  Numerical solutions to Newton's equations of motion for chaotic self
gravitating systems of more than 2 bodies are often regarded to be
irreversible. This is due to the exponential growth of errors introduced by the
integration scheme and the numerical round-off in the least significant figure.
This secular growth of error is sometimes attributed to the increase in entropy
of the system even though Newton's equations of motion are strictly time
reversible. We demonstrate that when numerical errors are reduced to below the
physical perturbation and its exponential growth during integration the
microscopic reversibility is retrieved. Time reversibility itself is not a
guarantee for a definitive solution to the chaotic N-body problem. However,
time reversible algorithms may be used to find initial conditions for which
perturbed trajectories converge rather than diverge. The ability to calculate
such a converging pair of solutions is a striking illustration which shows that
it is possible to compute a definitive solution to a highly unstable problem.
This works as follows: If you (i) use a code which is capable of producing a
definitive solution (and which will therefore handle converging pairs of
solutions correctly), (ii) use it to study the statistical result of some other
problem, and then (iii) find that some other code produces a solution S with
statistical properties which are indistinguishable from those of the definitive
solution, then solution S may be deemed veracious.
