Should we be astonished by the Principle of “Least” Action?

QuinceyFig2As one goes through more advanced expositions of quantum physics, the concept of action is gradually given more importance, with it being considered a fundamental piece in some introductions to Quantum Field Theory (Zee, 2003) through the use of the path integral approach. The basic idea behind using the action is to assign a number to each possible state of a system. The function that does so is named the Lagrangian function, and it encodes the physics of the system (i.e. how do different parts of the system affect each other). Then, to a trajectory of a system we associate the integral of this number over all the states in the trajectory. This contrasts with the classical Newtonian approach, where we study a system by specifying all the possible ways in which parts of the system exercise forces on each other (i.e. affect each other’s acceleration). Using the action usually results in nicer mathematics, while I’d argue that the Newtonian approach requires less training to feel intuitive.

In many of the expositions of the use of action in physics (see e.g. this one), I perceive an attempt at transmitting wonder about the world being such that it minimizes a function on its trajectory. This has indeed been the case historically, with Maupertuis supposed to have considered action minimization (and the corresponding unification of minimization principles between optics and mechanics) as the most definite proof available to him of the existence of God. However, along the spirit of this stack exchange question, I never really understood why such a wonder should be felt, even setting aside the fact that it assumes that our equations “are” the world, a perspective that Artem has criticized at length before.
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