Butterfield, Jeremy. “Some Worlds of Quantum Theory."

The over-arching aim of Jeremy Butterfield’s essay is to discuss the strange ontologies that emerge from various interpretations of quantum mechanics. He begins with various proposed solutions to the measurement problem and then focuses on the Everettian interpretation developed by Simon Saunders and David Wallace. At the very outset, however, Butterfield stresses the highly problematic character of quantum indeterminism: it only appears in some interpretations of quantum theory and it involves a highly nonclassical ontology. He acknowledges the enormous empirical success of quantum theory but notes that considerable problems arise in reconciling it with special and general relativity, and he argues strongly against reductionism. He then provides a brief summary of the formalism of quantum theory, including a discussion of pure states, mixed states, and the meaning of probability in quantum theory.

Butterfield begins his discussion of the measurement problem with the orthodox view: during the process of measurement both the quantum system and the measurement apparatus go to a definite state (the “collapse of the wavepacket” for both system and apparatus). Yet according to the linearity of the Schrödinger equation, there is no such “collapse” - the indefiniteness of the quantum system should be transmitted to the measurement apparatus, leaving the position of the “pointer” indefinite. How then can we justify ascribing a definite state to the pointer? According to Butterfield, recent work on decoherence suggests that the continual interaction of the pointer with its environment brings the pointer “very close” to a definite state by leaving it in a narrow mixture of definite states. Still, a complete solution to the measurement problem requires more than what decoherence can provide.

We thus face two choices. The first choice is either to abandon orthodox quantum theory’s law of temporal evolution (the Schrödinger equation) and to propose new equations so that the collapse of the wavepacket is a physical process (Butterfield calls this choice Dynamics), or to assign values to additional quantities not given by orthodox quantum theory (Extra Values). The second choice is either to secure definite values for familiar quantities like the position of macroscopic objects (DefMac) or to be satisfied if the macrorealm only appears definite (DefApp). Combining these two choices yields four broad strategies for solving the measurement problem. An example of the Dynamics/DefApp strategy is that of Wigner and Stapp, where mind or consciousness produces the collapse of the wavepacket, while the ExtraValues/DefMac strategy of de Broglie and Bohm ascribes definite values to the position of the quantum system and introduces a “pilot-wave” to guide the system.

Butterfield then develops the ExtraValues/DefApp strategy proposed by Everettians. Here one retains the Schrödinger evolution of a strictly isolated system and allows an indefinite macrorealm, but posits extra values to secure definite appearances (measurements) by appealing to decoherence. In its simplest version, this strategy ascribes a wavefunction, Y (specifically, a pure state), to the universe as follows: Y is a superposition corresponding to numerous different “macrorealms” (or “worlds” or “branches”) that evolves according to the Schrödinger equation. According to Butterfield, the Everettians now propose a “breath-taking main idea”: all these macrorealms are actual. He devotes much of the remainder of his essay to the meaning of macrorealms from the perspective of both “many-minds” and “many-worlds” interpretations, how macrorealms evolve over time, and what he sees as the attendant vagueness in these approaches.

His primary focus is the work of Saunders and Wallace, including their appeal to anthropocentrism, their definition of ‘world’ as relative state, their use of decoherence, and their arguments against a precise definition of ‘branch’. A central concern is that of identity over time. Philosophers treat change of properties over time in two rival ways: either as properties of objects that persist self-identically over time (i.e., objects that “endure”), or as properties of objects having stages or temporal parts (i.e., objects that “perdure”). Similarly, for Everettians, we could say that the pointer has different properties (e.g., positions) in different worlds, or that there are multiple pointers similar to one another (“copies”) but with different properties in different worlds. He discusses the pros and cons of the “copy” choice most Everettians make, and he endorses the analogy between “worlds” as conceived by Everettians and instants of time represented by a “block universe” conception of time.

In his final section, Butterfield discusses the dynamics of the universe as a whole and of its subsystems. Everettians find the deterministic evolution of the universe as a whole to be compatible with the indeterministic evolution of its open subsystems and with the “almost deterministic” evolution of isolated subsystems. He closes by suggesting that, although the relativistic invariance of the universe as a whole is clear, a lacuna remains concerning the relativistic invariance of its subsystems.

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