In 2008, Miguel Ramos read in the newspaper that 110-million-year-old amber bearing pristine Mesozoic insects had been discovered a few hours’ drive from Madrid, where he lived. A physicist who specializes in glass, Ramos had wanted for years to get his hands on ancient amber. He contacted the paleontologists working at the site, who invited him to visit.

“They provided me with the clear samples that are not good for them,” he said. “They have no interesting insects or whatever … but they are perfect for me.”

Ramos spent the next several years intermittently working on measurements of the ancient glass. He hoped that the fossilized tree resin, after aging for so long, might approach a hypothetical form of matter known as ideal glass.

For decades, physicists have dreamed of this perfect amorphous solid. They desire ideal glass not so much for its own sake (though it would have unique, useful properties) but because its existence would solve a deep mystery. It’s the mystery posed by every window and mirror, every piece of plastic and hard candy, and even the cytoplasm that fills every cell. All of these materials are technically glass, for glass is anything that’s solid and rigid but made of disordered molecules like those in a liquid. Glass is a liquid in suspended animation, a liquid whose molecules curiously cannot flow. Ideal glass, if it exists, would tell us why.

Inconveniently, ideal glass would take so long to form that it may not have done so in all of cosmic history. Physicists can only seek indirect evidence that, given unlimited time, it would. Ramos, an experimental physicist at the Autonomous University of Madrid, hoped that after 110 million years of aging, the Spanish amber might have started to show glimmers of perfection. If so, he would know what the molecules in ordinary glass are really doing when they appear to do nothing.

Ramos’s amber measurements are part of a surge of interest in ideal glass. In the past few years, new methods of making glass and simulating it on computers have led to unexpected progress. Major clues have emerged about the nature of ideal glass and its connection to ordinary glass. “These studies provide renewed support for the hypothesis of the existence of an ideal-glass state,” said Ludovic Berthier, a physicist at the University of Montpellier who was centrally involved in the recent computer simulations.

But the emerging picture of ideal glass only makes sense if we set aside one piece of evidence.

“Indeed,” Berthier said, “the amber work stands out as difficult to rationalize.”

The Paradox of Glass

When you cool a liquid, it will either crystallize or harden into glass. Which of the two happens depends on the substance and on the subtleties of the process that glassblowers have learned through trial and error over thousands of years. “Avoiding crystallization is a dark art,” said Paddy Royall, a glass physicist at the University of Bristol in the United Kingdom.

The two options differ greatly.

Crystallization is a dramatic switch from the liquid phase, in which molecules are disordered and free flowing, to the crystal phase, in which molecules are locked in a regular, repeating pattern. Water freezes into ice at zero degrees Celsius, for instance, because the H 2 O molecules stop jiggling around just enough at that temperature to feel each other’s forces and fall into lockstep.

Other liquids, when cooled, more easily become glass. Silica, for example — window glass — starts as a molten liquid well above 1,000 degrees Celsius; as it cools, its disordered molecules contract slightly, crowding a bit closer together, which makes the liquid increasingly viscous. Eventually, the molecules stop moving altogether. In this gradual glass transition, the molecules don’t reorganize. They simply grind to a halt.

Exactly why the cooling liquid hardens remains unknown. If the molecules in glass were simply too cold to flow, it should still be possible to squish them into new arrangements. But glass doesn’t squish; its jumbled molecules are truly rigid, despite looking the same as molecules in a liquid. “Liquid and glass have the same structure, but behave differently,” said Camille Scalliet, a glass theorist at the University of Cambridge. “Understanding that is the main question.”

A clue came in 1948, when a young chemist named Walter Kauzmann noticed what became known as the entropy crisis, a glassy paradox that later researchers realized ideal glass could resolve.

Kauzmann knew that the more slowly you cool a liquid, the more you can cool it before it transitions into glass. And slower-formed glass ends up denser and more stable, because its molecules had longer to shuffle around (while the liquid was still viscous) and find tighter, lower-energy arrangements. Measurements indicated a corresponding reduction in the entropy, or disorder, of the slower-formed glass — fewer ways its molecules could be arranged with the same low energy.

Extrapolating the trend, Kauzmann realized that if you could cool a liquid slowly enough, you could cool it all the way down to a temperature now known as the Kauzmann temperature before it fully hardened. At that temperature, the resulting glass would have an entropy as low as that of a crystal. But crystals are neat, orderly structures. How could glass, disordered by definition, possess equal order?

No ordinary glass could, which implied that something special must happen at the Kauzmann temperature. Crisis would be avoided if a liquid, upon reaching that temperature, attained the ideal-glass state — the densest possible random packing of molecules. Such a state would exhibit “long-range amorphous order,” where each molecule feels and affects the position of every other, so that in order to move, they must move as one. The hidden long-range order of this putative state could rival the more obvious orderliness of a crystal. “That observation right there was at the heart of why people thought there should be an ideal glass,” said Mark Ediger, a chemical physicist at the University of Wisconsin, Madison.

According to this theory, first advanced by Julian Gibbs and Edmund DiMarzio in 1958, ideal glass is a true phase of matter, akin to the liquid and crystal phases. The transition to this phase just takes too long, requiring too slow a cooling process, for scientists to ever see. The ideal-glass transition is “masked,” said Daniel Stein, a condensed matter physicist at New York University, by the liquid becoming “so viscous that everything is arrested.”

“It’s sort of like looking through a glass darkly,” Stein said. “We can’t get to [ideal glass] or see it. But we can theoretically try to create accurate models of what’s going on there.”

A New Glass

Unexpected help has come from experiments. There was never any hope of forming ideal glass by cooling a liquid, the glassmaking method humans have used for millennia. You’d have to cool a liquid impossibly slowly — perhaps even infinitely slowly — to keep it from hardening before it hit the Kauzmann temperature. But in 2007, Ediger, the Wisconsin physicist, developed a new method of glassmaking. “We figured out there was another way to make glasses that are high density and close to the ideal-glass state by a completely different route,” he said.

Ediger and his team discovered that they could create “ultra-stable glasses” that exist in a state somewhere between ordinary and ideal. Using a method called vapor deposition, they dropped molecules one by one onto a surface as if they were playing Tetris, allowing each molecule to settle into its snuggest fit in the forming glass before the next molecule came down. The resulting glass was denser, more stable, and lower in entropy than all of the glasses throughout human history. “These materials have the properties that you would expect if you took a liquid and cooled it over the course of a million years,” Ediger said.

Another property of ultra-stable glass would eventually reveal the most promising road map to ideal glass.

Two groups, one of them led by Miguel Ramos in Madrid, identified that property in 2014, when they found that ultra-stable glass departs from a universal characteristic of all ordinary glass.