Cushing, James T. “Determinism Versus Indeterminism in Quantum Mechanics: A “Free” Choice."
James T. Cushing sees the
question of determinism versus indeterminism as “the fundamental issue” regarding the possibilities for
particular divine action, and thus the importance of quantum mechanics. His
central point is that “considerations of empirical adequacy and logical
consistency alone” do not force one to chose the indeterministic view of
quantum mechanics as found in the Copenhagen interpretation - Bohm offers an
empirically valid deterministic alternative.
Cushing begins by defining a
theory as a formalism (i.e., a set of equations and a set of calculational
rules for making predictions that can be tested) and an interpretation (i.e.,
what the theory tells us about the underlying structure of the world). Quantum
mechanics presents us with one formalism but two different interpretations, and
thus two different theories. The Copenhagen version affirms the completeness of
the state-vector description, the principle of complementarity, nonclassical
probability, and a prohibition against “any possible alternative causal
description in a spacetime background.” Physical processes are thus both
indeterministic and nonlocal. Bohmian mechanics is an objective (realist) and
deterministic account in which the positions of the particles of the system
function as “hidden variables” and must be included in a complete state
description. As in the Copenhagen interpretation, the Schrödinger equation
governs the evolution of the wave function, but an additional “guidance
condition” governs the evolution of the particles’ positions. With the
inclusion of a quantum-equilibrium statistical distribution, Bohm’s theory is
empirically identical with standard quantum mechanics. Its ontology depicts
particles following definite trajectories that are completely deterministic and
observer-independent. The ontology, however, is nonlocal: instantaneous,
long-range influences are included. Still Bohmian nonlocality is “benign,”
since the “no-signaling” theory of quantum mechanics prohibits sending messages
faster than light.
In Bohm’s theory, the
quantum potential U conveys the
influence of the environment on the particle, while U is determined, in turn, by the wavefunction. This means
that the measurement process is “an act of discovery - there is no quantum-mechanical measurement
problem.” All observations are, ultimately, position measurements, a feature
which reflects our own existence in coordinate space. The classical limit corresponds
to U being negligible and is thus
more precise than h _ 0. From an
empirical perspective, Bohm’s theory is not only completely equivalent with
standard quantum mechanics, but it also captures Bohr’s concept of quantum
holism and his principle of complementarity. As Cushing puts it, observed
values in Bohm’s theory are “contextual.”
Bell’s theorem shows that
our world cannot be both objectively real and local. Cushing suggests that
locality is the real problem, but reminds us that Bohm offers a nonlocal, deterministic hidden-variables
theory. In order to discuss Bohmian ontology, Cushing points to “relational
holism” since it seems to offer a better conceptual framework than one which
distinguishes between separability and locality. It also suggests a world of
temporal becoming since it includes a preferred frame for instantaneous action.
Still this world is one in which everything, including the future, is
determined. Such a world is reminiscent of Newton’s idea of space as the divine
sensorium. It certainly poses a
challenge to our ideas of free will and divine action - as does the problem of
evil.
In short, then, the choice
to accept the Copenhagen view and reject that of Bohm is not a forced move
based on logic or empirical adequacy; it is made on other grounds. Similarly,
one might chose an indeterministic view of quantum mechanics for theological
reasons, but one should not claim that quantum mechanics provides independent,
scientifically arguable grounds for such a choice.
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