Jeffrey Barrett is a philosopher of science at University of California Irvine. He is a major expositor of Hugh Everett's theory of the universal wave function, which Everett and his thesis adviser John Wheeler called the "relative state" formulation of quantum mechanics. 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:
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.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: 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.
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 likeFor 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.Barrett tells the story of Einstein saying "Look, I don’t believe that when I am not in my bedroom my bed spreads out all over the room, and whenever I open the door and come in it jumps into the corner." Many physicists dislike the idea that something happens just because an observer is "looking," including 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. 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.