Example of Indeterminacy in Classical Dynamics

The developments in physics since the early decades of this century have shown that our physical world is not completely empirically deterministic, that is, the motion of a mechanical system cannot be fully determined from physical measurements of the initial positions and velocities of its points. In particular, chaos theory has shown that infinite precision is required in the measurements of initial conditions for the motion to be fully predicted even qualitatively. On the other hand, Heisenberg's uncertainty principle holds that simultaneous measurements of positions and velocities can be made only with limited precision. The presence of noise further limits the accuracy of measurement. In spite of these fundamental limitations on our ability to make predictions from empirical observations, it is generally believed that models obtained from classical mechanics are completely deterministic and, if obser-