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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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