[CTRL] Fwd: [ctrl] Spooky action-at-a-distance is the characteristic trait of quantum mechanics

Fri, 11 Nov 2005 09:04:17 -0800

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From: elvis oner <[EMAIL PROTECTED]>
Date: November 10, 2005 9:46:40 PM PST
Subject: [ctrl] Spooky action-at-a-distance is the characteristic trait of quantum mechanics


Spooky action-at-a-distance is the characteristic trait of quantum mechanics

The concept of nonlocality is well known through Bell’s famous mathematical theorem in which he addresses the problem of the Einstein–Podolsky–Rosen paradox. In a system exhibiting nonlocality, the consequences of events at one place propagate to other places instantaneously. Although Einstein, Podolsky and Rosen were attempting to demonstrate a different conclusion (the incompleteness of the quantum theory), their analysis served to point out the conditions under which (as would become evident after Bell’s work) nonlocality arises.

 
 
 

The existence of such conditions in quantum mechanics was regarded by Erwin Schrödinger as being of great significance, and in a work in which he generalized the EPR argument, he called these conditions “the characteristic trait of quantum mechanics, the one that forces its entire departure from classical lines.” Bell’s work essentially completed the proof that the quantum phenomenon discovered by EPR and elaborated by Schrödinger truly does entail nonlocality. Although the EPR paradox and Bell’s theorem are quite well known, there exists a misperception regarding the relationship these arguments bear to nonlocality. Some authors (mistakenly) conclude that the EPR paradox and Bell’s theorem imply that a conflict exists only between local theories of hidden variables and quantum mechanics, when a more general conclusion than this follows. When taken together, the EPR paradox and Bell’s theorem imply that any local theoretical explanation whatsoever must disagree with quantum mechanics. In Bell’s words: “It now seems that the non-locality is deeply rooted in quantum mechanics itself and will persist in any completion.” We can conclude from the EPR paradox and Bell’s theorem that the quantum theory is irreducibly nonlocal.

 
 

As we have mentioned, Erwin Schrödinger regarded the situation brought out in the Einstein, Podolsky, Rosen paper as a very important problem. His own work published just after the EPR paper provided a generalization of this analysis. This work contains Schrödinger’s presentation of the well known paradox of ‘Schrödinger’s cat’. However, a close look at the paper reveals much more. Schrödinger’s work contains a very extensive and thought provoking analysis of quantum theory. He begins with a statement of the nature of theoretical modeling and a comparison of this to the framework of quantum theory. He continues with the cat paradox, the measurement problem, and finally his generalization of the EPR paradox and its implications. In addition, he derives a result quite similar to that of von Neumann’s theorem.

 
 

Subsequent to our discussion of the issues of the EPR paradox, Bell’s theorem, and nonlocality, we will discuss a new form of quantum nonlocality proof based on Schrödinger’s generalization of the EPR paradox. The type of argument we shall present falls into the category of a “nonlocality without inequalities” proof. Such analyses—of which the first to be developed was that of Greenberger, Horne, and Zeilinger—differ from the nonlocality proof derived from the EPR paradox and Bell’s theorem in that they do not possess the statistical character of the latter.

 

—Douglas L. Hemmick, Hidden Variables and Nonlocality in Quantum Mechanics (dissertation, .pdf)

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