quantum mechanics - How isolated must a system be for it's wave function to be considered not collapsed?

As an undergrad I was often confused over people's bafflement with Schodinger's cat thought experiment. It seemed obvious to me that the term "observation" referred to the Geiger counter, not the person opening the box. Over time, I have come to realize that the Copenhagen interpretation actually is ambiguous and that "observer" cannot be so easily defined. Nonetheless, an objective collapse theory (which is what I was unknowingly assuming) still seems to me the simplest explanation of wave collapse phenomena.

I have read some of the objections cited in the Wikipedia article linked above, but it is still unclear to me why most physicists adopt the Copenhagen interpretation and reject objective collapse. For example, in this question on hidden observers, there was some discussion about the mechanism of wave collapse. It was suggested that perhaps the gravitational pull of a hidden observer would collapse the wave function. In response, it was pointed out that the gravitational pull would be negligible at the scales involved.

Okay, then imagine the following:

A hermetically sealed (i.e. isolated) box is balanced on a fulcrum. Inside the box is a radioactive isotope, a Geiger counter, and a trigger mechanism connected to a spring loaded with a mass on one side of the box. If the Geiger counter detects a decay, the trigger releases the spring and the mass shifts to the other side of the box. The shift in mass would, under observable conditions tilt the box on the fulcrum.

According to the interpretation of Schrodinger's cat that I often hear (the cat is in a superposition) it seems that the box should slowly tilt over as the wave function of the system evolves with the half-life of the isotope. I can't imagine that anyone thinks this is a realistic expectation.

I can see that people might object and say "But the contents of the box are interacting gravitationally with the outside system and observer so it is not really isolated!" Well, what of it? The same is true of the cat even if the interaction is less dramatic.

The question, then, is: How isolated must a system be for it's wave function to be considered not collapsed?

Answer

''How isolated must a system be for it's wave function to be considered not collapsed?''

Experimentally, a system whose collapse is observable must be so small that one can prepare it in a well-defined pure state. If this is not the case, one can only speculate about what happened, leaving much room to imagination.

This means that even when the carrier of the system is fairly big, the wave function collapsed models only extremely few degrees of freedom, and the real system considered is the one with these few degrees of freedom, not the bigger one.

For example, arXiv:1103.4081 discusses superposition and collapse of macroscopic objects. But prepared in a superposition is only a single degree of freedom, the distance; all other degrees of freedom are either uncontrolled (and hence presumably in a mixed state) or eliminated by extreme cooling. Thus the system measured is in effect a single quantum oscillator.

Now a typical quantum oscillator decoheres rapidly unless isolated, and a quantum oscillator of some size is hard to isolate. The experimental art consists in maintaining a superposition of two distances by isolating this particular degree of freedom from the environment. This isolation must be almost perfect, as otherwise decoherence effects responsible for the collapse set in extremely rapidly. (No special observer is needed. The environment does the observing by itself.)

''why most physicists [...] reject objective collapse.''

The main reason is that they want to maintain the simplicity of the traditional quantum mechanical foundations that are based on the assumption that the dynamics of quantum states is exactly linear, which seems to suffice for all applications. Objective collapse theories would require a tiny nonlinear modification of the basic laws, and spoil simplicity for (so far) uncheckable philosophy.

Note that ''no objective collapse'' doean't mean that collapse isn't observable (it is observed routinely), but only that the collapse is not due to decoherence (the approximation in which the collapse is derivable in terms of generally believed assumptions from statistical mechanics - needed already in classical physics) but to objective deviations from the Schroedinger equation. The latter has no observable basis, and hence is rejected by most physicists.