Question

In what sense (if any) is Action a physical observable?

Answer 1

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So, Thé ÃnSwer is ::-:: Or consider the Lagrangian from electrodynamics which includes a term proportional to the vector potential, which is itself not directly measurable.So if Action was actually a "physical observable", one could determine the "correct" Lagrangian, which to me sounds like nonsense.

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Answer 2

The system evolves in a clear path, so I guess we could try to measure all the terms in the Lagrangian and integrate them along the path. However, multiple Lagrangians can describe the same evolution classically. The trivial example being scaling by a constant.