Most of the laws of physics don't care which direction time moves. Forward, backward … anyway, laws work the same way. Newtonian physics, general relativity – time has nothing to do with mathematics: this is called time reversal symmetry.
In the real universe, things get a little complicated. And now a team of scientists led by astronomer Tjard Beckholt from the University of Aveiro in Portugal has proven that it takes only three gravitationally interacting bodies to break the time reversal symmetry.
“Until now, the quantitative relationship between chaos in dynamical systems of stars and the level of irreversibility has remained uncertain,” they wrote in their article.
'In this paper, we study three-body chaotic systems in free fall, initially using an accurate and precise n-body code that goes beyond standard double precision arithmetic. We demonstrate that the fraction of irreversible solutions decreases as a numerical power law. '
The n-body problem is a known problem in astrophysics. It occurs when you add more bodies to a gravitationally interacting system.
The movements of two bodies of comparable size in orbit around a central point are relatively simple for mathematical modeling, according to Newton's laws of motion and Newton's law of universal gravitation.
However, as soon as you add another body, things get more complicated. Bodies begin to gravitationally perturb each other's orbits, introducing an element of chaos into the interaction. This means that although solutions exist for special cases, there is no formula — within Newtonian physics or general relativity — that describes these interactions with precision.
Chaos in the universe is a feature, not a mistake.
When running n-body simulations, physicists sometimes get time irreversibility in their results – in other words, running simulations backwards does not return them to their original starting point.
Whether this is the result of the chaos of these systems or the problems with simulations leading to uncertainty about their reliability is still unknown.
So Beckholt and his colleagues developed a test to figure this out.
“Since Newton's equations of motion are reversible in time, direct integration followed by reverse integration at the same time should restore the original implementation of the system (albeit with a difference in the signs of the velocities),” they wrote in their paper.
'So the reversibility test result is known for sure.'
The three bodies in the system are black holes and they were tested in two scenarios. In the first case, black holes started moving towards each other in complex orbits before one of the black holes left the system.
The second scenario starts where the first ends and runs backward in time, trying to restore the system to its original state.
They found that 5 percent of the time, simulation could not be carried out. All it took was an interference to the system the size of a Planck length, at 0.000000000000000000000000000000000016 meters being the shortest possible length.
“The movement of three black holes can be so chaotic that the movement will be affected by something less than the length of the Planck,” said Beckholt. 'Perturbations the size of the Planck length have an exponential effect and break the symmetry of time.'
Five percent may not be that much, but since you can never predict which of your simulations will fall into the five percent, the researchers concluded that n-body systems are 'fundamentally unpredictable'.
“The inability to turn back time is no longer a statistical argument,” said Portegis Zwart. 'This is already hidden in the basic laws of nature. No system of three moving objects, large or small, planets or black holes, can escape the direction of time. '
The study was published in the Royal Astronomical Society's Monthly Notices.
