It is well known that panes of stained glass in old European churches are thicker at the bottom because glass is a slow-moving liquid that flows downward over centuries.

Well known, but wrong. Medieval stained-glass makers were simply unable to make perfectly flat panes, and the windows were just as unevenly thick when new.

The tale contains a grain of truth about glass resembling a liquid, however. The arrangement of atoms and molecules in glass is indistinguishable from that of a liquid. But how can a liquid be as strikingly hard as glass?

“They’re the thickest and gooiest of liquids, and the most disordered and structureless of rigid solids,” said Peter Harrowell, a professor of chemistry at the University of Sydney, in Australia, speaking of glasses, which can be formed from different raw materials. “They sit right at this really profound sort of puzzle.”

Philip Anderson, a Nobel Prize-winning physicist at Princeton, wrote in 1995: “The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition.”

He added, “This could be the next breakthrough in the coming decade.”

Thirteen years later, scientists still disagree, with some vehemence, about the nature of glass.

Peter Wolynes, a professor of chemistry at the University of California, San Diego, thinks he essentially solved the glass problem two decades ago based on ideas of what glass would look like if cooled infinitely slowly. “I think we have a very good constructive theory of that these days,” Wolynes said. “Many people tell me this is very contentious. I disagree violently with them.”

Others, like Juan Garrahan, professor of physics at the University of Nottingham, in England, and David Chandler, professor of chemistry at the University of California, Berkeley, have taken a different approach and are as certain that they are on the right track.

“It surprises most people that we still don’t understand this,” said David Reichman, a professor of chemistry at Columbia, who takes yet another approach to the glass problem. “We don’t understand why glass should be a solid and how it forms.”

Reichman said of Wolynes’ theory, “I think a lot of the elements in it are correct,” but he said it was not a complete picture. Theorists are drawn to the problem, Reichman said, “because we think it’s not solved yet — except for Peter, maybe.”

Trail of clues

Scientists are slowly accumulating more clues. A few years ago, experiments and computer simulations revealed something unexpected: As molten glass cools, the molecules do not slow down uniformly. Some areas jam rigid first, while in other regions the molecules continue to skitter around in a liquid-like fashion. More strangely, the fast-moving regions look no different from the slow-moving ones.

Meanwhile, computer simulations have become sophisticated and large enough to provide additional insights, and yet more theories have been proffered to explain glasses.

David Weitz, a physics professor at Harvard, joked, “There are more theories of the glass transition than there are theorists who propose them.” Weitz performs experiments using tiny particles suspended in liquids to mimic the behavior of glass, and he ducks out of the theoretical battles. “It just can get so controversial and so many loud arguments, and I don’t want to get involved with that myself.”

For scientists, glass is not just the glass of windows and jars, made of silica, sodium carbonate and calcium oxide. Rather, a glass is any solid in which the molecules are jumbled randomly. Many plastics like polycarbonate are glasses, as are many ceramics.

Understanding glass would not just solve a long-standing fundamental (and arguably Nobel-worthy) problem and perhaps lead to better glasses. That knowledge might benefit drug makers, for instance. Certain drugs, if they could be made in a stable glass structure instead of a crystalline form, would dissolve more quickly, allowing them to be taken orally instead of being injected. The tools and techniques applied to glass might also provide headway on other problems, in material science, biology and other fields, that look at general properties arising out of many disordered interactions.

“A glass is an example, probably the simplest example, of the truly complex,” Harrowell, the University of Sydney professor, said. In liquids, molecules jiggle around along random, jumbled paths. When cooled, a liquid either freezes, as water does into ice, or it does not freeze and forms a glass instead.

In freezing to a conventional solid, a liquid undergoes a so-called phase transition; the molecules line up next to and on top of one another in a simple, neat crystal pattern. When a liquid solidifies into a glass, this organized stacking is nowhere to be found. Instead, the molecules just move slower and slower and slower, until they are effectively not moving at all, trapped in a strange state between liquid and solid.

The glass transition differs from a usual phase transition in several other key ways. It takes energy, what is called latent heat, to line up the water molecules into ice. There is no latent heat in the formation of glass.

The glass transition does not occur at a single, well-defined temperature; the slower the cooling, the lower the transition temperature. Even the definition of glass is arbitrary — basically a rate of flow so slow that it is too boring and time-consuming to watch. The final structure of the glass also depends on how slowly it has been cooled.

By contrast, water, cooled quickly or cooled slowly, consistently crystallizes to the same ice structure at 32 degrees Fahrenheit.

‘Ideal glass’

To develop his theory, Wolynes zeroed in on an observation made decades ago, that the viscosity of a glass was related to the amount of entropy, a measure of disorder, in the glass. Further, if a glass could be formed by cooling at an infinitely slow rate, the entropy would vanish at a temperature well above absolute zero, violating the third law of thermodynamics, which states that entropy vanishes at absolute zero.

Wolynes and his collaborators came up with a mathematical model to describe this hypothetical, impossible glass, calling it an “ideal glass.” Based on this ideal glass, they said the properties of real glasses could be deduced, although exact calculations were too hard to perform. That was in the 1980s. “I thought, in 1990, the problem was solved,” Wolynes said, and he moved on to other work.

Not everyone found the theory satisfying. Wolynes and his collaborators so insisted they were right that “you had the impression they were trying to sell you an old car,” said Jean-Philippe Bouchaud of the Atomic Energy Commission in France. “I think Peter is not the best advocate of his own ideas. He tends to oversell his own theory.”

Around that time, the first hints of the dichotomy of fast-moving and slow-moving regions in a solidifying glass were seen in experiments, and computer simulations predicted that this pattern, called dynamical heterogeneity, should exist.

Weitz of Harvard had been working for a couple of decades with colloids, or suspensions of plastic spheres in liquids, and he thought he could use them to study the glass transition. As the liquid is squeezed out, the colloid particles undergo the same change as a cooling glass. With the colloids, Weitz could photograph the movements of each particle in a colloidal glass and show that some chunks of particles moved quickly while most hardly moved.

“You can see them,” Weitz said. “You can see them so clearly.”