Knocking on Heaven's Door by Lisa Randall Read Free Book Online

astronomy, and is used to develop new mirrors, telescopes, and microscopes. Classical optical scientists and engineers work out different examples of various physical phenomena. However, they are simply applying optics—not discovering new laws.
    In 2009, I was honored to be asked to give the Hamilton lecture at the University of Dublin—a lecture several of my most respected colleagues had given before me. It is named after Sir William Rowan Hamilton, the remarkable nineteenth-century Irish mathematician and physicist. I confess that the name Hamilton is so universally present in physics that I foolishly didn’t initially make the connection with an actual person who was in fact Irish. But I was fascinated by the many areas of math and physics that Hamilton had revolutionized, including, among them, geometrical optics.
    The celebration of Hamilton Day is really quite something. The day’s activities include a procession down the Royal Canal in Dublin where everyone stops at the Broom Bridge to watch the youngest member of the party write down the same equations on the bridge that Hamilton, in the excitement of discovery, had many years past carved into the bridge’s side. I visited the College Observatory of Dunsink where Hamilton lived and got to see the pulleys and wooden structure of a telescope from two centuries ago. Hamilton arrived there after his graduation from Trinity College in 1827, when he was made the chair of astronomy and Astronomer Royal of Ireland. Locals joke that despite Hamilton’s prodigious mathematical talent, he had no real knowledge of or interest in astronomy, and that despite his many theoretical advances, he might have set back observational astronomy in Ireland fifty years.
    Hamilton Day nonetheless pays homage to this great theorist’s many accomplishments. These included advances in optics and dynamics, the invention of the mathematical theory of quaternions (a generalization of complex numbers), as well as definitive demonstrations of the predictive power of math and science. The development of quaternions was no small advance. Quaternions are important for vector calculus, which underlies the way we mathematically study all three-dimensional phenomena. They are also now used in computer graphics and hence in the entertainment industry and video games. Anyone with a PlayStation or Xbox can thank Hamilton for some of the fun.
    Among his numerous and substantial contributions, Hamilton significantly advanced the field of optics. In 1832, he showed that light falling at a certain angle on a crystal that has two independent axes would be refracted to form a hollow cone of emergent rays. He thereby made predictions about internal and external conical refraction of light through a crystal. In a tremendous—and perhaps the first—triumph of mathematical science, this prediction was verified by Hamilton’s friend and colleague Humphrey Lloyd. It was a very big deal to see verified a mathematical prediction of a never-before-seen phenomenon and Hamilton was knighted for his achievement.
    When I visited Dublin, the locals proudly described this mathematical breakthrough—worked out purely on the basis of geometrical optics. Galileo helped pioneer observational science and experiments, and Francis Bacon was an initial advocate of inductive science —where one predicts what will happen based on what came before. But in terms of using math to describe a never-before-seen phenomenon, Hamilton’s prediction of conical refraction was probably the first. For this reason, at the very least, Hamilton’s contribution to the history of science is not to be ignored.
    Nonetheless, despite the significance of Hamilton’s discovery, classical geometrical optics is no longer a research subject. All the important phenomena were worked out long ago. Soon after Hamilton’s time, in the 1860s, the Scottish scientist James Clerk Maxwell, among others, developed the electromagnetic description of light.