The n-body problem

Being rather limited in math, to say the least, yours truly follows science and physics from the visual & verbal perspective so when brilliant researchers describe complex issues in ways I can follow, the topic discussed becomes fascinating to the max.

To whit:

The n-body problem is a famous problem in astrophysics. It arises as 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 to mathematically predict, according to Newton's laws of motion and Newton's law of universal gravitation.

However, once you add another body, things become tricky. The bodies start to gravitationally perturb each others' orbits, introducing an element of chaos into the interaction. This means that, although solutions exist for special cases, there is no one formula - under Newtonian physics or general relativity - that describes these interactions with complete accuracy.

Here's where it gets really interesting.

When running n-body simulations, physicists sometimes return time-irreversibility in their results - in other words, running the simulations backwards doesn't get them to the original starting point.

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".

How cool is that?

Chaos rules yet again as one cannot retrace exactly the paths
3 or more bodies take in any given length of time.

A animation of a double-rod pendulum at an intermediate energy showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a vastly different trajectory. The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions.