Insolubility Theorems and EPR Argument

Michael L. G. Redhead, Patrick La Rivière

Vincenzo Fano

Hideki Sabata, Kaoru Fujita

Travis Norsen

A new formulation of the EPR argument is presented, one which uses John Bell’s mathematically precise local causality condition in place of the looser locality assumption which was used in the original EPR paper and on which Niels Bohr seems to have based his objection to the EPR argument. The new formulation of EPR helps clarify the relation between this argument and Bell’s Theorem. The relation between these two arguments — in particular, the role of EPR as part one of Bell’s two‐part argument for nonlocality — is also discussed in detail.

Tore Wessel-Berg

Paul Busch, Abner Shimony

The quantum mechanical measurement problem is the difficulty of dealing with the indefiniteness of the pointer observable at the conclusion of a measurement process governed by unitary quantum dynamics. There has been hope to solve this problem by eliminating idealizations from the characterization of measurement. We state and prove two ‘insolubility theorems’ that disappoint this hope. In both the initial state of the apparatus is taken to be mixed rather than pure, and the correlation of the object observable and the pointer observable is allowed to be imperfect. In the insolubility theorem for sharp observables, which is only a modest extension of previous results, the object observable is taken to be an arbitrary projection valued measure. In the insolubility theorem for unsharp observables, which is essentially new, the object observable is taken to be a positive operator valued measure. Both theorems show that the measurement problem is not the consequence of neglecting the ever-present imperfections of actual measurements.