New Research Could Help Resolve the “Three-Body Problem”

Perhaps you’ve heard of the popular Netflix show and the science fiction novel on which it is based, The Three-Body Problem, by Chinese science fiction author Liu Cixin. The story’s premise is a star system where three stars orbit each other, which leads to periodic destruction on a planet orbiting one of them. As Isaac Newton described in his Philosophiæ Naturalis Principia Mathematica, the interaction of two massive bodies is easy to predict and calculate. However, the interaction of three bodies leads is where things become unpredictable (even chaotic) over time.

This problem has fascinated scientists ever since and remains one of the most famous unsolved mysteries in mathematics and theoretical physics. The theory states that the interaction of three gravitationally bound objects will evolve chaotically and in a way that is completely detached from their initial positions and velocities. However, in a recent study, an international team led by a researcher from the Niels Bohr Institute ran millions of simulations that showed “isles of regularity in a sea of chaos.” These results indicate that there could be a solution, or at least some predictability, to the Three-Body Problem.

The study was led by Alessandro Alberto Trani, a postdoctoral fellow at the University of Copenhagen’s Niels Bohr Institute (NBI), the Research Center for the Early Universe at The University of Tokyo, and the Okinawa Institute of Science and Technology (OIST). He was joined by researchers from the Universidad de Concepción in Chile, the American Museum of Natural History, the Leiden Observatory, and NASA’s Ames Research Center. The paper that details their findings was recently published in the journal Astronomy & Astrophysics.

Millions of simulations form a rough map of all conceivable outcomes when three objects meet, which is where the isles of regularity appear. Credit: Alessandro Alberto Trani

To investigate this problem, Trani and his colleagues used a software program he developed himself named Tsunami. This program calculates the movements of astronomical objects based on known physical laws, such as Newton’s Law of Universal Gravitation and Einstein’s Theory of General Relativity. They then set it to run millions of simulations of three-body encounters with specified parameters, including the positions of two co-orbiting objects (i.e., their phase along a 360-degree axis) and the angle of approach of the third object – varying by 90°. As Trani explained in a recent NBI Research News story:

“The Three-Body Problem is one of the most famous unsolvable problems in mathematics and theoretical physics. The theory states that when three objects meet, their interaction evolves chaotically, without regularity, and completely detached from the starting point. But our millions of simulations demonstrate that there are gaps in this chaos – ‘isles of regularity’ – which directly depend on how the three objects are positioned relative to each other when they meet, as well as their speed and angle of approach.”

The millions of simulations they conducted covered all possible combinations of this framework. The results formed a rough map of all conceivable outcomes from the threads of initial configurations, which is when the isles of regularity appeared. This discovery could lead to a deeper understanding of an otherwise impossible problem and represents a new challenge for researchers. Whereas it is possible to calculate our chaos using statistical methods, they become more complex when the chaos is interrupted by regularities. Said Trani:

“When some regions in this map of possible outcomes suddenly become regular, it throws off statistical probability calculations, leading to inaccurate predictions. Our challenge now is to learn how to blend statistical methods with the so-called numerical calculations, which offer high precision when the system behaves regularly. In that sense, my results have set us back to square one, but at the same time, they offer hope for an entirely new level of understanding in the long run.”

This illustration shows the merger of two supermassive black holes and the gravitational waves that ripple outward as the black holes spiral toward each other. Credit: LIGO/T. Pyle

Since the encounter of three objects in the Universe is a common occurrence, the Three-Body Problem is more than just a theoretical challenge. Trani hopes that this discovery will lead to a deeper understanding that will pave the way for improved astrophysics models:

“If we are to understand gravitational waves, which are emitted from black holes and other massive objects in motion, the interactions of black holes as they meet and merge are essential. Immense forces are at play, particularly when three of them meet. Therefore, our understanding of such encounters could be a key to comprehending phenomena such as gravitational waves, gravity itself and many other fundamental mysteries of the Universe.”

Further Reading: Neils Bohr Institute

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