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The EPR paradox is the argument given by Albert Einstein, Boris Podolsky, and Nathan Rosen in 1935. It is one of the most remarkable attacks on quantum theory ever launched. Recall that, according to quantum theory, measurements can be made of only one of any pair of complementary variables: position or momentum, energy or time. But simultaneous measurement of both members of such a pair is impossible. The Einstein, Podolsky and Rosen paper argued that such measurement were quite possible, and it gave a simple description of how to carry them out. Thus, according to their analysis, it was possible to obtain a more complete description of physical reality than that provided by quantum mechanics. Their conclusion was that quantum theory was incomplete.

For decades, paper after paper was written in an attempt to resolve this paradox, but not for thirty years was any real headway made on the matter. But in 1964 and 1966, two remarkable theorems were published by young physicist John Bell. These theorems showed that an experiment was possible that could conclusively test whether the EPR argument was correct. In the early 1980s a series of such experiments were carried out. They have conclusively shown that quantum mechanics is indeed correct, and that the EPR argument had relied upon incorrect assumptions.

The Argument.

The EPR paper claimed to show how to measure any pair of complementary variable. Bell’s theorem, on the other hand, was couched in terms of a particular version of the EPR paradox, developed by David Bohm. For this reason we will concentrate on Bohm’s version In what follows.

A particle’s spin is customarily measured by means of a so-called Stern-Gerlach analyzer. On the other hand, such a device only measure one component of spin, that along the analyzer’s vertical axis. Furthermore, recall that the operators for the x-component and z-component of spin do not commute, so that measurements of Sx and Sz obey on uncertainty relation. So no apparatus can possibly measure all three components. In contrast, ERP ague that these components can be measured to arbitrarily accuracy by use of the specific experimental apparatus. The apparatus consists of two Stern-Gerlach analyzers and two particle source.

The particle source shoots out two particles – always in opposite directions and always polarized with their spins pointing in opposite directions. Although the EPR argument does not depend on the details of how these particles are produced, we note that such pairs of particles can be actually produced in the laboratory in a number of ways. One technique is to prepare an atom of positronium – an electron and a positron bound together – in a state of orbital angular momentum zero and spin angular momentum zero as well. One can then “ionize” the positronium atom, yielding the required pair.

One particle is sent toward the first analyzer, the other toward the second. They are at widely separated points in space: we will call the first “location A” and the second “location B”. To make things specific, we will imagine two experimenters, Alice and Bob, operating the two analyzers. Alice and Bob are free to orient their analyzers in any direction. As the experiment begins, the emitter produces a pair of particles and sends them outward toward the two experimenters.

Suppose that initially Alice had chosen to orient her Stern-Gerlach analyzer perpendicular to the line of flight of the approaching particle and pointing vertically upward along the z-axis.

For decades, paper after paper was written in an attempt to resolve this paradox, but not for thirty years was any real headway made on the matter. But in 1964 and 1966, two remarkable theorems were published by young physicist John Bell. These theorems showed that an experiment was possible that could conclusively test whether the EPR argument was correct. In the early 1980s a series of such experiments were carried out. They have conclusively shown that quantum mechanics is indeed correct, and that the EPR argument had relied upon incorrect assumptions.

The Argument.

The EPR paper claimed to show how to measure any pair of complementary variable. Bell’s theorem, on the other hand, was couched in terms of a particular version of the EPR paradox, developed by David Bohm. For this reason we will concentrate on Bohm’s version In what follows.

A particle’s spin is customarily measured by means of a so-called Stern-Gerlach analyzer. On the other hand, such a device only measure one component of spin, that along the analyzer’s vertical axis. Furthermore, recall that the operators for the x-component and z-component of spin do not commute, so that measurements of Sx and Sz obey on uncertainty relation. So no apparatus can possibly measure all three components. In contrast, ERP ague that these components can be measured to arbitrarily accuracy by use of the specific experimental apparatus. The apparatus consists of two Stern-Gerlach analyzers and two particle source.

The particle source shoots out two particles – always in opposite directions and always polarized with their spins pointing in opposite directions. Although the EPR argument does not depend on the details of how these particles are produced, we note that such pairs of particles can be actually produced in the laboratory in a number of ways. One technique is to prepare an atom of positronium – an electron and a positron bound together – in a state of orbital angular momentum zero and spin angular momentum zero as well. One can then “ionize” the positronium atom, yielding the required pair.

One particle is sent toward the first analyzer, the other toward the second. They are at widely separated points in space: we will call the first “location A” and the second “location B”. To make things specific, we will imagine two experimenters, Alice and Bob, operating the two analyzers. Alice and Bob are free to orient their analyzers in any direction. As the experiment begins, the emitter produces a pair of particles and sends them outward toward the two experimenters.

Suppose that initially Alice had chosen to orient her Stern-Gerlach analyzer perpendicular to the line of flight of the approaching particle and pointing vertically upward along the z-axis.

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