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ConanConanConan

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1, For each experimental action(no matter how trivial or complex), can they ALWAYS be described by some corresponded operator? how to proof? For example, adding some energy to excit a particle can be described in operator language as up ladder operator in QM.

2, For each operator, is there AlWAYS existing some certain experimental realization way? if not, is it because theoretically impossible or such a relation is not found yet. For example, to realize ladder operator in QM(which is not an obsevable), we add/extract energy from a particle(wavefunction), to realize hamiltonian operator, we measure energy with, say, tracking detectors for ATLAS. But how to realize time reversal operator?

3, How to establish the link between operator and experimental action. For example, again, ladder operator case. we know such a mathematical form for ladder operator in QM. On the other hand, we know adding/extracting enengy can change wavefunction. Then the link between operator and experimental action is established. Such a process, to me, is, to some extent, guessing.

My answer to question 3(not so sure): if such an relation between operator and experimental action is not established, that theory model will be abandoned and we seek until find one which has such a relation. We just guess and try the right model to match the real world.

But is there any deep connection behind? Though I know guessing is a critical part in physics, especially in theory.

Thanks