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Does decoherence solve the measurement problem in quantum theory?

• H. D. Zeh, one of the leading experts in the field of decoherence, writes in his article "Basic Concepts and Their Interpretation," "Because of the dynamical superposition principle, an initial superposition does not lead to definite pointer positions. ...environment-induced decoherence by itself does not solve the measurement problem." (p.14) "The measurement problem can only be resolved if the Schrödinger dynamics is supplemented by a non unitary collapse." (p.21) Similar statements have been made by Joos and other decoherence experts. Nevertheless, some physicists maintain that decoherence solves the measurement problem. Are the glossing over some part of the problem? Do they have a different understanding of what the problem is? Or perhaps they have a different standard for what constitutes an acceptable solution? In any case, what do you think? Does decoherence solve the problem or not? Why or why not? For a survey of this issue, see http://plato.stanford.edu/entries/qm-decoherence/#SolMeaPro

• Answer:

  Zeh, Joos and others quoted above are correct.  Decoherence does not solve the measurement problem, and it does not claim to.  It solves some of it, not all of it.  There are physicists who claim that it solves the whole thing, and they are -- with respect -- wrong.  In technical terms, the distinction is between a proper and improper mixture.  A proper mixture is ignorance interpretable (i.e., the system is in one of the pure states, we just don't know which one), but an improper mixture is not -- it can only be interpreted as being the reduced part of a larger pure state.   And decoherence can only give us an improper mixture.  For a good run-through of the technical differences, I don't know anything better than Stephen Adler's paper, which is very patient and clear.  It's called  http://arxiv.org/abs/quant-ph/0112095 and was certainly enough to convince Anderson that he was wrong.In very non-technical terms, the distinction can be made like this.  Decoherence shows why things at the classical scale (e.g., measurement apparatus) "look classical" i.e., they're in one determinate place rather than smeared around in position or momentum space.  The answer decoherence gives is that the other states are unstable on any sensible timescale.  And this is a big step forward. But we're not there yet: unfortunately decoherence preserves ALL of the classical-looking states, corresponding to all possible results of the experiment.  So, it says that the state in which the measurement pointer is exactly at 1 is stable, but so's the one in which it's at 2, and the one that it's at 3 etc.  In does not show why only one of those is selected to make up classical reality rather than the others.  Indeed, not only decoherence, but ANY quantum mechanical process must preserve all the possible results, because the evolution of the wavefunction has to be unitary (and so, preserve linearity)So if you accept decoherence (and you should: it's a straightforward application of quantum mechanics), there are a variety of moves you can make to solve the last bit of the measurement problem:1) "It's just probability: you use the Born rule to determine which alternative is realised, and that's just a rule on measurement that I impose"  (congratulations, you're a Copenhagen interpretation person like Bohr or von Neumann).2) "It's just probability: you use the Born rule to determine which one is realised, and I have a new theory of dynamics that tells me how that happens" (congratulations, you're a stochastic collapse theorist like Ghirardi, Rimini and Weber)3) "The actual branch is selected by the position of a hidden variable which we were ignorant about until we did the measurement" (congratulations, you're a hidden variables theories list De Broglie or Bohm)4) "I am making no move at all, all the states are realised, it is just that I experience only one" (congratulations, you're a many worlds theorist like Everett)... and probably others.  The point is, you need an interpretation as well as decoherence to solve the measurement problem -- it doesn't do the job on its own.