Scientist propose solution to quantum measurement problem, explain further Link to Article
The scientists

In their recent opus magnum, Theo Nieuwenhuizen (Institute of Physics, UvA) and colleagues claim to have found a solution to the so-called quantum measurement problem

Their claim

After reviewing the literature on measurement models, they focus on the so-called Curie-Weiss model for quantum measurements. The joint dynamics of the tested system coupled to the measurement apparatus now produces results that explain the measurement postulates. It shows that the off-diagonal terms ("cat-terms") disappear in a physical process due to the coupling to the apparatus, on a basis selected by the interaction Hamiltonian. The registration of the measurement outcomes by the pointer of the apparatus occurs because the measurement triggers the transition from the initial metastable state to one of the stable final states; the apparatus being large, this means an amplification of the signal. The transition of the pointer variable from its initial metastable state to one of the final stable states is a process with classical features, such as the dumping of excess free energy in the bath.

I am by no means a physicist, but I do enjoy trying to understand some of the issues they face. From what I've read this quantum measurement problem, well is a problem. Could someone explain why it is a problem, and how these scientist from the Institute of Physics propose to solve it? (as layman as possible)
 A: You may wish to look at http://plato.stanford.edu/entries/qt-measurement/ (Ref. A) to get a better idea of the quantum measurement problem.
Let me say a few words about the article by Allahverdyan, Balian, Nieuwenhuizen (ABN) (it is published in Physics Reports, but you can also find a version of it at http://arxiv.org/abs/1107.2138 ). I should note that I am no expert on quantum measurements, so please take the following for what it's worth.
I think ABN's work is outstanding, and this is not just my opinion. I hear from different people that this is the best we have now on this issue. I remember I attended Balian's presentation a few years ago, and Scully (an author of quantum theory of laser) commented (I cannot be sure about the exact words): "Good work. Why did not I do it?"
You probably know that standard quantum mechanics typically includes two parts: unitary evolution (say, the Schroedinger equation) and the theory of quantum measurements (say, the collapse postulate). These two parts are, strictly speaking, mutually contradictory (please see Ref. A). Using a specific model of quantum measurement, ABN derive the theory of quantum measurements from unitary evolution. Of course, they could not derive it rigorously, as you cannot mathematically derive a conclusion that contradicts the assumption, but they derive it as a physical approximation valid under some conditions. Their model describes a measurement of a spin projection of a particle using a measurement apparatus containing a large number of spins interacting with a phonon bath. The spin system is initially in a metastable paramagnetic state. Due to interaction with the particle, this system transitions to a ferromagnetic state with a lower energy. The resulting magnetization reflects the particle spin projection. You may conclude from ABN's results that the theory of quantum measurements is not an independent part of quantum theory, but an approximate consequence of unitary evolution.
ABN claim a solution of the measurement problem, and they may be right in some sense. I would like to add though that their work is not only outstanding, it is also highly disruptive (in the same sense as a business idea can be disruptive). The side effect of their work is that the theory of quantum measurements is just an approximation in the best case, the collapse postulate and even the Born rule are just approximations. For example, strictly speaking, you cannot even have a unique outcome of measurement: while the spin system transitions to a ferromagnetic state, this state is not final, and the system will return to the paramagnetic state due to Poincare's reversal, although this will take enormous time. Another consequence of ABN's results: measurement is independent of an observer - the result is registered permanently (modulo extremely slow reversal).
You ask in your comment: "Does this have to relate with Einsteins, hidden variables?" I think so, as, for example, in the Bell theorem, you have to use both unitary evolution and the theory of quantum measurements to prove that the inequalities can be violated in standard quantum theory. And if the theory of quantum measurements is just an approximation, all bets are off, if you ask me, as I cannot imagine what "approximate nonlocality" can possibly be. Furthermore, ABN emphasize that registration of a measurement outcome is a relatively slow process, as the apparatus must be a macroscopic system, and this may be relevant to the locality loophole in Bell experiments.    
A: “quantum measurement problem”  is a not real "problem" which these authors say they offer a "physical way out of a mathematical embarrassment” to something that is certainly not an embarrassment. Instead quantum uncertainty is what nature tells us about what is and what we can know. They are reported to conclude that the "dynamical instabilities inside the apparatus near the end of the measurement." can permit the statistical outcomes without need for a physical collapse. 
But no collapse nor multiple universes are really needed at all. That gets to the point that QM is not classic physics and trying to make it that is not productive. The reporting is that:
"The statistical formulation of quantum mechanics, though abstract and minimalist, is sufficient to explain all relevant features. Since alternative interpretations involve unnecessary assumptions of one kind or another, the authors advocate the usage of the statistical formulation in physics education of quantum mechanics."
So their conclusion is correct but I don't get why they think they have added anything - that is unless somehow saying that some large collection of quantum states that we call a measuring device can form a meta-stable state that then does not collapse when an observation is made. Although it is controversial to say this it is I think most correct to say that there is no wave function collapse. there is no measurement problem. Uncertainty is inherent. QM requires that we give up usual notions of reality but it requires little beyond HS math to follow. The  description of the wave function is a math language that best allows us to describe what nature allows us to predict or know. It has withstood all tests. It is absolutely clear that one cannot separate measurer and measured. It requires no collapse to provide it's answers and it tells us that we cannot know more than probabilistic outcomes for what we choose subjectively as  observations. 
A: The quantum measurement problem is the open question of the seeming "collapse" of the quantum wavefunction, as well as the unexplained occurrence of the Born Rule.
When we perform an experiment with measurable quantum effects, we get some unintuitive (to most) results. There are equations that govern the evolution of a quantum system with respect to time, in a way, behaving like complex-numbered waves. These are variations on a theme discovered by Schrödinger, and put into Relativistic terms by DeWitt and others.
The problem arises in that apparently parts of the wave function ceases to be measurable when we measure it, the fact that quantum mechanics is counterintuitive to the untrained, that quantum mechanics was discovered eighty years ago and a few other factors.
The most well-known-to-the-pulic proposed solution is the "collapse" interpretation, developed by Niels Bohr and others. It proposes that there are two fundamental kinds of interaction: The evolution of a quantum system as governed by the aforementioned wave-like equations, and a "mysterious" collapse.
The other one is the interpretation that in fact the system does a kind of split, and we only observe one of the branches (while an alternate universe researcher observes the other). This is already implied by the aforementioned equations and need no other mechanisms.
The thing is that the common populace has a notion that QM ought to be mysterious, and that the universities teach historical methods instead of much newer and better interpretations. This severely hurts the abilities of researchers.
This issue is very deep, and is as much a question of psychology as it is mathematics.
For further reading I reccommend that you ask around for a decent textbook. I myself have no good standing recommendation.
A: If the work in question shows that there is no collapse but just the very quick evolution of the wave function into something that resembles collapse very closely whenever a large number of oscillators interact with something like an electron, then the problem is completely solved. I believe that that is what it shows but cannot prove it. No subjectivity is required for it to happen as the brain would work like the magnet they describe. 
The reason we only observe the states we observe, presumably, is because the brain, like the measuring magnet they describe, goes through a similar process whenever it interacts with something like an electron, and it generates our consciousness in a way the reflects its own physical state, and since its physical "state" is as they describes and resembles a single "collapsed" - almost - quantum state and not a broader superposition then that's what we experience. They did their proof not of the brain but of a magnet but the importance of their paper is that presumably the same approach could be used for other physical systems composed of large numbers of oscillators.
So except in the extremely unlikely cases we will observe the states and not something that resembles superposition or rather we experience only superpositions that add up to a function that is almost certainly so close to the state that we can't tell the difference, and we can never measure with enough precision to know the difference.  What we observe in the unlikely cases, or even if we observe and don't just die, or become unconscious for a while, is unanswered and probably will remain so because the probabilities of ever having it happen are so low and because it probably doesn't last long enough. It will take the finishing of David Chalmers program to decide all of that. Perhaps a step can now be made by associating experience with certain very high probabilities in the brain. Also, since the pseudo collapse occurs so quickly and the temporal resolution of our consciousness is so low then we don't actually see it happening. 
In the future there may be sufficient control of the brain to sort of time lapse the pseudo-collapse and experience it, or else that is not possible as the un-pseudo-collapsed brain does not result in consciousness or slows consciousness down so an instant seems like a long time defeating the experiment. 
