Ask your nearest physicist what their take on the “three-body problem” is and they may bust out cold sweats. This infamous problem has puzzled the greatest of minds for several decades now; ask physicists from Technion-Israel Institute of Technology (TIIT), however, and you may get a little bit more than what you asked for—at least according to LiveScience.
You see, the interactions of two gravitationally-locked bodies can be fully described by equations set in stone by Isaac Newton centuries ago; this is the reason why problems concerning the Earth and the Moon can be found in college textbooks and exams all over the world. However, things start to dip into the chaotic once you introduce a third gravitational body into the mix.
The three bodies, now locked in a gravitational dance with each other, are now extremely sensitive to factors called “initial conditions,” which are factors that end up lending a hand in what would amount to a rapidly-growing snowball of effects. As a result, the three bodies can no longer be easily described with elegant equations that would have otherwise been sufficient for just two bodies.
Luckily for us, physicists from TIIT may have given us crucial insights into the three-body problem using a process known as the “drunkard’s walk.” Their exploits were published in the journal Physical Review X.
Said study co-author and TIIT doctoral student Yonadav Barry Ginat to LiveScience: “[The three-body problem] depends very, very sensitively on initial conditions, so essentially it means that the outcome is basically random […] but that doesn’t mean that we cannot calculate what probability each outcome has.”
To give Ginat and team some leads into how they’ll approach the problem, they looked into a method that’s sometimes called the “drunkard’s walk.” More properly known as the Random Walk Theory, it is perhaps best simplified by the concept of a drunk person walking towrads a random direction: as such, the “drunkard” has an equal chance of taking a step to the left as they do to the right. Given these parameters, mathematicians can then give the chances of the drunkard ending up in a particular area later on.
Ginat, together with co-author TIIT physicist Hagai Perets, then decided to cover a particular instance of the three-body problem, where a third body is introduced to a “binary system,” or a system of two bodies already locked in a cosmic dance.
Ginat added: “One can calculate what the probabilities for each of those possible speeds of the third body [are], and then you can compose all those steps and all those probabilities to find the final probability of what’s going to happen to the three-body system in a long time from now.” This, according to Ginat and Perets, gives them insights into whether or not the third object gets locked in a dance together with the previous two bodies or if it gets flung out, never to return to the system.
Additionally, the “solution” proposed by Ginat and Perets now also accounts for additional complications that may arise from analyzing the three-body problem beyond just simple “point particles” in space. (This is perhaps best exemplified by how the Moon not only attracts the Earth gravitationally but also nudges its water ever so slightly, giving us the lunar tides.)
While the pair of authors are pleased with their results, the two also recognize that there are a lot of possibilities moving forward. The two hope to account for “special configurations” in the three-body problem, like when the three bodies lie on the same geometric plane.
(For more related news, check out how Google’s AlphaMind found a way through an old graphs problem and knots in math; afterward, check out how a mathematician figured out a solution to the “n-queens” chess problem.)
References
- Ginat, Y. B., & Perets, H. B. (2021). Analytical, statistical approximate solution of dissipative and nondissipative binary-single stellar encounters. Physical Review X, 11(3), 031020. https://doi.org/10.1103/PhysRevX.11.031020
- Hamer, A. (2022, January 4). Physicists crack unsolvable three-body problem using drunkard’s walk. LiveScience. https://www.livescience.com/three-body-problem-solution
