Knocking on Heaven's Door - Lisa Randall [17]
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. Geometrical optics, though clearly an approximation, is nonetheless a good description for a wave with wavelength small enough for interference effects to be irrelevant, and for the light to be treated as a linear ray. In other words, geometrical optics is an effective theory, valid in a limited regime.
That doesn’t mean we keep every idea that has ever been developed. Sometimes ideas are just proved wrong. Euclid’s initial description of light, resurrected in the Islamic world in the ninth century by Al-Kindi, which claimed that light was emitted by our eyes, was one such example. Although others, such as the Persian mathematician Ibn Sahl, correctly described phenomena such as refraction based on this false premise, Euclid and Al-Kindi’s theory—which predates science and modern scientific methods—was simply incorrect. It wasn’t absorbed into future theories. It was simply abandoned.
Newton didn’t anticipate a different aspect of the theory of light. He had developed a “corpuscular” theory that was inconsistent with the wave theory of light developed by his rival Robert Hooke in 1664 and Christian Huygens in 1690. The debate between them lasted a long time. In the nineteenth century, Thomas Young and Augustin-Jean Fresnel measured light interference, providing a clear verification that light had the properties of a wave.
Later developments in quantum theory demonstrated that Newton was correct in some sense too. Quantum mechanics now tells us that light is indeed composed of individual particles called photons that are responsible for communicating the electromagnetic force. But the modern theory of photons is based on light quanta, the individual particles of which light is made, that have a remarkable property. Even an individual particle of light, a photon, acts like a wave. That wave gives the probability of a single photon being found in any region of space. (See Figure 5.)
Geometrical Optics
Light travels in straight lines.
Wave Optics
Light travels in waves.
Photons
Light is transmitted by photons, particles that can act like waves.
[ FIGURE 5 ] Geometrical optics and waves were precursors to our modern understanding of light, and still apply