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?
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1$\begingroup$ Are you asking for "real life application" as the title suggests (which would be hard I think... how can a paradox have real world applications?) or for intuitive examples to make things understandable as the body suggest (which is a good question, +1)? Please edit the title or the body consistently $\endgroup$– glSCommented Jan 9, 2015 at 15:20
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$\begingroup$ There is a border case of quantum mechanics which can be explained classically in just one sentence: For two entangled photons in vacuum, both spacetime intervals are 0, everything is happening simultaneously. See the (still unanswered) question Local EPR-experiments with photons in vacuum? $\endgroup$– MoonrakerCommented Jan 9, 2015 at 15:44
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1$\begingroup$ I have just edited the title. Now it should be clearer. $\endgroup$– Javier AriasCommented Jan 9, 2015 at 15:49
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$\begingroup$ Some people use "EPR paradox" interchangeably with Bell's theorem showing that violations of Bell inequalities rule out local hidden variable explanations for QM statistics--they're closely related, but Bell's theorem was more definitive in ruling out all possible local hidden variable explanations. If you're interested in a simple illustration of why Bell inequality violations can't be explained with local hidden variables that predetermine measurement results, see my lotto card example here. $\endgroup$– HypnosiflCommented Jan 9, 2015 at 17:04
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$\begingroup$ This paper on doing practical quantum key distribution with polarization entangled photons might be a candidate. The EPR paradox facilitates distribution of correlations (in the measurement outcomes that can be converted into a stream of bits) to two parties in a secure way. Any act of eavesdropping during the communication disturbs the quantum states, changing the measurement outcomes. This results in errors that warn the parties of the eavesdropping. $\endgroup$– jayannCommented Jan 9, 2015 at 20:37
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1 Answer
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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?
answered Jan 9, 2015 at 21:12
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1$\begingroup$ So, is this EPR paradox basically the same thing as quantum entanglement? $\endgroup$– Time4TeaCommented Jan 9, 2015 at 21:39
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$\begingroup$ Interesting to learn more about the history of these ideas, thanks for posting the link to your blog. One minor correction: the name is "Feynman", not "Feynmann". $\endgroup$ Commented Jan 9, 2015 at 21:50
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$\begingroup$ It is in fact BORIS PODOLSKY, not Podalsky. Never mind, thanks a lot for the insightful comment. Would it be philosopically fair to say that the thorium and the alpha particle are somehow bounded by a trace (say, a sub-index with the same feature or number which relates them as, say, two separate occurrence of a unique underlying phenomenon? $\endgroup$ Commented Jan 10, 2015 at 12:21
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$\begingroup$ I can't comment on your question as to how the thorium atom is linked to the alpha particle. In standard QM, we say they do not each have their own independent wave function, but instead there is a single six-dimensional wave function which contains both of them. (That's the wave function that "collapses" when either one is detected.) $\endgroup$ Commented Jan 10, 2015 at 16:08
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1$\begingroup$ The answer to your question in the edit is the same as the ones I gave here and here to questions about why you can't use a delayed choice quantum eraser to create an FTL communicator--it turns out that if a particle is entangled in such a way that there's even the potential to learn which slit one went through by measuring the other in the right way, then there will be no double-slit interference pattern in the particle's total probability of landing at various points on the screen, $\endgroup$ Commented Jan 10, 2015 at 23:32