The central problem of quantum theory is that it involves an unexplained duality in nature. For the majority of time systems will evolve according to the Schrödinger equation, evolving in a way that makes the system more and more indeterminate, becoming more "random" in the sense that its physical qualities can take on a greater range of values. The second half of the duality occurs instantaneously during measurement of those physical qualities, at which time the system "selects" a single value of the range of possible values. This process is known as wavefunction collapse, and has no explanation. Worse, the process of observation occurs "outside" the system, which presents a problem on its own if one considers the universe itself to be a quantum system. This is known as the measurement problem.
Hugh Everett attempted to find a way out of this problem by suggesting that the universe is in fact indeterminate as a whole, and that the measurement action changes the universe as a whole. That is, if you were to measure the spin of a particle and find it to be "up", in fact there are two "yous", one who measured the spin up, the other down. This "relative state" formulation, where all states (sets of measures) can only be measured relative to other such states, avoids a number of problems in quantum theory, including the original duality - no "collapse" takes place, the indeterminacy simply grows (or moves) to a larger system. Effectively by looking at the system in question, you take on its in indeterminacy.
Albert and Loewer associate with each observer a continuous infinity of minds. For any measure, the physical result is that many of these minds end up in one state or the other, for instance, spin up or spin down minds. "You" select one of these to be your non-random reality, while the universe itself is unaffected. However, the process for selection of a single state remains unexplained. This is particularly problematic because it is not clear how different observers would thus end up agreeing on measurements, which happens all the time here in the "real world". There is assumed to be a sort of feedback between the mental process that leads to selection and the universal wavefunction, thereby effecting other mental states as a matter of course. In order to make the system work, the "mind" must be separate from the body, an old duality of philosophy to replace the new one of quantum mechanics.
In general the interpretation has received little attention, largely for this last reason.
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