In Part II of my series on symmetry, today, we'll take an initial look at what physicists see as the importance and usefulness of symmetry for their work. Harvard's Lisa Randall, in her book Warped Passages, writes that:
It is difficult to overstate the importance of symmetry in physical laws. Many physical theories, such as Maxwell's laws of electrodynamics and Einstein's theory of relativity, are deeply rooted in symmetry. And by exploiting various symmetries we can usually simplify the task of using theories to make physical predictions. For example, predictions of the orbital motion of the planets, the gravitational field of the universe (which is more or less rotationally symmetric), the behavior of particles in electromagnetic fields, and many other physical quantities are mathematically simpler once we take symmetry into account (pp. 193-194).
UCLA Emeritus Professor Marvin Chester has written an introduction to symmetry. In it, he quotes Nobel Laureate Leon Lederman as follows:
Fundamental symmetry principles dictate the basic laws of physics, control the st[r]ucture of matter, and define the fundamental forces in nature.
From my own layperson perspective, symmetry would appear to suggest that if we can transform "Situation A" into "Situation B" without altering important features, then we might be able to study Situations A and B with one mathematical formulation instead of two. The following quote from a University of Winnipeg webpage appears to be consistent with my thinking (although I obviously cannot claim it as an exact endorsement of my thinking):
By assuming that physical systems have, at least approximately, a high degree of symmetry, it is possible to radically simplify the equations that describe them.
In the next few postings, I will talk about how physicists and mathematicians are aided by symmetry-based formulations such as Galois groups, Lie groups, and Noether's theorem.