Thank you for the clarification; let me go step by step.
On 11 Aug., 23:53, Igor Khavkine
> There is the "action functional", S[x(t)], which is an integral
> expression involging the Lagrangian, which associates a number to any
> motion of the system, x(t). The variation of S[x(t)] with respect to
> x(t) gives the dynamical equations of motion for ths system. I don't
> know of any way to determine, empirically, the action functional for any
> given system. In fact, there are often different but equivalent action
> functionals that can correspond to the same physical system! So, the
> "action functional" is not a likely candidate for a physical observable
> (this statement can be made more technical and more forceful).
This was what I meant. Now S=int L dt in classical physics
can be determined (at least for the actual path) if L is
specifically
defined as Ekin-Epot. This quantity is surely measurable.
If we use the same definition in quantum theory, S
must be measurable as well !? (I add a question mark,
because I agree that this topic is not often discussed,
so I am somewhat in muddy waters.) Do you agree?
If there is agreement here, we can go on afterwards to see
how to measure it in quantum theory.
John