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As I understand it, there is a large contingent of physicists who believe that the measurement problem is "solved" by decoherence, without, for example, needing to postulate the existence of "many worlds." Yet at the same time my understanding is that in the decoherence picture there is only unitary evolution of the wave function, and that while the appearance of collapse is explained, the global superposition of states still in fact exists, and whether or not multiple states within the universal wave function observe the same appearance of collapse (but to different eigenvalues) is a question that is left completely unaddressed.

Therefore my reading of the decoherence picture is that it is virtually identical to an Everettian approach, except that it purposefully ignores an obvious interpretational consequence of its description. Is this true, or do decoherence-based approaches somehow argue that there really is only a unique observer within the universal wave function that observes a collapse to unique eigenvalues, and that there is some form of symmetry breaking that allows this to happen at the expense of all the other potentially conscious components of the universal wave function?

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A nontrivial issue here is what would qualify as "distinct." Usually we consider two scientific theories to be distinct if they make different predictions about the outcomes of experiments. By this criterion, for example, the Schrodinger wave picture and Heisenberg matrix picture are not distinct; they are different mathematical representations of the same underlying theory. But no interpretation of QM ever makes a prediction about the outcome of any experiment that differs from the predictions made by other interpretations. –  Ben Crowell Oct 20 '13 at 20:00
    
@Ben Crowell, I do not think that is a nontrivial issue. Two ontological descriptions, for example, can predict the same physics, and yet be distinct or non-distinct. Are the descriptions the same or not? Bohm's pilot wave description is obviously a distinct description from the two considered here, for example. –  user1247 Oct 20 '13 at 21:08
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I'm not saying that distinctness has to be defined by empirical testing. But if you're not defining it that way, then it's not clear that your question has a specific answer unless you clarify how you are defining it. –  Ben Crowell Oct 20 '13 at 21:13
    
@Ben Crowell, we may have to just disagree here, but I really think the last sentence of my post addresses your concern pretty clearly. –  user1247 Oct 20 '13 at 22:55
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This is a great question, and I hope someone has an answer to it. I've always shared your suspicion. All the arguments I've seen for the decoherence interpretation just boil down to "the off-diagonal terms disappear in the thermodynamic limit, therefore we can interpret it as a classical probability distribution", but as you point out this sweeps an awful lot under the carpet, including the fact that the system-plus-heat-bath is still unitary, as well as the fact that the thermodynamic limit is only an approximation anyway. Still, maybe a more principled argument exists in the literature. –  Nathaniel Oct 21 '13 at 2:54

2 Answers 2

Quantum research over the last 20-30 years into decoherence/open quantum systems has matured to the point that decoherence is now considered an undeniable feature of our world and most certainly plays a role in explaining the measurement problem.

Some of measurement type problems decoherence solves:

  1. Decoherence: How a coherent superposition of 2 different measurement options can locally evolve into an incoherent mixture of 2 different possibilities with probability outcomes given by the Born rule (i.e. wavefunction collapse).
  2. Einselection (Environmentally induced superselection): How classical states seem to have a preferred basis i.e. $\left|alive cat\right>$ or $\left|dead cat\right>$ cat but not $\left|alive cat\right>\pm\left|dead cat\right>$ (essentially into the basis represented by the Schmidt decomposition of the interaction Hamiltonian between the quantum and classical system).

Now 1 explains wavefuction collapse which is half of the measurement problem, but what decoherence by itself doesn't answer is how/why in a particular measurement, such as of alive cat + dead cat, does nature pick the specific outcome it does (say alive cat). This is where the MWI (with decoherence) differs from the other decoherence based interpretations.

To explain this difference, consider flipping a coin. I flip a coin and you have no idea what the outcome is until the coin comes up heads. So what decided it should be heads? In a classical (deterministic) world the initial conditions and the rules of mechanics decided what the outcome would be, so ontologically (i.e. the real state of reality "out there") the outcome was already determined, but epistemically (i.e. the state of the system based on your knowledge) was the only thing that was uncertain. So a probabilistic description of reality (in a classical world) is only needed due to subjective lack of full knowledge.

Now the quantum world is different, because it is demonstratively non-contextual, meaning that outcomes in general cannot have definite values in advance. So in a quantum world probabilities are not just a demonstration of a lack of knowledge, but are an intrinsic feature of reality itself. Wojciech H. Zurek (one of the main physicists who discovered decoherence and one of the biggest advocates of non-MWI, decoherence based interpretations of QM) describes such intrinsic uncertainty "epiontic" i.e. such uncertainty describes both the ontic and epistemic state.

So now if I flip a quantum coin and it comes up heads, what determined this outcome? The MWI makes the analogy with classical probability and says it is entirely due to the lack of full knowledge on the part of the observer, specifically concerning which universe the observer would end up it. Whereas the more mainline view (e.g. the view closest to the Copenhagen anti-realism) is to maintain that there was no definite outcome in advance, i.e. nature is intrinsically uncertain and random and additional universes are unnecessary to simply to maintain a form of ontic determinism.

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I am conserved if quantum world is really different than the classical ones. (1) The time evolution for the state vector is governed by the deterministic Schrodinger picture. (2) The measurement happens between microscopic system and marcroscopic equipment; The equipment has $10^{23}$ degrees of freedom. In practice, we neither know nor compute all the states of equipment, just like the air and material conditions of flipping the coin, we leave with a statistical result. If quantum world is really different than classical, we have to admit the Schrodinger picture is incomplete. –  user26143 Mar 13 at 4:46
    
My problem is that your last sentence seems directly at odds with assuming reality of the universal wave function. I don't see how you can maintain both pictures simultaneously. –  user1247 Mar 13 at 15:50
    
What do you mean by reality and both pictures? Or is your comment on Punk_Physicist's answer? P.S. I did not maintain deterministic and non-deterministic simultaneously. The statistical result in my first comment means like classical statistic in flipping coin, it is intrinsic deterministic (coming from Schrodinger picture), but we are technically unable to compute it, so we do statistics. The If quantum world is really different than classical means if quantum world is intrinsic non-deterministic. –  user26143 Mar 13 at 16:33

Decoherence and collapse/MWI are actually complementary, since they address completely different aspects of the classical limit. Decoherence explains what happens with interference terms on macroscopic systems, but it doesn't address the problem of individual measurements. The classical probability distribution of a mixed state describe what happens in a statistically large sample of measurements. Collapse and MWI both address what happens on a specific instance of measurement.

Individual measurements are fundamentally non-unitary transformations relative to the observer. They make losses of quantum state and information that are irrecoverable even in principle. We've know this for almost a century, but there are still a majority of physicists that are assuming that measurements can be explained as a complex interaction of purely unitary operations.

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