What is the physicists concept of symmetry?
(Submitted by Jessica Williamson, Birmingham, Alabama)A: In mathematics and physics, symmetry has a very precise and specific meaning that is related to, but narrower than, the everyday use of the word. Physicists say that something has symmetry if there are transformations that might have changed it, but in fact do not.This general formulation, which turns out to be very fruitful and powerful, may at first seem a little abstract. Some simple examples will make the meaning clear. For our transformations, we ll consider rotations of a plane around a chosen point C. What kind of geometric figures are left unchanged by all these transformations? The most basic ones are the circles centered at C; one can also combine such circles, for example to make disks or annuli. On the other hand, a square centered at C is changed by most rotations, but not by a rotation through 90°. So circles have more symmetry than squares; but squares do have significant symmetry. Illustration: Symmetry of geometr
