Background of Stevens F. Johnson's Homepage

Explanation of the Main Page Background

The Background is a tiling of a reduced-contrast version of the image below. It consists of eight Equations, of which five are Differential Equations, two are Algebraic Equations, and one (the bottom Equation) is a Result that naturally and automatically pops out of four of the five Differential Equations. A theoretical Space Physicist, Astrophysicist, or Plasma Physicist will recognize the significance of this combination: They are the foundational set of Equations of classical Plasma Physics.

Plasma Physics (which is synonomous with Plasma Engineering) is the study of matter in the plasma state. The so-called fourth state of Matter, a Plasma is basically an ionized Gas in combination with Free Electrons, where the source of those Electrons are the Atoms/Molecules of that Gas that have had one or more of their outer Electrons striped away. The resulting soup is a set of interpenetrating Fluids of Free Electrons and the left-over Ions. Since Electrons and Ions are electrically charged Particles, they create and are influenced by Electric and Magnetic Fields. The Equations prescribe the behavior of those Fluids as they interact with the Electromagnetic Fields. The reason why Space Physicists and Astrophysicists are interested in Plasmas arises from the observation that more than 99% of all the observable Matter in the Universe exists in the Plasma state (that includes interplanetary, interstellar, and intergalactic Space, in addition to Stars).

This set of Equations was selected for the background to establish the perspective that all that we are (as members and participants in the Universe) and can observe (of that Universe) is by virtue of electromagnetic phenomena. Electromagnetism is running all the time in the background of the Universe at all temporal and spatial Scales. The Speed of Light is placed at the vertex of the Triangle and at the bottom since it is the ultimate speed limit and ties together all things electromagnetic. Of course, on the truly cosmological scale, Gravity is the final arbiter, as moderated by Quantum Mechanics.

For those of you who are die-hards, the following is a more detailed but very brief description of the Equations. Alright, all in one sentence: The equation set consists of the Boltzmann Equation [top line], which controls the time evolution of the Particle Distribution Functions fn for each separate Fluid Species n of electrical particle in six-dimensional Phase Space (Electrons, Ions, and neutral Atoms); four coupled vector Partial Differential Equations (collectively called Maxwell's Equations) [second line and the first equations of the third and fourth line] that describe the relationships between the Electric Fields (E and D) and the Magnetic Fields (H and B) and their sources, the Volume Charge Density ρ and the Electrical Volume Current Density J; two Constituent Equations [second equations of the third and fourth lines] describing the relationship (1) between the Electric Field E, the Displacement Field D, and the local Polarization P of Matter (if any), and (2) between the Magnetic Field Intensity H, the Magnetic Flux Density B, and the local Magnetization M of Matter (if any); and one result [bottom equation], the Speed of Light in vacuum c in terms of the Permitivity of Free Space εo and the Permeability of Free Space μo (This is the natural result mentioned earlier that comes out of Maxwell's Equations, which indicates that light is an Electromagnetic Wave.*).

Whew! The study of Plasma Physics requires first a year's worth of study of Electromagnetic Fields and Waves (as a Junior or Senior), and an introduction to the theory of Fluid Mechanics, which is frequently combined with the introductory courses in Plasma Physics.

*This natural result marks the first time in the history of Science that a theoretical prediction came first and the experimental verification came second. As James Clerk Maxwell constructed what is now known as modern Electromagnetic Theory in the 1860's from what was experimentally known up to that time about Electric and Magnetic Fields, there had been no suspicion that Electric and Magnetic Fields had anything to do with Light. Maxwell intended simply to put all the collective (experimental) knowledge about such Fields on a solid mathematical basis. (He invented Vector Calculus and its notation as part of that effort.) One unexpected conclusion that arose from his mathematical theory was the existence of electric waves coupled with magnetic waves. These coupled Electromagnetic Waves are required to propagate at a very specific Velocity, equal to the inverse of the square root of the product of the Permitivity ε o and Permeability μ o of free space. The values of the Permitivity and Permeability were well known experimentally, but thought to be of significance only for electric and magnetic Forces. When Maxwell inserted the numerical values into the propagation velocity Equation (i.e., the bottom Equation of the triangle of Equations), out popped a value very close to the known Speed of Light, measured by completely different techniques than those for the Permitivity and Permeability. Although Light was well known by then to be a Wave, no one knew of what Light Waves could be constructed! (Water Waves are Perturbations of the surface height of a lake, and Sound Waves are Perturbations of the air pressure, for example, but no one had a clue of what Light Waves could be a Perturbation.) This strongly implied that Light is an Electromagnetic Wave. Further, Maxwell's theory predicted electromagnetic Waves of widely different frequencies, leading to the discovery Radio Waves, for example. Unfortunately, Maxwell did not live to learn of experimental verifications of his predictions, first performed by Heinrich Hertz in 1886.

James Clerk (the e in Clerk is pronounced as a long a, as in the word care) Maxwell ranks with Isaac Newton and Albert Einstein as one the best, brightest, and most influential Physicists of the past 450 years. Einstein constructed his Special Theory of Relativity from Maxwell's Electromagnetic Theory: Special Relativity is in fact buried in its entirety inside Maxwell's theory.

© 2002 Stevens F. Johnson and Dept. of Physics/Science, Bemidji State University.  All rights are reserved unless explicitly stated otherwise.

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