On the Inherent SelfExcited Macroscopic Randomness of Chaotic ThreeBody Systems
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), multiplescale (from 10^{60} to 10^{2}) numerical simulations of a chaotic threebody 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 threebody system enlarges exponentially into macroscopic randomness (at the level O(1)) until t = T*, the socalled physical limit time of prediction, but propagates algebraically thereafter when accurate prediction of orbit is impossible. Note that these 10 000 samples use microlevel, 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 threebody system is selfexcited, say, without any external force or disturbances, from the inherent microlevel uncertainty. It provides us the new concept "selfexcited 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 threebody system might randomly disrupt with symmetrybreaking at t = 1000 in about 25% probability, which provides us new concepts "selfexcited random disruption", "selfexcited random escape" and "selfexcited symmetry breaking" of the chaotic threebody system. Hence, it suggests that a chaotic threebody system might randomly evolve by itself, without any external forces or disturbance. Thus, the world is essentially uncertain, since such kind of selfexcited 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 socalled "moleculeeffect" (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.
 Publication:

International Journal of Bifurcation and Chaos
 Pub Date:
 2015
 DOI:
 10.1142/S0218127415300232
 arXiv:
 arXiv:1407.4019
 Bibcode:
 2015IJBC...2530023L
 Keywords:

 Origin of randomness;
 microscopic uncertainty;
 microlevel fluctuation;
 threebody system;
 chaos;
 Clean Numerical Simulation (CNS);
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 15 pages, 5 figures, accepted by Int. J. Bifurcation and Chaos, will be published via Open Access