Not every scoop of ice cream can be described as “fateful.” But a batch of ice cream Erasto Mpemba made as a teenager in Tanzania in 1963 made waves in physics that are still being felt nearly 60 years later. That’s because it appeared to be proof of a strange and counterintuitive idea: that a hot liquid may freeze faster than a cold one.
Homemade ice cream was a popular snack when he was a student at Magamba Secondary School, Mpemba wrote in a journal article published in 1969. “The boys at the school do this by boiling milk, mixing it with sugar and putting it into the freezing chamber in the refrigerator, after it has first cooled nearly to room temperature,” I explained. But competition for the freezer was intense. One afternoon, he and another boy took two different shortcuts as they jockeyed for space. Mpemba’s classmate mixed his milk with sugar and poured it straight into an ice tray without boiling it at all. Not to be outdone, Mpemba boiled his milk—but skipped the step of letting it cool so he could snag the last ice tray. An hour and a half later, “my tray of milk had frozen into ice-cream while his was still only a thick liquid,” Mpemba wrote.
A few years later, Mpemba asked his high school science teacher why this might be—why hot milk would freeze faster than cold milk, going against Newton’s law of cooling. The teacher’s response was, “All I can say is that that is Mpemba’s physics and not the universal physics.” The incident became a running joke in the classroom. Whenever Mpemba got a math problem wrong, the teacher and his classmates would call it “Mpemba’s mathematics.”
Determined to find an explanation, Mpemba repeated the experiment with hot and cold water. And when physicist Denis Osborne visited his high school, he asked him about the incident as well. Intrigued, Osborne invited Mpemba to visit what is now the University of Dar es Salaam and discuss the issue further, then set up the related research that was eventually published. The article helped a principle that Aristotle, René Descartes, and Sir Francis Bacon had all observed over the centuries become known as the Mpemba effect.
Mpemba and Osborne’s claims created decades of controversy within the physics world, since they challenged fundamental theories about how matter behaves. Many researchers tried to recreate their results, with limited success. In 2016, physicist Henry Burridge of Imperial College London and mathematician Paul Linden of the University of Cambridge published a sweeping review of many of the studies that had attempted to confirm the phenomenon, reporting “sadly” that they were not able to find any proof of a Mpemba effect. Worse, they concluded, all of those studies—including Mpemba’s original experiment—could have been easily skewed by tiny experimental factors such as the setup of equipment insulation or placement of thermometers.
cool and chaos
Starting in 2017, a new contingent of studies finally turned the corner on confirming Mpemba’s observation, suggesting that the explanation lies in the mysterious mechanics of chaos. And, it turns out, water itself may have been a major obstacle in providing the larger theory. It behaves differently than most other substances, especially as it changes states between solid, liquid, and gas, so scientists on the Mpemba effect case looked to remove water from the equation altogether.
In an abstract experiment meant to zero in on the forces at work, physicist John Bechhoefer and his colleagues heated microscopic glass beads (meant to stand in for water molecules) with lasers and looked at the speed of cooling. They found that not only did some hot beads cool more quickly than their cold counterparts, but sometimes they did so exponentially faster. “The simplicity of the study is part of its beauty,” theoretical physicist Marija Vucelja told Science News. “It’s one of these very simple setups, and it is already rich enough to show this effect.”
Not long after that, another group of physicists published a follow-up article suggesting a more abstract framework for understanding the Mpemba effect, which involved modeling the random dynamics of particles. The results suggest that the key to the Mpemba mystery is a dose of chaos. In particular, a liquid moving quickly from hot to cold is said to be “out of equilibrium,” meaning that it is a system that does not follow the linear rules we (or Newton) might expect it to.
“We all have this naive picture that says temperature should change monotonically,” study author Oren Raz told Quanta magazine (meaning that we might assume a liquid that is cooling keeps going steadily in one direction without making significant reversals). “You start at a high temperature, then a medium temperature, and go to a low temperature.” But in a system out of equilibrium, “you can have strange shortcuts,” Raz said.
Various publications offered evocative metaphors to explain those shortcuts: Science News compared a hot liquid cooling under the Mpemba effect to “how a hiker might arrive at a destination more quickly by starting farther away, if that starting point allows the hiker to avoid an arduous climb” over a mountain.” Alternatively, Physics Today suggested it is a bit like someone using stepping stones to cross a river, writing, “If you have the right starting energy, you can jump straight from the first to the third without ever landing on the second.” Since a hot liquid is more out of equilibrium than a cold one, it might have just the right energy to hop over stones.
Another word for that is kurtosis, a statistical term that refers to the deviation from an average, which appears to play an important role in Mpemba effect-related behavior. The temperature of a fluid generally refers to the mean speed of its molecules—but every fluid will have outlier molecules behaving much differently than the others. In cases where the Mpemba effect occurs, these outliers seem to play an outsize role, Antonio Lasanta, a physicist who has published several papers confirming the phenomenon, told Cosmos. By taking into account kurtosis in experiments related to this kind of cooling and heating, “we can make analytical calculations to know how and when the Mpemba effect will occur,” Lasanta said. It’s certainly a step toward unraveling the Mpemba mystery, though there’s plenty left to figure out about when the effect shows up and how strong it is when it does.
Erasto Mpemba grew up to work as a game officer in Tanzania’s Ministry of Natural Resources and Tourism and died around 2020, his ice cream having been vindicated. Though there’s still a lot we do n’t know about the effect that bears his name, it seems that it is “Mpemba’s physics” after all.