Reversing the arrow of time is not always possible

When three or more celestial bodies interact with each other, it is impossible to reverse their movement. This is the conclusion of an international team of researchers, led by Tjarda Boekholt, from the Physics Centre of the University of Coimbra (UC), through computer simulations of the movement of three black holes.

The study contributes to a better “microscopic” understanding of the arrow of time, one of the greatest mysteries of physics, and will be published in the April issue of the scientific journal “The Monthly Notices of the Royal Astronomical Society”.

The majority of the fundamental laws of physics have no problems with the direction in which they occur. As scientists like to say, they are symmetrical through time. However, we all know that time cannot go backward. A glass that falls and breaks cannot come back in one piece. Up to now, scientists have explained the break in symmetry over time due to the statistical interaction between a large number of particles. Now, astronomers Tjarda Boekholt (University of Coimbra, Portugal), Simon Portegies Zwart (University of Leiden, Netherlands) and Mauri Valtonen (University of Turku, Finland) show that not many particles are needed, but only three are enough to break symmetry in time.

The researchers calculated the orbits of three black holes which interact with each other. They carried out two types of simulations. In the first one, black holes are initially at rest. However, because of gravity, they attract each other and cross each other in chaotic orbits, until one of the black holes escapes the attraction of the other two. In the second simulation, the system starts with the final situation of the previous simulation, and tries to revert time back to the initial situation.

These simulations show that time cannot be reversed in 5% of the calculations. Even if the computer uses more than 100 decimal places, the symmetry of time is interrupted by the exponential growth of disturbances the size of Planck’s length, which is about 10-35 meters. This 5% is therefore not a question of better computers or smarter calculation methods, as previously thought.

Astronomers explain irreversibility using Planck’s concept of length. This is a known principle in physics that applies to phenomena at the level of the atom. The principal investigator, Tjarda Boekholt, says that “the movement of the three black holes can be so chaotic that something as small as Planck’s length comes into play. The symmetry of time is broken by disturbances in the size of the Planck length».

Co-author Portegies Zwart adds that «not being able to go back in time is no longer a statistical argument. This phenomenon is 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 main result of this work, highlights Tjarda Boekholt, «is to show that there are systems in the Universe that are fundamentally unpredictable. This is a consequence of chaos theory and the exponential growth of small-size disturbances in Planck’s length. So astronomers have to try to understand systems in a more qualitative way».

Another consequence, concludes the UC researcher, «is that systems become asymmetric in time, even if the underlying equations are symmetric in time. Now there is a preferable direction, that is, we can distinguish the future from the past. Our study is a first step towards a better “microscopic” understanding of the arrow of time».

You can see the video that illustrates the study at: https://www.youtube.com/watch?v=c2Mbx5BKyfM.

Scientific Paper: “Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length”. By: T.C.N. Boekholt, S.F. Portegies Zwart, M. Valtonen. In: Monthly Notices of the Royal Astronomical Society, Volume 493, Issue 3, April 2020, Pages 3932–3937, https://doi.org/10.1093/mnras/staa452 (original) https://arxiv.org/abs/2002.04029 (free preprint).

^{Translation by Diana Taborda}