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Two Israeli physicists have adopted a random wandering model called "Drunken Wandering", which introduces new ideas to the "three-body problem".
When Newton first discovered the gravitational interaction between two objects, he had already cracked the code for matter to move and interact in the vast expanse of space-time. However, this discovery is about the interaction between two objects, the interaction between three objects that surround each other, the "three-body problem", which Newton did not solve.
It has been three centuries since Newton proposed the "three-body problem", but no one has been able to solve it. But it inspired writer Liu Cixin to write the science fiction work "The Three-Body Problem".
The three-body problem is a chaotic system, which means that making any meaningful prediction requires a very accurate understanding of the initial positions of three objects, which is extremely challenging.
In such a system, the "butterfly effect" becomes extremely real, and even the slightest mistake can cause the object to take a completely different trajectory than expected. There is no equation that can predict how these objects will move, and there is no way to determine whether the trajectory of an object will remain stable over time.
Due to the lack of a solution to the three-body problem, scientists can't currently predict what will happen when a binary system (two orbiting stars) collides with a nearby third star. The only way to do this is to do a computer simulation of the case and see how the three-body system evolves over time.
These simulations reveal that the interaction occurs in two phases: first a chaotic phase: three celestial bodies violently pushing each other until one star pops out of the other two; then a stabilization phase in which the positions of the three celestial bodies form an ellipse that surrounds each other.
If the third star is in a bound orbit, it can re-approach the other two stars and re-enter the first stage. This entanglement ends forever when one of the stars escapes into an infinite orbit in the second stage.
The three-body problem relies heavily on initial conditions, meaning that its outcomes are essentially random, but that doesn't mean that the probabilities for each outcome can't be calculated.
In a recent study published in the journal Physical Review X, Yonadav Barry Ginat from technion and mentor Hagai Perets used this unpredictability to come up with a statistical solution for the two phases of the process. They calculated the likelihood of any potential outcome in each first-stage contact, rather than predicting actual events. Although there is yet a comprehensive solution to the problem, the random nature of chaos allows one to calculate the likelihood that a triple interaction will end in one of two ways.
Thesis link: https://journals.aps.org/prx/pdf/10.1103/PhysRevX.11.031020
Yonadav Barry Ginat is a theoretical physicist currently pursuing his PhD at the Haifa Institute of Technology in Israel under the supervision of Vincent Desjacques and Hagai Perets. His research interests include large-scale and small-scale gravitational studies in cosmology, including the motion of individual stars under the influence of gravitational interactions and gravitational waves.
Hagai Perets, another author of the paper, is an associate professor in the Department of Physics at Technion-Israel Institute of Technology and a member of the astrophysics group.
Random walks, also known as "drunk walks", can be used to represent approximations of the entire series. The term was coined by mathematicians who imagined how a drunkard would walk and conceived it as a random process: the drunk didn't know where he was, and each time he took the next step in some random direction. The probabilities of a drunk taking a step to the right and a step to the left are the same, and knowing these probabilities, you can calculate the likelihood that a drunkard will appear at any given location at some point in time.
Essentially, the three-body problem involves the same principle. In fact, after each close-up collision, one of the stars is randomly thrown. And this pattern can be analogous to an alcoholic walking. One star is randomly catapulted and returned, another (or the same star) is catapulted in a different random direction (similar to the footsteps of a drunkard), and so on, until the star is completely expelled, just as the drunkard has fallen into a ditch and will not return.
In other words, Ginat and Perets' research shows how the same statistical system can be applied to the three-body problem. So they estimated the likelihood of each binary configuration and then used random walk theory to determine the final probability of any potential outcome, similar to creating a long-term weather forecast.
"We came up with the random walk model in 2017 when I was an undergraduate," says Ginat, "and I took a course taught by Professor Perets, where I had to write an article about the three-body problem." We didn't publish this article at the time, but when I started my PhD, we decided to expand the article and publish it."
Many teams have solved the same problem in recent years, and Ginat and Perets' solutions statistically address all potential types of interactions.
For Perest, the work "has important implications for understanding gravitational systems, especially in the case of multiple collisions between three stars, such as dense clusters." In these regions, many bizarre systems are formed through three-body collisions, resulting in collisions between stars and dense objects such as black holes, neutron stars, and white dwarfs, which also produce gravitational waves that have not been directly detected until recent years. Statistical solutions can be an important step in modeling and predicting the formation of such systems."
A random walk model, on the other hand, can accomplish more tasks. Until now, in the study of the three-body, individual stars have been treated as idealized point particles.
Of course, they do not exist in reality, and their internal structure may have an impact on motion, such as tides.
The Moon causes tides on Earth, which significantly alter the shape of the Earth. Due to friction between the oceans and the rest of the planet, some of the tides dissipate in the form of heat. But because of conservation of energy, this heat must come from the energy of the Moon as it orbits the Earth. Tides can also extract orbital energy from the motion of the three celestial bodies in the three-body problem.
Ginat explains that the random walk model considers these phenomena in a natural way. All you have to do is remove the heat from the total energy tide in each step and then compose all the steps. We found that in this case, the probability of the outcome can be calculated.
"Who would have thought that a drunken man's shaky walking posture could explain some of the most basic problems in physics?"
Reference links: https://www.revyuh.com/top-news/featured/drunkards-walk-can-help-solve-three-centuries-old-three-body-problem/
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