Schr\"odinger's paradox and proofs of nonlocality using only perfect correlations

We discuss proofs of nonlocality based on a generalization by Erwin Schr\"odinger of the argument of Einstein, Podolsky and Rosen. These proofs do not appeal in any way to Bell's inequalities. Indeed, one striking feature of the proofs is that they can be used to establish nonlocality solely on the basis of suitably robust perfect correlations. First we explain that Schr\"odinger's argument shows that locality and the perfect correlations between measurements of observables on spatially separated systems implies the existence of a non-contextual value-map for quantum observables; non-contextual means that the observable has a particular value before its measurement, for any given quantum system, and that any experiment "measuring this observable" will reveal that value. Then, we establish the impossibility of a non-contextual value-map for quantum observables {\it without invoking any further quantum predictions}. Combining this with Schr\"odinger's argument implies nonlocality. Finally, we illustrate how Bohmian mechanics is compatible with the impossibility of a non-contextual value-map.Comment: 30 pages, 2 figure

Bell's Theorem and Quantum Realism: Reassessment in Light of the Schrödinger Paradox

Quantum theory presents a strange picture of the world, offering no real account of physical properties apart from observation. Neils Bohr felt that this reflected a core truth of nature: "There is no quantum world. There is only an abstract mathematical description." Among the most significant developments since Bohr’s day has been the theorem of John S. Bell. It is important to consider whether Bell’s analysis supports such a denial of microrealism. In this book, we evaluate the situation in terms of an early work of Erwin Schrödinger. Doing so, we see how Bell’s theorem is conceptually related to the Conway and Kochen Free Will theorem and also to all the major anti-realism efforts. It is easy to show that none of these analyses imply the impossibility of objective realism. We find that Schrödinger’s work leads to the derivation of a new series of theoretical proofs and potential experiments, each involving “entanglement,” the link between particles in some quantum systems.