Christopher T. Hill received his Bachelor's and Master's degrees from M.I.T. in 1972 and completed a Ph.D. in Elementary Particle Physics at Cal Tech in 1977. After two years at the University of Chicago, he joined the Fermilab Theory Group in 1979 and is now a Scientist II at the Laboratory. His work is focused primarily upon understanding the mechanism of electroweak symmetry breaking, i.e., "why are the weak forces weak?" which he views as the most important issue in particle physics today. He has emphasized with his colleagues the possible role of heavy fermions, such as the top quark, in the electroweak symmetry breaking dynamics. He has authored more than 100 papers and review articles in elementary particle physics and cosmology. He was elected a Fellow of the American Physical Society in 1989.
Introductory Comments: SymmetryThe principles of symmetry play a fundamental, yet relatively recent (20th century) role in physics. These are generally not taught in the high school or introductory college physics and mathematics courses. Should such ideas become incorporated into the introductory physics and mathematics curriculum?
I think the answer is yes. That which attracts the beginning student to the subject of physics are the modern, relevant, highly visible end product, e.g., semiconductors, the laser, nuclear and atomic processes, superconductors, superfluids, the formation of galaxies and black holes. These represent the culmination of the long arduous process of scientific research extending over many centuries. The serious student of physics will retrace this process through the study of classical mechanics and differential equations, leading to electromagnetic theory, relativity, quantum mechanics and statistical mechanics. This process takes some six to eight years of undergraduate and graduate physics courses. Only then, if the student chooses the very abstract field study, such as theoretical physics, will he or she begin to see the fundamental role of symmetry in the basic laws of physics. Indeed, even today many practicing physicists have no idea about the concept of, e.g., non-abelian gauge invarianance, which is the basic symmetry principle underlying all known forces in nature!
I certainly do not propose, or even consider it possible, that these concepts be taught in the detailed way in which the theoretical physicist must use them to beginning students. However, it is a tragedy that these fundamental ideas are accessible only to those who follow the long road to them. These are, after all, defining principles that govern everything in the universe.
Fortunately, it is possible to incorporate some of the underlying ideas of symmetry and its relationship to nature into beginning courses in physics and mathematics. An introduction to the mathematical ideas underlying symmetry, such as the discussion of the symmetry group of the equilateral triangle (S_3), can be taught at almost any level after a course in basic algebra and geometry. It enriches the latter and can be immediately applied to simple physics problems. When the elementary courses are spiced with these ideas, they begin to take on some of the dimensions of a humanities or fine arts study: Symmetry is one of the most beautiful mathematical concepts, and its expression in nature is perhaps the most stunning aspect of our physical world.
Given the declining interest and enrollment in the subject of physics, it is imperative that significant, new and fresh ideas be incorporated into the beginning programs. Symmetry is a vehicle for maintaining the student's interest in physics at the outset and connecting to the deeper aspects of our relationship and understanding of the physical world. The answer to the question "Why teach symmetry?" is simply an equation: Physics = Symmetry = Beauty.