Abstract
What is the origin of macroscopic randomness (uncertainty)? This is one of the most fundamental open questions for human beings. In this paper, 10 000 samples of reliable (convergent), multiple-scale (from 10(-60) to 10(2)) numerical simulations of a chaotic three-body system indicate that, without any external disturbance, the microscopic inherent uncertainty (in the level of 10-60) due to physical fluctuation of initial positions of the three-body system enlarges exponentially into macroscopic randomness (at the level O(1)) until t = T*, the so-called physical limit time of prediction, but propagates algebraically thereafter when accurate prediction of orbit is impossible. Note that these 10 000 samples use micro-level, inherent physical fluctuations of initial position, which have nothing to do with human beings. Especially, the differences of these 10 000 fluctuations are mathematically so small (in the level of 10(-60)) that they are physically the same since a distance shorter than a Planck length does not make physical sense according to the string theory. This indicates that the macroscopic randomness of the chaotic three-body system is self-excited, say, without any external force or disturbances, from the inherent micro-level uncertainty. It provides us the new concept "self-excited macroscopic randomness (uncertainty)". The macroscopic randomness is found to be dependent upon microscopic uncertainty, from the statistical viewpoint. In addition, it is found that, without any external disturbance, the chaotic three-body system might randomly disrupt with symmetry-breaking at t = 1000 in about 25% probability, which provides us new concepts " self-excited random disruption", "self-excited random escape" and " self-excited symmetry breaking" of the chaotic three-body system. Hence, it suggests that a chaotic three-body system might randomly evolve by itself, without any external forces or disturbance. Thus, the world is essentially uncertain, since such kind of self-excited macroscopic randomness (uncertainty) is inherent and unavailable. This work also implies that an universe could randomly evolve by itself into complicated structures, without any external forces. To emphasize this point, the so-called " molecule-effect" (or "nonbutterfly effect") of chaos is suggested in this paper. All of these reliable computations could deepen our understandings of chaos from physical viewpoints, and reveal a kind of origin of macroscopic randomness/uncertainty.