The Einstein-Podolsky-Rosen paradox is that measurement in quantum mechanics seems to require faster-than-light communication under certain circumstances. This, they claimed, is absurd, and proves quantum mechanics to be incomplete -- certain things must be decided in advance.
This argued towards a local hidden variables theory: a theory which maintains locality better than quantum mechanics and - more pertinently to the three theorists - lacks quantum weirdness. How was it less weird? The distributions of the properties of particles were all now statistical distributions over unknown quantities, and not intrinsic distributions over quantum operator eigenvalues.
At first, there was no known way to actually test whether the seemingly absurd result of faster-than-light communication was true or not: no one could think of a prediction quantum mechanics made that no local hidden variables theory could make. In 1951, some progress was made as David Bohm created a more tractable variant of the paradox involving spin, but still no specific different predictions could be found.
In 1964, this changed: John Bell used Bohm's special case to devise his famous inequality, which pointed out a difference between the two schema. That is, though there were a variety of ways a local hidden variables theory could make things work, there was a limit to how coordinated they could make things. Quantum mechanics could cross this limit.
To explain this notion - suppose you can make one of 3 binary measurements - A, B, or C. Measurements A and B are closely related and read, say, 75% the same, with only 25% reading the opposite way. B and C are closely related and also 75% the same, with 25% flipped. So, if you compare the results of measurements A and C, you should classically expect not more than 50% of your results to flip.
This is what quantum mechanics disagrees on. You can set up situations in which you expect 75% of the results to flip when you compare A with C. And as it turns out, you can pull this off with separated particles like EPR were talking about. It seems in this case like information must be transmitted to help A and C be more opposite than random.
Alain Aspect used a special case of the inequality to form the basis of his famous experiment, which was finished in 1982.
The final form of the Aspect experiment went so:
- Set up a device which creates Einstein-Podolsky-Rosen pairs (EPR pairs) of photons proceeding in opposite directions. What makes each pair an EPR pair is that the two photons' polarizations are oriented the opposite way*, not by picking them to be some specific opposite pair of values, but by assigning that constraint without constraining their individual polarizations. This quantum dependence is known as entanglement.
To get technical, the spinor ket of the photon pair is X | + - > + X' | - + > for some X and X', in a linear polarization basis. (There's more that could be said, but the algebra would suddenly get very intense and it wouldn't materially help.)
- Place three detectors to detect each photon, each detecting the polarization along an axis at 60° from the other two. Use only one detector at a time at each end. Let's call these A, B, and C at one end, and A', B', and C' at the other. This setup gives the sameness ratio predictions used above.
- Rapidly randomly determine which axis is used on each detector, and reset the choice after each photon is detected. Make sure the switching is good enough to keep the switching events spacelike separated.
There are two cases here: the photons' polarization is detected along the same axis, or the photons' polarization is detected along different axes. In the event that the photons were detected along the same axis (A & A', B & B', or C & C'), things are simple -- they will be read oppositely. This serves as a check on the efficiency of the setup.
In the other case, in which the photons are measured along different directions (A & B', say - 6 combinations), the Bell Inequality comes into play: quantum mechanics and local-hidden-variables theories make different predictions on how often the two spins will look 'more opposite' than 'more aligned'.
As it turned out, quantum mechanics' prediction was strongly validated.
Even after this experiment, there were a few loopholes through which it was conceivable that one could fit a local hidden variables theory: the theory could involve 'looking ahead' at the detectors and finding what orientations they would be, going so far as to examine the state of the randomization mechanism. With improving randomization, this became an increasingly wild supposition. As time progressed, the various loopholes were closed tighter and tighter: supposing local hidden variables now requires incredibly complicated and un-physics-like 'conspiracy'-style theories.
Taking this to mean that local hidden variables theories are false, what does that leave?
- Quantum mechanics
Up side: we already know what it is, it has succeeded all tests.
Down side: under the Copenhagen interpretation, locality is violated.
- A global hidden variables theory
Up side: at least Quantum mechanics and all of its weirdness isn't true.
Down side: we don't know what such a theory would be (though one has been devised, by David Bohm), and since there isn't a single difference in testable predictions between any of them and quantum mechanics, pursuing it has entered the realm of metaphysics. To snag a quote from a Nobel-Winner** "If it makes different predictions from Quantum Mechanics, I'm not interested. If it makes the same predictions as Quantum Mechanics, I'm not interested."
At first, it seems like we're stuck with nonlocality in our physical theory, whether by global variables or by a global wavefunction which collapses superluminally. This would be downright ugly. But the locality problem is not with Quantum Mechanics itself, but with the Copenhagen Interpretation: it is the collapse of the wavefunction which is a problem. If we consider the measurement process to be another case of entanglement, then the consistency of the results follows straightforwardly and involves only local information exchange -- the exchange occurring when you bring together the various results (note that this one supposition is the entire basis of the Many-Worlds Interpretation).
Entirely separate from the philosophical implications, this paradox yielded a tool of practical utility: EPR pairs form the basis of Quantum Teleportation, and play a major role in Quantum Computing.
* An entangled system can have any sort of relation, not only opposite spin. The relationship does not even have to deal with spin. There can be more than two particles, and they do not even need to be the same type. The case used in the experiment kept things as simple as possible.
** I believe it was John Schrieffer, but I could be wrong; it's hard to track these things.
Einstein, A.; Podolsky, B.; and Rosen, N. "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" Phys. Rev. 47, 777-780, 1935.
Bohm, D. "The Paradox of Einstein, Rosen, and Podolsky." Quantum Th., 611-623, 1951
Bell, J. S. "On the Einstein-Podolsky-Rosen Paradox." Physics 1, 195-200, 1964.
Aspect, A.; Grangier, P.; and Roger, G. "Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell's Inequalities." Phys. Rev. Let. 49, 91-94, 1982.