Even the Smallest Disturbances Can Make Three-Body Systems Chaotic and Unpredictable.

## TL;DR

A team of scientists led by astronomer Tjarda Boekholt has discovered that just three gravitationally interacting bodies can disrupt time-reversal symmetry, challenging our understanding of predictability in the universe. Using the highly precise Brutus n-body code, they demonstrated that even minute disturbances as small as a Planck length can cause irreversible outcomes in three-body systems. Their findings show that chaos is inherent to these systems, making them fundamentally unpredictable. The research suggests that the arrow of time is unavoidable in any system of three interacting objects, whether black holes or planets. Don’t forget to share your thoughts in the comment section below!

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Most laws of physics are indifferent to the direction of time. Whether it’s moving forward or backward, the laws hold true either way. In Newtonian physics and general relativity, time doesn’t affect the equations: This concept is known as time-reversal symmetry.

However, in the real Universe, things get more complicated. A group of scientists led by astronomer Tjarda Boekholt from the University of Aveiro in Portugal has shown that just three gravitationally interacting bodies are enough to disrupt time-reversal symmetry.

“So far, a quantitative link between chaos in stellar dynamical systems and the extent of irreversibility has not been established,” they wrote in their paper.

“In this study, we examine chaotic three-body systems initially in free fall using the highly accurate and precise n-body code Brutus, which surpasses standard double-precision arithmetic. We show that the proportion of irreversible outcomes decreases following a power law as numerical accuracy increases.”

The n-body problem is a well-known challenge in astrophysics. It arises when more bodies are added to a gravitationally interacting system.

Predicting the motion of two similarly sized bodies orbiting a common center is relatively straightforward using Newton’s laws of motion and universal gravitation.

However, adding a third body complicates things. The bodies start to perturb each other’s orbits through gravitational interactions, introducing chaos into the system. While solutions exist for some specific scenarios, there isn’t a single formula—under Newtonian physics or general relativity—that fully captures these interactions.

Even in our Solar System, which is well understood, we can only forecast a few million years ahead. Chaos in the Universe is inherent, not an error.

In running n-body simulations, physicists sometimes encounter time-irreversibility—meaning the simulations, when run backward, do not return to the initial conditions.

What hasn’t been clear is whether this is due to the inherent chaos of these systems or flaws in the simulations, casting doubt on their reliability.

To address this, Boekholt and his team devised a test. He and computational astrophysicist Simon Portegies Zwart from Leiden University in the Netherlands previously developed an n-body simulation code called Brutus that uses brute-force computing power to minimize numerical errors.

They used Brutus to test time-reversibility in a three-body system.

“Since Newton’s equations of motion are time reversible, a forward integration followed by a backward integration of the same time should return the system to its initial state (except for a change in the sign of the velocities),” they wrote in their paper.

“The result of a reversibility test is therefore precisely known.”

The three bodies tested in the system were black holes, evaluated in two scenarios. In the first, the black holes began at rest, moved towards each other in complex orbits, and eventually one black hole was expelled from the system.

The second scenario began where the first ended and was run backward in time to try to restore the system to its initial state.

They discovered that in 5 percent of cases, the simulation could not be reversed. A disturbance as small as a Planck length—about 0.000000000000000000000000000000000016 meters, the smallest possible length—was enough to disrupt the system.

“The movement of the three black holes can be so intensely chaotic that even something as tiny as the Planck length can impact the movements,” Boekholt explained. “Disturbances of the size of a Planck length have an exponential impact and disrupt time symmetry.”

Five percent might seem minor, but because it’s impossible to know which simulations will be affected, the researchers concluded that n-body systems are “fundamentally unpredictable.”

Their findings show that the issue is not with the simulations.

“Not being able to reverse time is no longer merely a statistical argument,” Portegies Zwart said. “It’s rooted in the fundamental laws of nature. No system of three moving objects—whether large or small, planets or black holes—can escape the arrow of time.”

The research has been published in the *Monthly Notices of the Royal Astronomical Society*.

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I’m assuming and hoping this applies to the three quarks in a proton or neutron, that subatomic particles also are time-irreversible. Superposition suggests that the wave function is time-reversible, but once observed, collapses into a fixed “reality” that is time-irreversible. There’s no going back in our 3S1T spacetime as there is no resting in T once particles/objects interact. Cool article!