The three-body problem is real and unsolvable

Everyone seems to be talking about it 3 Body problem, the new Netflix series based on Cixin Liu’s Remembrance of Earth’s Past book trilogy. Fewer people talk about the namesake of the two series: the unsolvable physics problem of the same name.

This makes sense, because it is true confusing. In physics, the three-body problem attempts to find a way to predict the motions of three objects whose gravity interacts with each of the others – such as three stars close together in space. Sounds simple enough, right? Yet I recently visited myself the Wikipedia article about the three-body problem and closed the tab in the same way someone might stagger away from a bright light. Apparently the Earth, Sun and Moon are a three-body system? Will you tell me? we don’t know how the moon moves? Scientists have published several solutions to the three-body problem? Are you telling me that Cixin Liu’s books are outdated?

All I wanted to know was Why the problem was considered unsolvable, and now the memories of my one semester of high school physics flashed before my eyes like so many glowing doomsday numbers. Despite my pain, however, I have come up with several ways in which we non-physicists can be confident that the three-body problem is in fact unsolvable.

Reason 1: This is a special definition of ‘unsolvable’

The three-body problem is especially confusing because scientists are seemingly constantly finding new solutions to the three-body problem! They just don’t mean one solution for everything. Such a formula do exist for a two-body system, and apparently Isaac Newton discovered it in 1687. But systems with more than two bodies are, according to physicists, too chaotic (that is, not in the sense of a child’s messy bedroom, but in the sense of ‘chaos theory’) to be contained by a single solution .

When physicists say they have a new solution to the three-body problem, they mean that they have found a specific solution for three-body systems that have certain theoretical parameters. Don’t ask me to explain those parameters, because they’re all things like “the three masses are collinear at all times” or “a zero angular momentum solution with three equal masses moving around a figure eight shape.” But basically, by limiting the focus of the problem to certain arrangements of three-body systems, physicists have been able to derive formulas that predict the motions of some of them, such as in our solar system. The mass of the Earth and the Sun create a “restricted three-body problem”, where a smaller body (in this case the moon) moves under the influence of two massive ones (the Earth and the Sun).

What physicists mean when they say that the three-body problem has no solution is simply that there is no one-formula-fits-all solution to every way in which the gravity of three objects can cause those objects to move—and that’s exactly what physicists what they mean when they say that there is no solution to the three-body problem. Three-body problem bases its entire premise on.

Reason 2: 3 Body Problem deliberately chose an unresolved three-body system

Image: Netflix

Henri Poincare research into a general solution to the three-body problem formed the basis of what would become known as chaos theory (you may know it from his co-starring role in Jurassic Park). And 3 Body problem itself does not go away each ancient three-body system. Specifically, it is about an extremely chaotic three-body system, exactly the kind of arrangement of bodies that Poincaré focused on when he showed that the problem is “unsolvable.”

(Ed. remark: The rest of this section contains some spoilers for 3 Body problem.)

In both Liu’s and Netflix’s books 3 Body problemhumanity faces an invasion by aliens (called Trisolarans in the English translation of the books, and San-Ti in the TV series) whose home solar system has three suns in a chaotic three-body relationship. It is a world in which heaven, unlike ours, is fundamentally unpredictable. Periods of icy cold give way to scorching heat that give way to fluctuations in gravity that turn into temporary reprieves that can never be trusted. The unpredictable nature of the San-Ti environment is the source of every detail of their physicality, their philosophy, and their desire to claim the Earth for themselves.

In other words, 3 Body problem‘s three-body problem is unsolvable because Liu wanted to write a story with an unsolvable three-body system, so he chose one of the three-body systems for which we have not yet discovered a solution, and perhaps never will.

Reason 3: Scientists are still working on the three-body problem

Perhaps the best reason I can give you to believe that the three-body problem is real, and truly unsolvable, is that some scientists have published a whole host of new solutions to specific three-body systems. very recently.

If physicists are still working on the three-body problem, we can safely assume that it has not yet been solved. After all, scientists are the real experts. And I’m certainly not.