2025/10/20
2025/05/01
The Strike Equation: How Physics and Friction Unlock Bowling’s Perfect Shot
The Strike Equation: How Physics and Friction Unlock Bowling’s Perfect Shot
A team of researchers from top universities has developed a groundbreaking mathematical model that could change how bowling is played and analyzed.
Unlike previous methods that relied on player stats, this model factors in lane oil patterns, friction, and even ball asymmetry to pinpoint optimal strike conditions. It not only simulates ball trajectories using advanced physics but also offers a “miss-room” buffer for human error, aiming to give players a scientific edge in a sport with millions on the line.
A New Mathematical Approach to Bowling
Bowling remains one of the most popular sports in the U.S., with over 45 million people playing each year and millions of dollars awarded in tournaments. Yet despite its popularity, there’s still no widely accepted model that can accurately predict how a bowling ball moves down the lane.
In a new study published today (April 15) in AIP Advances, researchers from Princeton, MIT, the University of New Mexico, Loughborough University, and Swarthmore College present a model designed to pinpoint the optimal placement of a bowling ball. The model uses six differential equations, based on Euler’s equations for rotating rigid bodies, to generate a map of the best conditions for achieving a strike.
Why Accurate Ball Prediction Matters
“The simulation model we created could become a useful tool for players, coaches, equipment companies, and tournament designers,” said author Curtis Hooper. “The ability to accurately predict ball trajectories could lead to the discoveries of new strategies and equipment designs.”
Until now, most prediction methods have focused on analyzing statistics from real players rather than the physics of the ball’s motion. These approaches often fall short when bowlers slightly change their technique or style.
Instead, the group’s model accounts for a variety of factors. One example is the thin layer of oil applied to bowling lanes; the oil layer can vary widely in volume and shape between competitive tournaments, requiring specific styles and targeting strategies for each. The oil is seldom applied uniformly, which creates an uneven friction surface.
Bridging Instinct with Science
The issue is that bowlers and coaches can currently only rely on their own experience and instinct, which Hooper said is often imprecise and suboptimal.
“Our model provides a solution to both of these problems by constructing a bowling model that accurately computes bowling trajectories when given inputs for all significant factors that may affect ball motion,” Hooper said. “A ‘miss-room’ is also calculated to account for human inaccuracies which allows bowlers to find their own optimal targeting strategy.”
Modeling a Complex and Asymmetric Sport
Making the model posed several challenges, including how to describe the motion of the subtly asymmetric bowling ball. More challenging still was distilling the inputs required for predicting the trajectory into terms that a bowler or coach could understand and that could be measured with accessories bowlers already use.
What’s Next for Bowling Science
In the future, the group aims to improve the model’s accuracy by incorporating even more factors, including uneven bowling lanes, as well as connect with professionals in the industry to better understand how the model may be tailored to fit their applications.
Reference: “Using physics simulations to find targeting strategies in competitive tenpin bowling” by Simon Si Ming Ji, Shouzhuo Yang, Wilber Dominguez, Curtis George Hooper, and Cacey Stevens Bester, 15 April 2025, AIP Advances.
DOI: 10.1063/5.0247761
2025/04/25
In the Quantum Realm, Time’s Arrow Might Fly in Two Directions
In the Quantum Realm, Time’s Arrow Might Fly in Two Directions
Scientists studying a centuries-old mystery of physics suggest two “arrows of time” control the evolution of quantum systems
In that way, time as we experience it is asymmetric. We have memories of the past rather than the future, and spilled water doesn’t flow back to its cup, just as an arrow that has been let fly doesn’t return to its bow. In our everyday lives, the “arrow of time” goes only in one direction: forward.
“We know [this] is something that’s part of our common experience,” says Andrea Rocco, a theoretical physicist at the University of Surrey in England. But how exactly time’s arrow arises is less clear to physicists, in part because the math they use to describe most of the world makes no distinction between time that moves forward and time that moves backward; either direction is perfectly viable, as far as their equations are concerned.
Relatedly, the concept of “time” becomes somewhat illusory in the absence of change. For instance, if our cup of water was held in stasis in a magic, perfectly insulated and physically impervious box floating in deep space, this “system” would seem the same whether it was examined five years ago or five millennia from now. So which way is time’s arrow flying inside the magic stasis box? For such isolated systems, time is thus considered to be symmetric; only when it is “open” to influence from the external environment is this symmetry broken, whether via water evaporating or the cup tipping over to spill its contents.
And yet open and isolated systems are inherently linked. Even if our cup of water was isolated from the external world, its molecules would still be randomly jostled by microscopic effects—changes that potentially break time’s symmetry, like the ticking of the cosmic clock. So why does this discrepancy exist, and what does it imply about the validity of the models physicists use to study the role of time in the reality we experience?
Different researchers have tackled these questions in different ways, but Rocco and his colleagues revisited some of the math behind the inconsistency to see if an alternative approach could resolve the apparent asymmetry. Their conclusions, recently published in Scientific Reports, detail the existence of not one but two opposing arrows of time within open quantum systems.
This is a bit like if our water cup were precariously balanced on a knife-edge: it could topple to spill down either side, each side being an opposite-facing arrow of time. But the cup falling one way versus the other doesn’t make the water spill differently. Either way, mathematically speaking, the end result is exactly the same—it preserves the symmetry for both possible instances. “In a sense, we are stuck in this universe in which time actually goes in one direction,” Rocco explains. “But the equations of motion that we are considering would have allowed the universe to go in the other direction.”
This way, the existence of both instances is a reflection of time symmetry, in contrast to the conventional understanding that the environment is imposing or “defining an arrow of time,” Rocco says. In other words, the researchers’ work suggests that two time’s arrows, rather than one, are a spontaneous feature of an open quantum system.
The new work adds to some interesting questions about what physicists deem relevant in their studies of time. Michele Campisi, a theoretical physicist at the Italian National Research Council’s Nanoscience Institute, who was not involved in the study, commends the paper for its bold take but notes that it also implies a strange, subjective malleability to the origins of time’s arrow. The “hows” and “whys” of the way time flies are “a reflection of an approximation,” he says, dependent on a physicist’s preferred interpretation of quantum mechanics itself—of which there are several. One’s view of a quantum system is set to some degree by one’s expectations, he says. For instance, a more “global” view of events could also see a purported open system as just another part of a much larger, isolated one in which complications with time asymmetry wouldn’t occur at all.
Nevertheless, this paper demonstrates how our quest to understand the quantum realm is still far from complete, says James Cresser, a now retired professor of physics. “This [helps] shake up a commonly held idea that certain equations describing dissipative behavior are not time-reversal invariant and are therefore a theoretical indicator of a particular physical state of affairs,” Cresser says. (Cresser was thanked for “illuminating discussions” in the study and had taught its lead author Thomas Guff as an undergraduate, but he did not directly contribute to the work.)
For instance, the way water acts when it spills is akin to a type of dissipative behavior in quantum mechanics and thermodynamics called decoherence, in which a system progressively spreads out, or “decoheres,” and “loses” information. In this example, the information is the particular arrangement of water molecules previously inside the cup. Dissipative processes are considered asymmetric with regard to time because the initial configuration ends up irrelevant to the final state of affairs, explains Nicole Yunger Halpern, a physicist at the National Institute of Standards and Technology, who was not a part of the new study.
But even this kind of interpretation necessarily depends on our expectations of how a system must evolve as energy flows through it. For example, if we were to see two movies, one in which the water spills and another in which the water preternaturally returns to the cup, we’d be inclined to say that the second movie is illusory and impossible and that it is merely the first played backward. Thus, an asymmetric arrow of time is, in some ways, an “emergent phenomenon,” Yunger Halpern says. “We can all recognize it in our daily experiences.”
All that said, perhaps the concept of time—arrow or no—is nothing but “scaffolding” for the human brain to grasp at as we try to “label all the events that take place in the world around us,” Cresser says. “But the events themselves don’t rely on the scaffolding. And what we’re doing with these equations is applying one kind of temporal scaffolding as compared to another possible temporal scaffolding.”
In that case, our questions about time might never have answers—making them, well, timeless. “We are unavoidably buried in time—that is a profound part of our existence that we can never, ever escape,” Cresser says.
Editor’s Note (2/27/25): This article was edited after posting to better clarify Andrea Rocco’s and Nicole Yunger Halpern’s respective comments about arrows of time.
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Scientists Have Discovered the Pathway to Element 120—the Holy Grail of Chemistry
Scientists Have Discovered the Pathway to Element 120—the Holy Grail of Chemistry
It’s all thanks to a titanium beam.
- We’ve reached the limit of a very successful way to make new elements in the lab.
- In new research, scientists unveil a new take on that technology and report its success.
- The heaviest elements could have new uses and properties we haven't dreamt of.
Lawrence Berkeley National Laboratory has announced a new way to reliably make element 116, livermorium. The results, made by using a titanium beam to irradiate a sample, could point toward the elusive “island of stability” for even heavier nuclear elements—and show researchers a route to create the next feasible element, number 120.
Many of us remember a time when the periodic table appeared with some curious blank spots. Your age determines what those blank spots were, but they’ve been consistent, because discovery of elements has never been in full numerical order. Their availability has depended on location, stability, and accessibility of both the naturally occurring forms and a method to separate them.
After a certain point, the elements transition from naturally occurring to laboratory-prepared. These elements may exist somewhere in the universe, but Earth is not cold enough, high-pressure enough, and so forth to create those conditions outside a lab. But inside labs like Berkeley, they use increasingly advanced technologies to jam more protons inside the nuclei of atoms in order to create these new elements.
In their new preprint paper—meaning it’s not yet peer-reviewed—a large team of scientists explain that we’ve reached the limits of a current generation method to make new heavy elements. The heaviest discovery to date, element 118 oganesson, was made using a beam of calcium isotope 48 particles. Calcium 48, with its definitive 20 protons plus 28 neutrons, is a common and very effective starter for physical chemistry.
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Among individuals, as among nations, respect for the rights of others is peace. -Benito Juárez, President of Mexico (21 Mar 1806-1872)
