Online research in philosophy

This paper attempts an interpretation of Everett''s relative state formulation of quantum mechanics that avoids the commitment to new metaphysical entities like worlds or minds. Starting from Everett''s quantum mechanical model of an observer, it is argued that an observer''s belief to be in an eigenstate of the measurement (corresponding to the observation of a well-defined measurement outcome) is consistent with the fact that she objectively is in a superposition of such states. Subjective states corresponding to such beliefs are constructed. From an analysis of these subjective states and their dynamics it is argued that Everett''s pure wave mechanics is subjectively consistent with von Neumann''s classical formulation of quantum mechanics. It follows from the argument that the objective state of a system is in principle unobservable. Nevertheless, an adequate concept of empirical reality can be constructed.

A complete reappraisal of the philosophical meaning of Everett's interpretation of quantum mechanics is carried out, by analysing carefully the role of the concept of "observer" in physics. It is shown that Everett's interpretation is the limiting case of a series of conceptions of the measurement problem which leave less and less of the observer out of the quantum description of the measuring interaction. This limiting case, however, should not be considered as one wherein nothing is left outside the description. Something is still needed besides this description: pure cognitive capacity, the subject, or, in a very abstract sense: "mind". The set of branches which arise, according to Everett, from a measuring interaction, gain a renewed signification. They do not refer to distinct "worlds", but to the points of view "mind" can identify itself to. This idea is compared and contrasted with Squires' "selection" of a branch by the mind (without quotation marks). Finally, the notion of indeterminism in quantum mechanics gains an unexpected and new light from a strict application of the previous ideas.

Following Lewis, it is widely held that branching worlds differ in important ways from diverging worlds. There is, however, a simple and natural semantics under which ordinary sentences uttered in branching worlds have much the same truth values as they conventionally have in diverging worlds. Under this semantics, whether branching or diverging, speakers cannot say in advance which branch or world is theirs. They are uncertain as to the outcome. This same semantics ensures the truth of utterances typically made about quantum mechanical contingencies, including statements of uncertainty, if the Everett interpretation of quantum mechanics is true. The 'incoherence problem' of the Everett interpretation, that it can give no meaning to the notion of uncertainty, is thereby solved.

Everett's relative-state formulation of quantum mechanics is an attempt to solve the measurement problem by dropping the collapse dynamics from the standard von Neumann-Dirac theory of quantum mechanics. The main problem with Everett's theory is that it is not at all clear how it is supposed to work. In particular, while it is clear that he wanted to explain why we get determinate measurement results in the context of his theory, it is unclear how he intended to do this. There have been many attempts to reconstruct Everett's no-collapse theory in order to account for the apparent determinateness of measurement outcomes. These attempts have led to such formulations of quantum mechanics as the many-worlds, many-minds, many-histories, and relative-fact theories. Each of these captures part of what Everett claimed for his theory, but each also encounters problems.

The Everett (many-worlds) interpretation of quantum mechanics faces a prima facie problem concerning quantum probabilities. Research in this area has been fast-paced over the last few years, following a controversial suggestion by David Deutsch that decision theory can solve the problem. This article provides a non-technical introduction to the decision-theoretic program, and a sketch of the current state of the debate.

This paper attempts an interpretation of Everett's relative state formulation of quantum mechanics that avoids the commitment to new metaphysical entities like ‘worlds’ or ‘minds’. Starting from Everett's quantum mechanical model of an observer, it is argued that an observer's belief to be in an eigenstate of the measurement (corresponding to the observation of a well-defined measurement outcome) is consistent with the fact that she objectively is in a superposition of such states. Subjective states corresponding to such beliefs are constructed. From an analysis of these subjective states and their dynamics it is argued that Everett's pure wave mechanics is subjectively consistent with von Neumann's classical formulation of quantum mechanics. It follows from the argument that the objective state of a system is in principle unobservable. Nevertheless, an adequate concept of empirical reality can be constructed.

An interpretation of quantum mechanics must, at a minimum, explain how we come to experience a determinate result when we measure a system in a linear superposition of states. Many have taken this to require the addition of some new physics to the quantum formalism – either hidden variables or a description of the wave function’s collapse. But Hugh Everett famously suggested that we leave the theory as is, and explain our experiences as features of a universal wavefunction which never collapses, even when a measurement is made. Subsequent thinkers have taken him to mean that quantum mechanics describes not one world, but a collection of many interacting worlds. During this decade and the last, this “many-worlds” interpretation has gained acceptance among many physicists and philosophers.

The Many-Worlds Interpretation (MWI) is an approach to quantum mechanics according to which, in addition to the world we are aware of directly, there are many other similar worlds which exist in parallel at the same space and time. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics.

This unpublished 1990 preprint argues that a crucial distinction in discussions of the many-worlds interpretation of quantum mechanics (MWI) is that between versions of the interpretation positing a physical multiplicity of worlds, and those in which the multiplicity is merely psychological, and due to the splitting of consciousness upon interaction with amplified quantum superpositions. It is argued that Everett's original version of the MWI belongs to the latter class, and that most of the criticisms leveled against the MWI, in particular that it is illogical or incoherent, are not valid against such "psychological-multiplicity" versions. Attempts to derive the quantum-mechanical probabilities from the many-worlds interpretation are reviewed, and Everett's initial derivation is extended in an attempt to show that these are the unique possible probabilities. But there remains a challenge for proponents of the MWI: to show that their interpretation requires probabilities, rather than merely nonprobabilistic indeterminacy. A 2002 preface, revised in 2004, briefly discusses the extent to which I still agree with the claims in the paper. While its derivation of probabilities used, and failed to justify, noncontextuality, I still agree with the paper's general interpretation of the MWI, though not with the MWI itself.

This is a discussion of how we can understand the world-view given to us by the Everett interpretation of quantum mechanics, and in particular the role played by the concept of 'world'. The view presented is that we are entitled to use 'many-worlds' terminology even if the theory does not specify the worlds in the formalism; this is defended by means of an extensive analogy with the concept of an 'instant' or moment of time in relativity, with the lack of a preferred foliation of spacetime being compared with the lack of a preferred basis in quantum theory. Implications for identity of worlds over time, and for relativistic quantum mechanics, are discussed.