The Objectivity and Invariance of Quantum Predictions

Abstract
A recent argument by Pitowsky (1991), leading to the relativity (as opposed to objectivity) of quantum predictions, is refuted. The refutation proceeds by taking into account the hyperplane dependence of the quantum predictions emerging from the three mutually space-like separated measurements, performed on an entangled state of three spin 1/2 particles, that Pitowsky considers. From this hyperplane dependence one finds that the logical step of conjoining the predictions from distinct measurements is ineffective since those predictions apply either, locally, to sets of points with an intersection that is inaccessible to the particles, or globally, to sets of hyperplanes with an intersection that is empty. We also see how explicit reference to the hyperplane dependence of the predictions gives covariant expression to the invariant content of the predictions, which are thereby shown to be objective.
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