Redhead, Michael. “The Tangled Story of Nonlocality in Quantum Mechanics."

Michael Redhead’s essay is based on the assumption that nonlocality as instantaneous causal action-at-a-distance is to be avoided since it violates “the spirit of special relativity.” He therefore undertakes a meticulous examination of a variety of proofs of nonlocality in the quantum mechanical treatment of many-particle entangled states, seeking to detect and assess their assumptions.

Redhead starts with the assumption that relativity is more than a phenomenological invariance principle; instead it is grounded in the causal structure of spacetime. Specifically, Redhead claims that relativity entails the Philosophically Grounded Invariance Principle (PIP), which asserts that causal influences cannot operate outside the light-cone. If, alternatively, relativity entailed the First Signal Principle (FSP), it would disallow faster than light signals, where “signals” are controllable causal processes. David Bohm’s interpretation of quantum mechanics is both deterministic and, to many scholars, consistent with relativity since it does not allow superluminal signaling - although it does allow superluminal causal processes. But since Redhead believes that relativity entails PIP, and since PIP _ FSP, Redhead claims that Bohm’s interpretation violates relativity. He also objects to it on theological grounds, since its determinism does not allow “room” for incompatibilist divine action. He therefore turns to indeterministic approaches involving nonlocality in both nonrelativistic and relativistic quantum mechanics.

He begins with John Bell’s analysis of the (nonrelativistic) EPR argument, which delineated between two meanings of nonlocality: a) action-at-a-distance between individual particles, and b) nonseparability, in which at least some properties cannot be attached to individual particles. Bell’s argument, in turn, rested on assumptions involving joint probability distributions and determinism, both of which Redhead explores in detail. He then discusses algebraic proofs of nonlocality that seek to demonstrate that local hidden-variable theories are self-contradictory.

Next, Redhead turns to the search for a relativistic EPR argument. First, he reviews the problems encountered in seeking to translate the nonrelativistic EPR argument into a relativistic context, paying particular attention the need to reformulate the “reality criterion” (e.g., every element of physical reality must have a counterpart in the theory). A relativistic EPR argument must employ a relativistic wavefunction and must not depend on the existence of absolute time- ordering for space-like events. Redhead describes in detail one proposal for a relativistic reality criterion by Ghirardi and Grassi and its reliance on the truth of certain classes of counterfactual statements. Ghirardi and Grassi’s argument involves a distinction between what Redhead describes as OM-Loc, that the outcome of a measurement cannot be influenced by performing nonlocal measurements, and ER-Loc, that elements of reality cannot be created by performing nonlocal measurements. Ghirardi and Grassi claim to show that relativity and quantum mechanics are in “peaceful coexistence,” but to do so they must also claim that violating ER-Loc is more serious than violating OM-Loc. Redhead disagrees, but offers a further assumption which he calls the “Principle of Local Counterfactual Definiteness (PLCD).” With this he shows that Ghirardi and Grassi’s relativistic reformulation of the EPR argument is less general than they suggest; it is in fact limited to deterministic systems.

In his concluding section Redhead first argues that nonlocality seems unavoidable for any reconstruction of quantum mechanics which is both realist, i.e., in which all observables have sharp values at all times, and deterministic. We either turn to a stochastic hidden-variable framework or seek to understand correlations in terms of what Shimony describes as “passion-at- a-distance.” In the anti-realist option pursued by Ghirardi and Grassi, Redhead challenges the claim that the existence of action-at-a-distance is not a valid deduction from the EPR argument, but he then rescues the claim by the additional assumption of determinism. He regards his results as closing further gaps in the peaceful co-existence argument, but the “mysterious harmony” of quantum correlations remains “spooky” even if it does not involve causal dependence. For the anti-realist, the role of measurement is to actualize potentialities. But when quantum mechanics is applied to cosmology, where there is nothing “outside” the universe to serve as a measuring device, the realist option may be preferred, and with it the notion of nonseparability.

Redhead’s essay thus gives arguments for invoking either indeterminism or holistic nonseparability. The author sees these as having important theological implications: indeterminism is important for theories of divine action on particular occasions, while holism is an anti- reductionist thesis “which shows how every element of the universe has for its ground of being the totality of the whole, which pantheists would want to identify with God.”

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