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With quantum decoherence, are there still any "gaps" in our knowledge of quantum mechanics that hint (either in terms of the physics, philosophy, or otherwise) at the need for further interpretation?

For instance, prior to decoherence, the "collapse" of the wave function lacked any mechanism or justification which hinted at the need for a deeper understanding. What explanatory power (or even interpretational satisfaction) do models such as many worlds give us that the laws of the quantum mechanics with decoherence alone do not?

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    $\begingroup$ Decoherence doesn't at all explain "collapse." It only explains the loss of coherence (ie interference effects). State reduction is still a "mystery" given an understanding of decoherence, and as such, all the various interpretational issues are still relevant. Long before Zurek et al even Bohm (of pilot wave theory) and Everett (of Many Worlds) had a basic development of decoherence in order to explain the loss of coherence in their interpretations. The main interpretational dichotomy comes into how you explain state reduction and whether you take the wave function as 'epistemic' or 'ontic'. $\endgroup$ – user1247 Feb 6 '16 at 21:30
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    $\begingroup$ But if we take the wave function and decoherence "seriously" can it not be suggested that there is no callapse, no state reduction - rather that the state of the system under observation is just entangled with its environment? Are you saying that even with decoherence, there is no explanation for why a system under a superposition of states appears to take a definite state when observed even if we don't presuppose that this state reduction be "real"? (by "real" I mean that the system actually ceases to be in superposition) $\endgroup$ – Jke Feb 6 '16 at 21:47
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    $\begingroup$ In this context I'd take collapse to mean that while decoherence reduces an entangled pure state to a mixed one, we still don't know why only one possiblity is chosen, or how. It's possible that the question has no answer. $\endgroup$ – Javier Feb 6 '16 at 23:22
  • $\begingroup$ @Jke, by taking the wave function "seriously", you are inadvertently making the philosophic commitment that the wavefunction is "ontic," i.e. "real," and not "epistemic," i.e. just a tool for accounting for our lack of knowledge about the state of a system. These are useful google keywords to help you understand the situation. Under Everett et al there is indeed an explanation for how superposed states can appear to reduce to a definite state despite not admitting that state reduction is "real": that is just the many worlds argument. But decoherence does not commit one to that position. $\endgroup$ – user1247 Feb 7 '16 at 1:42
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What explanatory power (or even interpretational satisfaction) do models such as many worlds give us that the laws of quantum mechanics with decoherence alone do not?

It should be noted that interpretation of quantum mechanics do not provide any explanatory power. An interpretation is a way for us to try to "intuitively" understand what the equations are telling us, and as such might help to guide further research, but in itself, it does not explain anything.

In this sense "decoherence", in the sense of the work of people such as for example Zurek et al., might be a little different than many-world, in that it attempts to model the mechanism for which a pure state becomes a "classical" mixture. In this sense, it is less an interpretation than a model for the measurement process.

Still, I would argue that decoherence models do not really "explain" the collapse of the wavefunction, as the interpretation of the eigenvalues of the density matrix as outcome probabilities still relies on the Born rule in the larger system+environment space. It might explain why, neglecting the larger environment, measurement results have a well-defined value, but it does not explain how one the possible outcomes is "chosen" any more than Born's rule/axiom does.

More generally, I don't think there is any commonly agreed-upon answer to the question "are there still gaps in our knowledge of quantum mechanics that need further explanation". Many would argue that the answer is yes, others that it is no. We will likely only know that the answer was yes if/when someone comes up with a better theory.

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