Relation between operator and experimental action

[ConanConanConan]

Hi I have some questions about operator and experimental action

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

 

[LightHero]

!The answer to your first question is yes, any experimental action can be described by some corresponding operator. This is because of the principle of conservation of energy, which states that energy cannot be created or destroyed but only changed from one form to another. This means that any action can be expressed as an operator acting on a system of particles, which then causes a change in the energy of the system.The answer to your second question is also yes, there is always some experimental realization for each operator. The way to realize a particular operator can vary depending on the physical system being studied. For example, the time reversal operator can be realized experimentally by reversing the direction of motion of a particle.The answer to your third question is that the link between operators and experimental action is established through theoretical models. A theoretical model is used to describe a physical system mathematically, and the mathematical expressions in the model can then be translated into operators. Once the operators have been identified, they can then be related to the physical processes they represent. This process is not just guesswork, but relies on a deep understanding of the underlying physics.