In his 1987 best seller Chaos: Making a New Science, science journalist James Gleick wrote, “Where chaos begins, classical science stops.” Indeed, after relativity and quantum mechanics, chaos became the 20th century’s third great revolution in physical sciences. Chaos results from the sensitivity of a nonlinear system to initial conditions, and it makes classical evolution appear random with time (see the article by Adilson Motter and David Campbell, Physics Today, May 2013, page 27). That sensitivity is the origin of Edward Lorenz’s well-known butterfly effect1—named for the idea that a butterfly flapping its wings in South America could set off a tornado in Kansas—which rules out any hope for long-term weather forecasting.
Chaotic behavior manifests in quantum and relativistic systems, and classical chaos can lead to new manifestations in systems that are both relativistic and quantum mechanical—such as graphene, whose electrons can behave like massless...
