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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.
Roger V.
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    This: https://arxiv.org/abs/1210.2353 – QuantumLattice Sep 20 '21 at 15:05
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    In the actual classical limit, QM stops existing, so we can't take the full limit - the Copenhagen explanation of measurement treats the measuring apparatus as a quantum system with a quasi-classical wave function, that's vital, and describes the measurement as an interaction between them but unavoidably invokes the classical nature of the measuring apparatus to claim a single measurement results from the process, otherwise even the system we're measuring does not even have a wave function after the measurement. See my answer here. – bolbteppa Sep 20 '21 at 16:21
  • Take a look at semiclassical approximations. – Mauricio Sep 20 '21 at 20:15
  • @Mauricio this is not what I mean really. As I understand quasiclassical approximation, it is about limited precision - it is a mathematical approxion. – Roger V. Sep 21 '21 at 04:55

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