# Quantum mechanics means some black hole orbits are impossible to predict

Foreseeing the paths of three orbiting objects sometimes requires precision better than the quantum limit

Even if you could measure three black holes’ locations as precisely as physically possible, you still might not know where the black holes would go. Such a trio’s complex dance can be so chaotic that the motions are fundamentally unpredictable, new computer simulations show.

The paths of three black holes orbiting each other can be calculated based on their positions and velocities at one point in time. But in some cases, the orbits depend so sensitively on the black holes’ exact positions that the uncertainty of quantum physics comes into play. Tiny quantum uncertainties in specifying the locations of objects can explode as the black holes’ gyrations continue over tens of millions of years, astrophysicist Tjarda Boekholt and colleagues report in the April *Monthly Notices of the Royal Astronomical Society*. So the distant future of the black holes’ orbits is impossible to foresee.

Such extreme sensitivity to initial conditions is known as chaos. The new study suggests, in the case of three black holes, “quantum mechanics imprints into the universe chaos at a fundamental level,” says astrophysicist Nathan Leigh of Universidad de Concepción in Chile, who was not involved with the research.

In chaotic systems, tiny changes can generate
wildly different outcomes. The classic example is a butterfly flapping its wings, thereby altering weather patterns, possibly
producing a distant tornado that otherwise wouldn’t have formed (*SN: 9/16/13*). This chaos also shows up
in the orbits of three black holes and other collections of three or more objects,
making such orbits difficult to calculate, a conundrum known as the three-body
problem.

To test whether the black holes’ motions were predictable, Boekholt, of the University of Coimbra in Portugal, and colleagues checked if they could run computer simulations of the orbits both forward and backward and achieve the same result. Starting with a given set of locations for three initially stationary black holes, the researchers evolved those orbits forward in time to an end point tens of millions of years in the future. Then, they rewound the simulation, reversing the motions to see if the black holes ended up where they started from.

Computer simulations have a limited level of accuracy. In this case, for example, the locations of black holes were known only to a certain number of decimal places. That tiny imprecision can balloon over millions of years of the simulation.

According to quantum mechanics, it is
impossible to determine the position of any object better than an utterly tiny
distance called the Planck length, about 1.6
times 10^{-35} meters, or 16 billionths of a trillionth of a trillionth
of a millimeter (*SN: 4/8/11*). Yet even
with accuracy the size of the Planck length, the researchers found that about 5
percent of the time the three black holes wouldn’t return to the same spots
when the simulation was reversed. That means, even if you measured where the black
holes were to the quantum mechanical limit, you couldn’t rewind to find out
where they had come from.

“These systems are fundamentally irreversible,” says Boekholt. “You can’t go forwards and backwards for these 5 percent of systems in nature. And that was quite a surprising result.”

The result is theoretical and can’t be applied to real black holes, says astrophysicist Nicholas Stone of the Hebrew University of Jerusalem. For example, measurement errors would swamp the importance of quantum physics. But that doesn’t detract from the study’s importance, he says: “It is still quite interesting from a conceptual perspective.”