Some applications of the Einstein-Podolsky-Rosen (EPR) paradox? If you were to explain the Einstein-Podolsky-Rosen paradox to high school students (age 16, with no particular strength in math), what kind of intuitive example would you provide to make things understandable? 
 A: The EPR paradox is based on something that would seem obvious to any good high school student. If you have a uranium atom and wait for it to decay, then you get a thorium atom and an alpha particle. The alpha particle has a lot of energy, so it shoots off in one direction, and the thorium atom, by recoil, shoots off in the other direction. So if the uranium atom starts off in the middle of a football field, and you sit with a geiger counter at one end, then if you catch an alpha particle, the guy at the other end of the field will catch a thorium atom. It's not much of a paradox.
The sticky point is that according to the Copenhagen interpretation of quantum mechanics, until the moment you detected the alpha particle, it MIGHT have been anywhere: because up to that point, the alpha particle has something called a "wave function". The actual moment of detection is called the "collapse of the wave function" and it's a major philosophical issue in quantum mechanics. But that's not the point of the EPR paradox.
The real problem is that just as the alpha particle might have been anywhere, the thorium atom "might" have been anywhere too...because it also has a wave function. But once you find the alpha particle at one end of the field, suddenly there's no choice for the thorium atom...it has to be at the other end. The paradox is that something which happened at one end of the field instantaneously affected the possible outcomes that could take place a hundred yards (or a hundred light-years) away.
It sounds like an easy paradox to resolve: you just have to realize that at the moment the uranium atom decayed, the alpha particle went one way and the thorium atom went the other. That would solve the problem, but .... for reasons you can't explain to a high-school student, that would lead to enormous contradictions in the whole theory of quantum mechanics.
I'm not sure if anyone in 1936 thought that the EPR was a practical problem and not just a philosophical problem. The "thought experiment" proposed by EPR (Podalsky specifically, if I'm not mistaken), while not identical to the version I've posted here, was not something you could set up in practise. People talk a lot about how Bell changed everything when he proposed his famous inequality in 1964, but for my money it was Bohm who turned this into a practical question in 1950 when he proposed a version of EPR paradox involving spin states. 
I talk about this in greater detail in my blogpost "Einstein => Bohm => Feynmann => Bell": http://marty-green.blogspot.ca/2011/11/einsteinbohmfeynmannbell.html
EDIT: I said the other day that you could "solve" the paradox by simply assuming that the thorium and alpha particles took off on specific pathways at the moment they were created, but this would create "enormous difficulties" which you "couldn't explain to a high school student". When someone (like me) says something like that, what he really means is that he doesn't understand it himself. So I thought about it and I'm going to try to explain what the contradictions are.
The problem is that both alpha "particles" and thorium "atoms" behave as waves. They interfere like waves. In particular, you could set up double-slit experiments at opposite ends of the football field and observe diffraction patterns...
Well actually, you can't do it with a single uranium atom in the middle. You could do it but there's no diffraction pattern with only one particle. You'd need a block of uranium, so it's constantly emitting particles in all directions. Then you could set up a double-slit at each end of the field (or a hundred light-years apart) and observe diffraction patterns. 
But the thing about the two-slit experiment is if you watch the "particles" as they pass through the slit, you destroy the diffraction pattern. So what you do is set up your geiger counters at one end and catch the particles before they can go through the slits. They have to be really small geiger counters because the slits are really close together...but that's just a technical problem. The point is that assuming you can distinguish which slit they were going for, you now know which slit the other particles are heading for at the far end of the field...or a hundred light years away. So this should destroy the interference pattern.
But that means something you did at one end of the field (or the universe) instantly affected something that someone else could observe at the other end. That's a real problem.
And that's where the EPR paradox leads. I'm afraid I've actually overstated the case, because I appear to have designed a "practical" system that allows for faster-than-light communication. And that's not allowed in anyone's quantum mechanics. So I've done something wrong, but I can't exactly see what. Anyone care to weigh in?
