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Jul 15th 2020

From a Black Hole’s Orbit, Chaos Erupts

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What happens when three black holes share the same region of space, all orbiting one another? As Science News reports, it remains a mystery. Their orbits may be so unpredictable that even if their motions were measured to the maximum precision theoretically possible, their orbital paths would still elude us.

Computer simulation of a black hole’s orbit may thus demonstrate some fundamental characteristics of time. And, according to astrophysicist Nathan Leigh, the results show that “Quantum mechanics imprints into the universe chaos at a fundamental level.”

No Harmony of the Spheres

The very idea of science is rooted in our experience that the world around us can be fairly predictable. If you drop an apple, it will probably fall straight down, not sideways or up. On the big scale of astronomical events, this predictability or regularity of nature is particularly strong, like the sun rising in the east every morning.

The first great triumph of science was the ability to construct an accurate calendar and predict events such as a solar eclipse. These accomplishments were based on the regularity of celestial orbits. Today, this same predictability of orbits allows NASA to send spacecraft to the outer planets and measure the orbits of exoplanets many light-years away. If a black hole’s orbit is not predictable, even in theory, that shakes things up.

Running the Time Tape Backwards

Orbital simulations and similar scientific models, explains Interesting Engineering, are based on a principle known as time symmetry. That is, if you simulate an orbit, then run the simulation backwards, it will work just as well. The simulated object will be orbiting in the opposite direction, but it won’t fly off into the void in an unexpected way.

The real universe, as Interesting Engineering notes, isn’t quite so neat. If you drop a cup, it will shatter and won’t piece itself back together.

Astronomers and mathematicians have long known that orbits involving three objects can’t be calculated with the precision attainable for two objects orbiting each other. This is commonly known as the three-body problem. The normal solution for this problem is to simulate the orbit step by step, as precisely as the available programming and computing power allow.

Researchers have found that these simulated orbits can’t always be run in reverse — that attempts to do so do not always end by reproducing the initial start conditions, as they should, according to the principle of time symmetry.

What they didn’t know was whether these failures were due to the nature of the universe, or only to the technical limitations of a particular simulation, such as how many decimal places it could calculate.

Black Holes, Gravity and Quantum Mechanics

Now a team led by astronomer Tjarda Boekholt has built a simulation model so precise that the precision limit of the simulation is set not by the available computing power, but by the structure of the universe itself. It’s specifically set by a distance known as the Planck length, which according to the theory of quantum mechanics is the shortest length that can be measured in the universe, according to Science Alert.

(How long is the Planck length? About 0.000000000000000000000000000000000016 meters. Aren’t you glad you asked?)

The researchers tested their model by simulating the process of predicting the behavior of a black hole, or in fact three black holes. Why black holes? Because their gravitational fields, which are so intense that not even light can escape, magnify quantum effects — usually noticeable only on the subatomic scale — to the point where they can have large-scale effects.

What the simulation research team found was that, even with Planck-length precision, their model couldn’t play back about 5% of simulation runs in reverse to return to the model’s initial conditions. These runs break time symmetry because predicting the behavior of a black hole in these runs turns out to be impossible.

What’s more, there is no way to know in advance which 5% of runs will break time symmetry, which means that time symmetry cannot ever be entirely counted on.

A Touch of Chaos

Physicists and mathematicians use the term chaos for systems in which tiny changes in initial conditions can produce dramatic changes in the final outcome. The study results, says Science News, confirm that orbital systems involving three black holes are fundamentally chaotic, and can never be reliably predicted over long periods of time.

Says Science Alert, quoting team member Portegies Zwart, “Not being able to turn back time is no longer just a statistical argument … It is already hidden in the basic laws of nature.”

By odd coincidence, reports Universe Today, astronomers recently discovered three supermassive black holes orbiting each other in a galaxy a billion light-years away. But they cannot provide a direct test of orbital chaos, because as Science News notes, we can’t measure actual black holes with the accuracy needed to model their orbits to Planck-length precision.

We can also be glad, perhaps, that the black holes’ chaotic orbits are a billion light-years from Earth.

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