One of the innate yet perhaps underappreciated functions of physics is its ability to explain and generalize how things work in the real world. This capability extends even to phenomena as seemingly random as the way objects break and shatter. A new universal rule has emerged to explain these fragmentation processes, challenging previous assumptions about their unpredictability.
According to this groundbreaking law, any solid capable of shattering—whether it’s a glass plate, falling rocks, or crumbly cookies—follows the same physical processes of fragmentation. In a recent paper published in Physical Review Letters, Emmanuel Villermaux, a mechanics expert at Aix-Marseille University in France, proposed an overarching equation that reveals an unexpectedly logical, mathematical pattern in the way things break.
A Crack in the Physics
Imagine recording a glass cup shattering with a high-speed camera. You would observe how the cracks in the surface branch out and merge sporadically, eventually creating large, chunky sections that splinter apart. Predicting how these ruptures form might seem like a thankless task, but physicists have long suspected that a universal mechanism drives what appears to be a random process.
“Fragmentation processes have long fascinated physicists because they combine elements of geometry, dynamics, and disorder,” commented Ferenc Kun, a physicist at the University of Debrecen in Hungary, who was not involved in the new work, in an accompanying Viewpoint.
Before Villermaux’s research, scientists generally focused on the tinier details, such as the motion of each crack or the distribution of stress on a solid’s surface when dropped. Other attempts described fragmentation as a “kind of phase transition,” Kun explained. However, none were able to capture completely random, outside-the-lab instances of shattering.
Seeing the Bigger Picture
In contrast, Villermaux approached the problem from a different angle, focusing not on the cracks themselves but on the outcomes of shattering events. In his paper, he cataloged all the possible ways something could break in terms of entropy, a measure of chaos. For instance, the simplest, low-entropy outcome might be a glass plate shattering into four equal pieces, whereas higher entropy outcomes result in the plate fragmenting into many uneven, grainy shards.
According to Villermaux, the more realistic scenario is the latter, which he attributes to a principle called maximal randomness. “This is similar to the way many laws concerning large ensembles of particles were derived in the 19th century,” Villermaux explained to New Scientist.
He further incorporated a global conservation law, previously derived by him and his colleagues, to impose a physical constraint on how chaotic these fragments could become. Villermaux then applied his new equation to a wide range of real-life objects, including plates, shells, spaghetti, ocean litter, flaky rocks used as chimpanzee hammers, and even liquid droplets and bubbles.
Implications and Future Applications
The equation demonstrated remarkable accuracy across these cases, Villermaux reported. However, unlike previous work on similar topics, his equation is most effective for truly random fragmentation and is less applicable to softer materials like some plastics.
Despite these limitations, the model’s strength lies in its ability to provide the first truly general, statistical foundation for random shattering, according to Kun. Such a sweeping principle could “help scientists determine how different physical processes influence fragment-size distributions in industrial, geophysical, and astrophysical settings,” he added.
This development follows a long history of attempts to understand and predict fragmentation. The move represents a significant step forward in physics, potentially informing a range of scientific and industrial applications. As researchers continue to explore the implications of this new rule, it may lead to innovations in material science, engineering, and beyond.
