Noether's Theorem: To every differentiable symmetry generated by local actions, there corresponds a conserved current.
Nobel laureate Leon M. Lederman and physicist Christopher T. Hill explain how modern physics is shaped by the theorem of German mathematician Emmy Noether (1882-1935) -- stating a deep correspondence between conservation laws and symmetry principles. Symmetry, they point out, is the basic underlying principle that defines the laws of nature and controls the universe. It has become one of the most reliable lodestars for scientists working on the fundamental laws governing the universe.
"Physicists in earlier times viewed the physical world as composed of 'gears and pulley,.'" the authors point out. "They tended to view symmetry as more of a sideshow, a toy, arising in an occasional situation involving a symmetrical configuration that could help simplify a specific physics problem but that played no profound role in the deeper dynamic fabric of the physical world.
"It was Albert Einstein who brought in a new kind of thinking with his development of the theory of special relativity. Einstein's perspective was modern: he sought a kind of underlying naturalness to extract the true laws of physics and discovered far deeper principles of symmetry than had been seen before. Noether's theorem was born out of this new perspective.
"The idea of underlying symmetries and Noether's theorem have led ultimately to the discovery of the unifying principle governing all the known forces in nature."
The authors endeavor to explain the elegant concept of symmetry and its profound ramifications to understanding life on Earth and the nature of the universe at large. They address topics like time, energy, spacetime, inertia, parity, quantum mechanics, and even time reversal.
This book is more topical than mathematical, however, and readers with a basic understanding of math and physics should be able to comprehend the profound importance of symmetry.
"The scientific history of the universe has been divined from countless experiments, observations, and measurements, using telescopes and microscopes (particle accelerators), ultimately synthesized into mathematics," the authors point out.
"Our intent is to show that this photograph of knowledge -- here sharp and well focused, there still fuzzy, and way over there still shrouded in total mystery -- is nonetheless governed by a universal and steadfast set of laws of physics. These laws are not yet completely understood, but they endure, govern, and control the awesome history of the universe itself."