Chaos - James Gleick [61]
Like so much of chaos itself, phase transitions involve a kind of macroscopic behavior that seems hard to predict by looking at the microscopic details. When a solid is heated, its molecules vibrate with the added energy. They push outward against their bonds and force the substance to expand. The more heat, the more expansion. Yet at a certain temperature and pressure, the change becomes sudden and discontinuous. A rope has been stretching; now it breaks. Crystalline form dissolves, and the molecules slide away from one another. They obey fluid laws that could not have been inferred from any aspect of the solid. The average atomic energy has barely changed, but the material—now a liquid, or a magnet, or a superconductor—has entered a new realm.
Günter Ahlers, at AT&T Bell Laboratories in New Jersey, had examined the so-called superfluid transition in liquid helium, in which, as temperature falls, the material becomes a sort of magical flowing liquid with no perceptible viscosity or friction. Others had studied superconductivity. Swinney had studied the critical point where matter changes between liquid and vapor. Swinney, Ahlers, Pierre Bergé, Jerry Gollub, Marzio Giglio—by the middle 1970s these experimenters and others in the United States, France, and Italy, all from the young tradition of exploring phase transitions, were looking for new problems. As intimately as a mail carrier learns the stoops and alleys of his neighborhood, they had learned the peculiar signposts of substances changing their fundamental state. They had studied a brink upon which matter stands poised.
The march of phase transition research had proceeded along stepping stones of analogy: a nonmagnet-magnet phase transition proved to be like a liquid-vapor phase transition. The fluid-superfluid phase transition proved to be like the conductor-superconductor phase transition. The mathematics of one experiment applied to many other experiments. By the 1970s the problem had been largely solved. A question, though, was how far the theory could be extended. What other changes in the world, when examined closely, would prove to be phase transitions?
It was neither the most original idea nor the most obvious to apply phase transition techniques to flow in fluids. Not the most original because the great hydrodynamic pioneers, Reynolds and Rayleigh and their followers in the early twentieth century, had already noted that a carefully controlled fluid experiment produces a change in the quality of motion—in mathematical terms a bifurcation. In a fluid cell, for example, liquid heated from the bottom suddenly goes from motionlessness to motion. Physicists were tempted to suppose that the physical character of that bifurcation resembled the changes in a substance that fell under the rubric of phase transitions.
It was not the most obvious sort of experiment because, unlike real phase transitions, these fluid bifurcations entailed no change in the substance itself. Instead they added a new element: motion. A still liquid becomes a flowing liquid. Why should the mathematics of such a change correspond to the mathematics of a condensing vapor?
IN 1973 SWINNEY was teaching at the City College of New York. Jerry Gollub, a serious and boyish graduate of Harvard, was teaching at Haverford. Haverford, a mildly bucolic liberal arts