It seems to me, it should be possible to model the wave function collapse by describing the macroscopic object (i.e., the measurement device) in purely quantum terms and then taking the classical limit. I have in mind here the analogy with phase transitions, where the non-analytical behavior of the partition function emerges only in the thermodynamic limit ($N\rightarrow+\infty$, $N/V\rightarrow const$). The question is then two-fold:
- What is the minimal quantum mechanical model for describing the collapse? (Perhaps something like the system of interest coupled to a bath of oscillators, which model the macroscopic object.)
- What are the limits for the object to be considered as macroscopic (infinite number of particles is not enough; finite temperature (=thermodynamic equilibrium) would probably do the trick, but is this really necessary?)
Updates
- One way of seeing it is literally in terms of phase transitions: wave function collapse is treated as spontaneous symmetry breaking, after which the system finds itself in a well-defined state. The relevant reference proposed by @QuantumLattice is arxiv.org/abs/1210.2353.