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In 1983 Leggett and Caldeira published a paper (see also here) that shows the evolution of the density matrix in a dissipative system. Follow-up work by Zurek and others shows the relevance to resolving the measurement problem.

Nevertheless my quantum information lecturer and the science community seem to think that the measurement problem is an unsolved mystery. Other people deny that the problem existed in the first place.

With this in mind: Why is it not widely accepted that Leggett and Caldeira solved the measurement problem?

For clarification: by measurement problem I mean the issue that there are two evolutions of of the wavefunction: a continuous one (Schrödinger equation) and a discontinuous one (measurement). Standard decoherence only says that we have to work in the measurement basis and thus gets around the problem of how the measurement actually occurs by ignoring it. In the Leggett-Caldeira-Zurek framework the discontinuous change simply disappears. Or does it?

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – David Z
    Commented Feb 24, 2016 at 9:36
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    $\begingroup$ The linked papers in the following post answer my question: physics.stackexchange.com/q/22745 $\endgroup$
    – Wolpertinger
    Commented Apr 10, 2016 at 17:46
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    $\begingroup$ @ACuriousMind it always seems to say "this question already has an answer here:" when a duplicate is marked, so I assumed the feature could be used to indicate when a question is answered somewhere else even though the question is not the same. Sorry if that was wrong, should I take any action to reverse the process? This is actually a special case as well because I was simply not informed well enough to ask the correct question that gets to the core of the problem of what I meant, but the other question did. $\endgroup$
    – Wolpertinger
    Commented Apr 10, 2016 at 20:33
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    $\begingroup$ @Numrok: You might also consider writing up your own answer for the benefit of all. Point out where you think you asked the wrong question and how to correct it and then answer it. $\endgroup$
    – Martin
    Commented Apr 13, 2016 at 9:26
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    $\begingroup$ @Numrok ah, I see what you're coming from, but that's not the intent of duplicate closure. When one question is closed as a duplicate of another, the idea is that any answer which addresses the first question would also be considered a valid answer to the other one. It's not enough that there happens to exist an answer to the other question which addresses the one you're closing. If you've found an answer to your question, I suggest going with Martin's advice. $\endgroup$
    – David Z
    Commented Apr 13, 2016 at 9:54

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As I stated in the comments the post by Arnold Neumaier in reply to this question answer mine too. In particular the papers he links (arXiv papers cond-mat/0102428 and cond-mat/0203460). In my mind the two papers are essentially a continuation of what Leggett and Caldeira showed (that the density matrix becomes diagonal when coupling to certain statistical ensembles). Namely Nieuwenhuizen et al. demonstrate by solving a representative system analytically that the complete measurement process (or "collapse of the wavefunction") can be seen as such a statistical coupling. From the abstract to the first paper:

A model of quantum measurement is proposed, which aims to describe statistical mechanical aspects of this phenomenon, starting from a purely Hamiltonian formulation. The macroscopic measurement apparatus is modeled as an ideal Bose gas, the order parameter of which, that is, the amplitude of the condensate, is the pointer variable. It is shown that properties of irreversibility and ergodicity breaking, which are inherent in the model apparatus, ensure the appearance of definite results of the measurement, and provide a dynamical realization of wave-function reduction or collapse. The measurement process takes place in two steps: First, the reduction of the state of the tested system occurs over a time of order ℏ/(TN1/4), where T is the temperature of the apparatus, and N is the number of its degrees of freedom. This decoherence process is governed by the apparatus-system interaction. During the second step classical correlations are established between the apparatus and the tested system over the much longer time-scale of equilibration of the apparatus. The influence of the parameters of the model on non-ideality of the measurement is discussed. Schrödinger kittens, EPR setups and information transfer are analyzed.

For me this answers what I was trying to get at (though didn't really succeed at formulating) in my question: that just claiming a statistical process "does the job" for collapsing the wavefunction is not enough, there are non-trivial features of the collapse that have to be explained and modeled appropriately. In the two papers this is done for analytically solvable systems.

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