Butterfield, Jeremy. “Some Worlds of Quantum Theory."
The overarching 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 “pilotwave” 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 “breathtaking 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 “manyminds” and “manyworlds”
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 selfidentically 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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