Breaking Time-Reversal Symmetry

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The three bodies in the system are black holes, and they were tested in two scenarios. In the first, the black holes started from rest, moving towards each other into complicated orbits, before one of the black holes is kicked out of the system.

The second scenario starts where the first one ends, and is run backwards in time, trying to restore the system to its initial state.

They found that, 5 percent of the time, the simulation could not be reversed. All it took was a disturbance to the system the size of a Planck length, which, at 0.000000000000000000000000000000000016 metres, is the smallest length possible.

“The movement of the three black holes can be so enormously chaotic that something as small as the Planck length will influence the movements,” Boekholt said. “The disturbances the size of the Planck length have an exponential effect and break the time symmetry.”

Five percent may not seem like much, but since you can never predict which of your simulations will fall within that five percent, the researchers have concluded that n-body systems are therefore “fundamentally unpredictable”.

And they have shown that the problem is not with the simulations after all.

“Not being able to turn back time is no longer just a statistical argument,” Portegies Zwart said. “It is already hidden in the basic laws of nature. Not a single system of three moving objects, big or small, planets or black holes, can escape the direction of time.”

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

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