quanta: A better way to teach quantum physics in introductory general physics courses

I propose a conceptual change in the way we teach nonrelativistic quantum physics in introductory survey courses and general modern physics courses. Traditional instruction treats radiation as a quantized electromagnetic wave that, because it is quantized, is observable only as discrete field quanta, while treating matter as particles that are accompanied by a wave function. In other words, traditional instruction views radiation as fundamentally a field phenomenon, and matter as fundamentally a particle phenomenon. But quantum field theory has a more unified view, according to which both radiation and matter are continuous fields while both photons and material particles are quanta of these fields. The quantum field theory view of radiation and matter clarifies particle identity issues, dispels students’ Newtonian misconceptions about matter, arguably resolves the wave-particle paradox, is the accepted view of contemporary physics, and might be the simplest and most effective teaching approach for all st...

Irreversibility in Simple Systems

In order to illustrate some of the basic principles of statistical mechanics, a study is made of the nonequilibrium behavior of a one-dimensional particle confined to a finite box with perfectly reflecting walls. The statistical aspects of the analysis are due to the incompleteness of the initial information. Liouvilles equation is solved exactly and completely, and it is shown that this finite, isolated, reversible system exhibits irreversible statistical behavior. By applying information theory to the results obtained, it is shown that the irreversibility exhibited by this system consists in the information becoming less relevant to the experiments which can be performed on the system.

The Surprising Effectiveness of College Scientific Literacy Courses

Research by Jon Miller, professor of Interdisciplinary Studies and director of the International Center for Scientific Literacy at Michigan State University, shows that the U.S. scientific literacy course requirements for nonscience college students pull the United States into second place in international rankings of adult scientific literacy. This despite the poor science scores of U.S. primary and secondary school students as compared with other nations. The far lower adult scientific literacy rankings of most European nations and other industrialized nations appear to be due to the lack of any such college scientific literacy requirement in those nations. Instituting such a requirement in all nations, and improving the quality and quantity of such courses on U.S. campuses, would increase global scientific literacy significantly, arguably doubling Europes scientific literacy rate. In view of this result and todays crying need for scientific literacy, physics educators should make physics for nonscientists their top priority.

Ergodic properties of a particle moving elastically inside a polygon

The flow of a classical particle bouncing elastically inside an arbitrary polygon is investigated. If every interior angle is a rational multiple of π, there exists precisely one isolating integral in addition to the energy; this integral is described in detail; any possible third integral is nonisolating. If one or more interior angles is an irrational multiple of π, the second integral becomes everywhere nonisolating and non‐Lebesgue‐measurable, i.e., the second integral disappears. The flow of two hard points bouncing elastically in a finite one‐dimensional box is equivalent to the flow of a point particle moving elastically inside a right triangle having interior angle tan−1 (m2/m1)1/2, so the preceding remarks apply to this model. Nonrigorous arguments are given in support of the notion that the polygon model is ergodic and mixing, but is not a C‐system.

Teaching Quantum Physics without Paradoxes.

Although the resolution to the wave-particle paradox has been known for 80 years,1,2 it is seldom presented. Briefly, the resolution is that material particles and photons are the quanta of extended spatially continuous but energetically quantized fields. But because the resolution resides in quantum field theory and is not usually spelled out in ordinary language, it is neither generally understood nor generally taught, especially not in the context of nonrelativistic quantum physics. The purpose of this paper is to provide that resolution and to suggest that we teach introductory quantum physics from this viewpoint.

Physics literacy, energy and the environment

Socially aware science literacy courses are sorely needed in every nation that is industrialized and democratic. This article puts societal topics into the more general context of science literacy, suggests that socially significant topics can fit comfortably into a physics literacy course, looks at energy and environment issues, and discusses how one might teach three such issues: energy use in transportation, global ozone depletion and global warming.