Allen Stairs is a professor of the philosophy of religion at the University of Maryland.

In 1988 Stairs wrote the paper "Jarrett's Locality Condition and Causal Paradox" in which he wrote...

In this paper, I want to present a family of results that may seem to add up to a new proof of the impossibility of hidden variables. In fact, I very much doubt that that's really what really emerges, but I think the results are nonetheless interesting because they help to sharpen the discussion of Jon Jarrett's very useful decompostion theorem, in particular, of the condition he calls locality. Jarrett (1984) and Ballentine and Jarrett (1987) have suggested that the so-called condition of locality is the one that provides the conceptual link between hidden variable theories and relativity: if locality is violated, so is relativity. On the other hand, a theory may violate the condition Jarrett calls completeness without running afoul of relativity. Now I agree with Jarrett and Ballentine about completeness, but I strongly suspect that we have quite a way to go before we really understand what would be involved in a violation of locality.

Jon Jarrett's "decomposition theorem" divides Bell’s "local causality" condition into two distinct logical requirements that Jarrett calls "locality" and "completeness" to explain the nonlocality of quantum mechanics.

Abner Shimony subsequently recast Jarrett's "locality" and "completeness" as "parameter independence" and "outcome independence."

Parameter independence refers to the independent settings of the spacelike separated experiments in a Bell test. Outcome independence refers to the fact that the left outcome cannot influence the right outcome and vice versa. Since they occur at the same time, any dependence would violate special relativity.

The origin of "hidden variables" was the Einstein, Podolsky, Rosen paper's suggestion that additional parameters might be needed to explain what Einstein later called spooky action-at-a-distance.

That these hidden variables could be "local" is the idea that information about their outcomes might be traveling along with the particles (as href="/solutions/scientists/mermin/">David Mermin's "instruction sets") or at least somewhere in the backward light cones of the particles as (as href="/solutions/scientists/bell/">John Bell's "beables."

In one of his last papers, Bell wrote...

A theory can be said to be locally causal if the probabilities attached to values of local beables in a spacetime region 1 are unaltered by specification of values of local beables in a space-like separated region 2, when what happens in the backward light cone of 1 is already sufficiently specified, for example by a full specification of local beables in a space-time region 3 (Fig. 4).

Fig. 4. Full specification of what happens in 3 makes events in 2 irrelevant for predictions about 1 in a locally causal theory.

It is important that region 3 completely shields off from 1 the overlap of the backward light cones of 1 and 2. And it is important that events in 3 be specified completely. Otherwise the traces in region 2 of causes of events in 1 could well supplement whatever else was being used for calculating probabilities about 1. The hypothesis is that any such information about 2 becomes redundant when 3 is specified completely.

("La Nouvelle Cuisine," republished in Speakable and Unspeakable in Quantum Mechanics," 1987, p. 240)

But a common cause from the initial entanglement is still in the past light cone of the "separated" measurements at A and B, as shown by Travis Norsen.

As long as Bell's "local beables" (which he sometimes presents as "λ") either don't exist or do not interfere with the travelling particles, one particle will have spin-up and the other spin-down to conserve the total spin angular momentum's zero and preserve the symmetry of the original entanglement preparation state.

The initial entanglement of the two particles in the past light cone and a powerful conservation principle explains the appearance of nonlocality without any "hidden variables" but with what we can call a "hidden constant of the motion," the total spin zero!

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