Experiments that can falsify the Copenhagen quantum theory?

Question

Are there experiments that can falsify the Copenhagen interpretation, specifically the quantum-classical threshold? Though welcomed, I'm not asking for a historical review, but actual experiments that might be doable in the future, or thought experiments.

All quantum experiments that I have seen can be concluded into the following three steps:

1. We prepare a quantum system at either a classically deterministic pure state $\psi$ or a classically random mixed state $\rho$.
2. We apply a unitary transformation $U$ on it.
3. We measure an observable $O$ on the result state $U\psi$, and $O$ corresponds to certain classical physical quantity such as $x,p,E,\cdots$.

In steps 1 and 2, we apply Schodinger's equation, or say, QFT incorporating special relativity. In step 3, we apply Born's rule. All experiments in this framework will not contradict the Copenhagen interpretation. Are there experiments that are not in this framework?

Different from the question Is the Copenhagen interpretation falsifiable? I am not asking to falsify the Copenhagen interpretation, as said by people an interpretation cannot be falsifwant experiments to falsify the theory: There is a quantum-classical threshold. Below the threshold, everything evolves following Schodinger's equation. Above threshold, everythign evolves clasically. When we use a clasical system to measure a quantum system (interaction), the results follows the Born's rule.

Answer 1

Sure, there are experiments that deviate from this idealized scheme. For example, measurement of absorption spectrum (or index of refraction) of macroscopic sample of matter with many identical copies of the studied system (atom, molecule).

1. It is not us who prepare any quantum state, we just typically assume density matrix for the atom/molecule close to thermal equilibrium, perturbed by light.

2. We do use unitary transformation on the quantum state for atom/molecule in very simplified models, but to get more realistic results, we use (approximate, effective) evolution equations for density matrix of an open quantum system that can suppress coherences and describe dephasing and energy dissipation. This preserves probabilities, but it is not really a unitary (reversible) transformation like when single atom evolves in a known fully specified environment.

3. We can often calculate intensity of light from semi-classical model, where the system is quantum, but EM field is classical (described by classical Maxwell's equations). So no operator for measured intensity and no Born rule is used. This is an approximate method, and can be made more quantum-theoretical by using full quantum theory of light, and then we do have operator for intensity of light, but typically we are interested in expectation values as functions of time, not in probabilities of particular values. Also, the measured light isn't used in further quantum modelling, so there is no use for projection.

This scheme, with effective evolution for density matrix, not explicitly using projection as instant change, deviates quite a bit from the idealized story in QT postulates with two types of evolution, but I wouldn't say it falsifies the Copenhagen interpretation. CI interprets what QT means when the idealized measurement scheme is applicable, like when measuring(preparing) spin projection of atom, or polarization projection of light. It doesn't require, I think, that all uses of QT have to follow that simplified scheme.