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29 August 2003

Outstanding in Their Fields

by George Hrabovsky, President of MAST

News from MAST

Due to scheduling conflicts we were unable to have our meeting this month!

Three Fields and Their Coupling

Last week for the Theory Challenge I asked for opinions as to where to go next. I now see that my choices were impish. Electromagnetism and relativity are intimately related and I will lump them together under the title of Classical Field Theory.

So, then, we are doing field theory right? Field theory, hmmmm. Okay, what is a field? We have discussed this before, but it was a long time ago. If we are considering a region to have some property such that the property is present everywhere in the region then it is a field. If, for example, we are measuring temperature at every point on a metal plate, that is a temperature field; or more generally it is a scalar field. If we are measuring the velocity of wind over the same metal plate, then we are measuring the wid field; or more generally a vector field. If we are measuring the moment of inertia of the metal plate then we are measuring the inertia field; or more generally a tensor field.

Some fields seem to produce a somewhat weird and generally disturbing effect. These fields allow something to influence something else at great distances without touching. This is called action at a distance.

The most familiar field is generated by the accumulation of mass. An attractive force between masses is exerted that is inversely proportional to the distance between the masses. This is called the gravitational field and it can be seen to couple masses together at great distances.

There is an analogy to mass in electricity. This analogy comes in two kinds, what we call positive and negative. This analogy is called charge. Like kinds of charge repel and opposites attract. The accumulation of charges creates the electric field. This is also an inverse square field.

There is also an analogy to mass in magnetism. This analogy comes is called current and represent the motion of charges through a volume of space. The accumulation of currents creates the magnetic field. This is also an inverse square field.

Over the weeks (or more probably months) to come we will explore electric, magnetic, and gravitational fields. This journey will lead us into the humble resistor, we will glimpse the dawning of quantum mechanics in the heart of magnetism, we will explore how electricity and magnetism are inevitably intertwined in the realm of special relativity, we will learn that gravitation is best viewed geometrically, and will even plumb the depths of black holes. I hope you all join me as we finish up with classical physics.

Theory Challenge

For what we are about to receive I will give you all a break this week.

Created by Mathematica (August 28, 2003)