On Failure of Determinism in Classical Mechanics

Abstract

Newtonian mechanics is generally considered to be deterministic: Once the initial conditions are known, all the future behaviour of a system can be predicted by solving the equations of motion. (That is the idea of Laplace’s demon.) But a simple example will reveal that the solution of the initial value problem need not be unique. A prediction thus becomes impossible. An effect can happen without a cause, so that causality is annulled.