Principle of Least Action, 3.1

Moreover, in the usual formulation of classical action principles, the initial and final states of the system are fixed, e.g.,

    Given that the particle begins at position x1 at time t1 and ends at position x2 at time t2, the physical trajectory that connects these two endpoints is an extremum of the action integral.

In particular, the fixing of the final state appears to give the action principle a teleological character which has been controversial historically. However, this apparent teleology occurs only because of the way in which the question was asked. By specifying some but not all aspects of both the initial and final conditions (the positions but not the velocities) we are making some inferences about the initial conditions from the final conditions, and it is this “backward” inference that can be mistaken for a teleological causal influence.

— Wikipedia on Principle of least action

2011.05.30 Monday ACHK