In this series of articles, I give a simple introductory presentation of Bell's inequalities and non-locality, subjects which have been at the root of much recent controversy. 
An Introduction to Bell's Inequalities and Non-Locality
By Travis Norsen (January 2002, Part 1 of 5)

[OBJECTIVE SCIENCE.COM]  In this series of articles, I give a simple introductory presentation of Bell's inequalities and non-locality, subjects which have been at the root of much recent controversy. 

After a quick review of the relevant predictions of standard Quantum Mechanics, and an overview of why one might be motivated to construct a "local realist hidden variable theory", I show how the predictions of the two theories necessary conflict. 

I finish with some discussion of what this entails physically, and how the results can be integrated with our knowledge of philosophy and earlier physics.  The presentation closely follows several accounts already existing in the literature, so its only real novelty is that it will be made available to people who might not find Bell's own papers on the subject easily accessible. [1]

***

It is commonly known that Quantum Mechanics (QM) gives a highly counter-intuitive account of microphysical processes.  In its basic formalism, particles are described by a mathematical object called the wave function, which evolves in time according to Schroedinger's equation.  One might be bothered by the fact that particles (discrete localized point-like objects) are described as waves (objects which spread out over potentially large spatial regions).  That alone seems dubious and raises several fundamental questions, e.g.:  Does the particle itself spread out like a wave, or does the wave represent merely our imperfect knowledge of the particle's actual location?  The standard answer of the Copenhagen interpretation is that one should not ask such questions, since there is no known experimental procedure for answering them.  

The situation gets even worse when one learns that the deterministic time-evolution of the wave function is only half of the story.  According to QM, that's what happens when nobody is looking at the wave.  But when a measurement is made, the wave function changes suddenly and unpredictably -- it "collapses" into a new state representing a definite result of measurement.  For example, if one initially has a spread-out wave function and brings in a detector to measure the position of the particle, QM says that, at the moment the measurement occurs, the wave function collapses into an eigenstate of the position operator.  That is, it begins spread out over a finite region of space, but becomes after the measurement a "spike" (a Dirac delta function) at a precise position, and zero everywhere else.  The measurement (according to the standard interpretation) forces the particle (which has no well-defined position before measurement; it exists in some kind of indeterminate limbo) to "choose" a definite location.

For about a hundred years now, realists have been tremendously bothered by this basic picture, since it appears to give a kind of undeserved fundamentality to the act of observation.  Indeed, the question of what counts as an observation or measurement has been a perennial crack in the foundations of QM.  When we measure the position of an electron, for example, does the "measurement" occur as soon as the electron interacts with the closest atom in the detector?  Or when some specific level of amplification occurs inside the detector?  Or when the detector sends its output to a computer to be stored to hard disk?  Or, perhaps, even later, when a scientist reads (and becomes consciously aware of) the result on the computer monitor? 

Quantum theory alone gives no coherent answer to these questions.  It merely says that in order to get the right answer, one must choose some level at which to place a "cut" – that is, at which to treat the wave function as having collapsed.  But this, of course, is no answer at all, if one's concern is not merely with "getting the right answer" but with understanding the physical meaning of the quantum formalism.


Further Reading:
Quantum Mechanics and Non-Locality
By Travis Norsen (February 2002, Part 2 of 5)
Measuring a certain property of one of the particles, allows one to predict with certainty a property of the other particle a hundred miles away.


References and Notes:

[1] The discussion in the text is fairly elementary.  It is expected that interesting debates may take place at the level of points made in the footnotes, which I would take as a favorable development.  Right now, too many people are arguing about the details and subtleties, without first understanding the fundamental points. 

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