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3-body system will destroy the inversion symmetry of time

3-body system will destroy the inversion symmetry of time


Most laws of physics do not care about the direction of time. Forward, backward , Either way, nature's laws apply perfectly. Newtonian physics, general relativity-time has nothing to do with mathematics: this is called time inversion symmetry.

In the real universe, things get complicated. Now, a team led by astronomer Tjarda Boekholt of the University of Aveiro, Portugal, proves that only three gravity-interacting celestial bodies can break the symmetry of time reversal.

They wrote in the paper, that To date, the quantitative relationship between chaos and irreversible levels in stellar dynamical systems remains uncertain. In this work, we pioneered the use of an accurate Brutus n-body simulation algorithm program Chaotic three-body systems in gravitational systems go beyond standard double-precision algorithms. We prove that the proportion of irreversible solution systems is a power-law distribution that increases with the degree of chaos in the system.

The n-body problem is a well-known problem in astrophysics. The root is in mathematics. Even just applying Newton's laws of motion and Newton's law of gravitation and examining three or more celestial bodies interacting with each other's gravitation can make things extremely tricky.

Even the solar system, which we are very familiar with, we can only predict the development of millions of years in the future. In the universe, chaos is a feature, not a mistake.

When simulating n-body motion, physicists sometimes return results that are irreversible in time,in other words, inverse simulations do not return them to their original starting point.

It is unclear whether they come from the problem of the chaotic system itself or the problem of calculation accuracy, which leads to its uncertainty.

Therefore, Boekholt and his colleagues designed a model to solve this problem. He and computational astrophysicist Simon Portegies Zwart of the University of Leiden in the Netherlands previously wrote an n-body simulation program called Brutus that uses brute force calculations to reduce the magnitude of numerical errors.

Now they use it to test the time reversibility of the three-body system.

Because Newton's equation of motion is time-reversible, running forward and then running backward should restore the initial state of the system (although there are sign differences in speed). Therefore, the results of the reversibility test are exactly known. 

The celestial body used to simulate is 3 black holes. First, black holes start at rest and approach each other, creating complex orbits. Then, due to the effect of gravitational slingshots, a black hole is thrown out of the orbit.

This concludes the forward simulation. Now take the above last frame as the starting point, and give the relevant objects reverse physical quantities, and try to restore the system to the initial state.

They found that simulations were irreversible 5% of the time. The returned result is equivalent to slightly disturbing the initial state, and the scale is Planck length-0.000000000000000000000000000000000000000016 meters, the smallest possible length.

The movements of the three black holes may be very chaotic. In the original state, there was only a disturbance of the Planck length, but due to the exponential effect, the subsequent development was tens of millions of miles away. Therefore, chaos destroyed the symmetry of time.

The 5% ratio does not seem to be high, but because the chaotic system is fundamentally unpredictable, we can never predict which simulation will fall within this 5% range.

They have proven that the problem comes from chaos itself.

Portegies Zwart said that The inability to trace back time is no longer just a statistical point of view. It is hidden in the basic laws of nature. No single system consisting of 3 moving celestial bodies (planets or black holes) can get rid of the direction of time.

The study has been published in the Royal Astronomical Society Monthly.

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