Bryce DeWitt popularized Everett's notion of the universe "splitting" at any measurement-like event. DeWitt said it implies the simultaneous existence of many possible "parallel" worlds, and Everett's work became widely known as the "many-worlds" interpretation of quantum mechanics.

Barrett has published several articles and three books on the Everett interpretation. With writer Peter Byrne, he is a curator of Everett papers at UC Irvine. They compiled The Everett Interpretation of Quantum Mechanics: Collected Works 1955-1980 with Commentary in 2012.

Following Everett, Barrett argues for a logical inconsistency between the two dynamical laws in the standard theory of quantum mechanics:

• the unitary time evolution of the wave function deterministically generated by Schrödinger equation (See von Neumann Process 2.)

• the random collapse of the wave function from a superposition of quantum states into a single state, with the probability of collapsing into a given state proportional to the overlap of the wave functions of new state with each of the superposition states. (See von Neumann Process 1.)

In the context of the standard theory, the measurement problem results from the fact that the two dynamical laws are mutually incompatible. Since the first is deterministic and continuous and the second is stochastic and discontinuous, no physical system can be governed by both laws simultaneously — indeed, as we shall see, the two laws would typically lead to very different physical states. There is nothing wrong with a theory having mutually incompatible dynamical laws as long as it also provides clear and disjoint conditions for when each correctly describes the evolution of a system, but this is where our loose talk of things behaving one way when someone is looking and another way when no one is looking catches up to us.

In the information interpretation of quantum mechanics, there is a temporal sequence, the deterministic unitary law describes isolated systems (for example, a gas particle in free flight between collisions), the random collapse law describes the interaction during
the next collision.

If information is recorded, the
collision might be a measurement.

The standard theory tells us that the deterministic dynamics describes the evolution of a system unless it is measured, in which case the random dynamics kicks in. But the theory does not tell us what constitutes a measurement. One is left to one's own intuitions concerning what interactions ought to count as measurements. While it turns out that one can typically use such intuitions to get good empirical predictions from the theory, the fact that our intuitions concerning what it takes for an interaction to count as a measurement are ultimately vague means that quantum mechanics is at best ambiguous. Further, if one supposes that measuring devices are ordinary physical systems just like any other, constructed of fundamental particles interacting in their usual deterministic way (and why wouldn't they be?), then the standard theory is logically inconsistent since no system can obey both the deterministic and stochastic dynamical laws simultaneously. This is the measurement problem.

(The Quantum Mechanics of Minds and Worlds, pp.14-15)

Barrett explains that quantum mechanics is an incomplete theory because it does not tell us which of the possible outcomes of an experiment actually occurs:

If one accepts Everett's model of a good measuring device and if one insists that the usual deterministic linear dynamics always correctly describes the time-evolution of the quantum-mechanical state, then, as we have seen, an ideal observer M who begins in an eigenstate of being ready to measure the x-spin of a system S that is initially in an eigenstate of z-spin will end up in a post-measurement state like

< ψ > = (1 / √2) ( | x-spin up > _M | ↑_x >_S   +   | x-spin down > _M | ↓_x >_S ).

There are several strategies for interpreting | ψ >. One strategy would be to insist that, contrary to what the standard eigenvalue-eigenstate link tells us about | ψ >, there is a single post-measurement observer who has recorded a single determinate measurement result. If this is right, then | ψ > must be an incomplete description of the state of the composite system M + S since it clearly fails to tell us what result M recorded. Further, even if the coefficients on the two terms in the post-measurement superposition (in the determinate-record basis) were different, one would not want to say that the quantum-mechanical state was complete since we know from experience that any term in the post-measurement state with a nonzero coefficient represents a possible measurement record (and the usual quantum-mechanical state would not tell us which term represented the observer's actual record).

It is of the essence of statistical indeterministic theories that the exact outcome cannot be predicted.

In this sense, Einstein was right that quantum mechanics is incomplete. Bohr was too proud to simply accept this fact.

Classical mechanics, with twice as many simultaneously determinate variables (e.g., position and momentum) has twice the information of quantum mechanics.

On this strategy, one would have to supplement the usual quantum-mechanical state description with a parameter that effectively selects one of the terms in the final state (in the determinate-record basis) as the one that correctly describes what result the observer in fact recorded. That is, if one insists that the usual linear dynamics always correctly describes the time-evolution of the quantum-mechanical state and that there is a single post-measurement observer who records a single determinate measurement result, then one is naturally led to abandon the assumption that the quantum-mechanical state provides a complete description of the post-measurement state of the observer and his object system. Given this, one might try to complete the state by (1) choosing a particular physical quantity as always determinate (the path taken by standard hidden-variable theories) or (2) choosing a rule that itself chooses a determinate physical quantity given the current quantum-mechanical state and the system in which one is interested (the path taken by some so-called modal theories). But in either case, one must also have a rule for determining the value of the determinate physical quantity. What quantity is determinate, its value, and the quantum-mechanical state would then together provide a complete physical description of a system at a time.

(The Quantum Mechanics of Minds and Worlds, pp.92-93)

For Barrett, a "determinate" quantity is one that yields an eigenvalue when measured (it is found in an eigenstate). Otherwise, a quantum system can be in a superposition of states.

the most immediate explanatory demand on quantum mechanics is to explain why we never directly observe a system in a superposition of possessing and not possessing a given property; or, put somewhat differently, quantum mechanics should explain why measurements typically yield determinate measurement records.

In the information interpretation of quantum mechanics, an isolated system S evolves continuously. When it interacts with another system, it jumps instantaneously and randomly to a state of the combined system.

A measurement is not required, only an interaction.

If information is recorded, the
interaction might be a measurement.

The standard explanation replies on the dual structure of the dynamics in the standard collapse formulation of quantum mechanics: (A) if no measurement is made, then a system S evolves continuously according to the linear, deterministic dynamics, which depends only on the energy properties of the system, but (B) if a measurement is made, then the system S instantaneously and randomly jumps to a state where it either determinately has or determinately does not have the property being measured, where the probability of each possible post-measurement state depends on the system’s initial state. While this does explain why measurements typically yield determinate physical records, the dual structure of the dynamics and the occurrence of measurement as an undefined primitive term in the theory is at least curious. Albert Einstein, for one, did not believe that this aspect of the theory could be right.

(A Quantum-Mechanical Argument for Mind-Body Dualism, Erkenntnis (2006) 65, p.98)

Many physicists dislike the idea that something happens just because an observer is "looking," including David Bohm, John Bell, and Everett.

Barrett writes that there are many "many-worlds" models and many "many-minds" models as well. He personally supports a "single-mind Q theory" (Minds and Worlds, pp.204-206)

In the effort to guarantee that one has made an observer’s measurement records determinate, one might add a physical hidden-variable Q to the standard quantum-mechanical state such that Q is that physical quantity on which mental records in fact supervene, whatever this happens to be. The quantum-mechanical state evolves in the usual linear way, and an auxiliary dynamics describes the evolution of the determinate value of Q just as the auxiliary dynamics describes the evolution of determinate particle positions in Bohmian mechanics. The value of Q plays the role of the determinate mental states in the single-mind theory by guaranteeing determinate mental records, but here one seeks to exchange mind–body dualism for a variety of physical–physical dualism.

This Q-theory solves the quantum measurement problem if and only if there is a single physical quantity Q on which all mental records in fact supervene. Simply stipulating that there is a just-right physical quantity Q that is always determinate and in fact determines all mental states looks more than a little ad hoc. Moreover, since one is left with a hidden-variable theory where there are two very different types of physical parameters, the quantum-mechanical state and the determinate physical quantities, each with their own dynamical laws, one has arguably not altogether escaped from committing to a strong metaphysical dualism.

(A Quantum-Mechanical Argument for Mind-Body Dualism, Erkenntnis (2006) 65, pp.109-110)