EPR stands for Albert Einstein, Boris Podolsky, and Nathan Rosen. Why there is no picture with all three men together is beyond me. I couldn't find one. These three together wrote a paper titled "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" It became a centerpiece in the argument over the interpretations of quantum reality.
Whereas the original argument was with two momentum correlated quons, it's easier to use Bohm's polarization correlated quons. Imagine a source that emits two photons in opposite directions. We'll call one a blue photon and one a green photon. They travel a distance and then both hit a polarization device at opposite ends of our experiment. These photons are phase entangled (as we discussed before). What's important to understand about these photons is that they are both described by a single Psi. And since they are unmeasured they do not possess a particular polarization before they hit their polarization devices. We also note that the photons are not emitted with any polarization state - they are unpolarized. Therefore from before we know that any measurement P(angle) gives 50% hits and 50% misses.However, since these are phase entangled, they always give the same measurement as long as both polarization devices are set at the same angle. If blue gets a hit at P(45) then green gets a hit at P(45). If blue gets a miss at P(45) the next time, then green gets a miss at P(45) the next time. This is both predicted by quantum mechanics and also shown to be true in experiments. It is a fact.
It's also true that this result is independent of how long it takes to measure the photon's polarization. Measure blue 1 foot from the emitter and measure green a googol miles away and you get the same results.
Once again, the photons have no definite polarization before measurement, but when measured the polarizer devices will match.
Einstein asks the question,
Is the polarization of the green photon after it is emitted but before it is actually measured truly indefinite as Bohr would suggest or is it really definite but unknown?In other words is our ignorance classical or quantum? Bohr would say the photon does not have a definite attribute before measurement. Now Einstein goes in for the kill. Suppose our blue detector moves in a bit so it is measuring the polarization of the blue photon before the green detector measures the green photon. Imagine that the blue detector is set at P(0) and it records a hit. What would Bohr and Einstein say about the green photon's polarization state?
Bohr: "Given that the blue detector has measured the blue photon to have a vertical polarization state, quantum theory predicts that if the green detector is set to P(0) or vertical it will record a hit. It also predicts that if it measures P(90) or horizontal it will record a miss."
Einstein: "We agree on this. What if the green detector is positioned at some other angle?"
Bohr: "QT gives no certain results. If we measure P(45) we'll get 50%/50% hits and misses."
Einstein: "We agree again. However, what are you willing to say about the reality of this particular photon traveling through the air?"
Bohr: "I believe QT is complete. Therefore, before it is actually measured, the green photon only has a definite polarization in the vertical and horizontal position. To speak of a definite polarization in any other direction would be to speak nonsense."
Einstein: "I disagree. I believe that it possesses a definite polarization attribute for every single angle."
Bohr: "You are wrong."
Einstein: "Forgive me but my friends Boris and Nathan have devised a simple argument that convinces us the green photon traveling in front of us indeed has a specific polarization attribute for each angle. Allow me to show you. Let us both agree to the 'locality assumption'. We assume that the real situation of the green photon is not affected by the angle that the blue detector is set to. This seems reasonable because the photons are traveling the speed of light. Therefore the green photon cannot 'learn' about the other photon's measurement except if it could signal to the green photon at a speed faster than the speed of light. So let's assume that doesn't happen."
Bohr: "Okay."
Einstein: "Blue chose to measure P(0) and got a hit. It could have been set to any other angle, let's say P(45), and we would have obtained some result - either a hit or a miss. We do not know which. Because we have entangled pairs we know that the green photon is obliged to have the same polarization as the blue photon at 45 degrees. To generalize we could have set any angle of measurement and green would be obliged to concur with the measurement at blue."
Bohr: "Yes."
Einstein: "If the green photon must have the same polarization as blue at a given angle of the detectors and if (by locality assumption) blue's measurement does not affect the green photon, then the green photon must already possess a definite polarization for each angle. Thus before green hits the detector, it must have 'made up it's mind' what polarization state it must be in for each angle. Quantum theory is thus incomplete."
Bohr: "Sneaky! But I cannot accept your conclusion. Of course there is no question of any mechanical influence traveling from the blue detector to the green photon, but there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future behavior of the green light."
Bohr is on shaky ground here. Einstein has shown that if we are going to fall on the sword for quantum theory, then something is terribly wrong with this experiment. How can the green photon have it's result influenced by the measurement of the blue photon if nothing can travel faster than the speed of light and there is no 'force' that we know of to do the influencing? This would deny locality. And if there was a concept that is held onto hard by pretty much every single scientist it was that locality must exists.
To absorb this better consider this alteration of the experiment. The detectors are a billion miles from the light source. The photons get emitted and just milliseconds before they hit the detectors, the detectors are moved to the position you wish to measure the polarization. Before then we have not made up our mind about what we are going to measure. For the green photon and detector to match up with blue photon and detector suggest that the act of turning the detector to measure a particular polarization state influences what happens to the other detector and photon which are two billion miles away. And it does this clearly in a vanishingly small amount of time. It seems to throw some doubt that quantum is a complete description. Surely the photons knew what polarization state the would result in for each angular measurement of polarization long before they made it to the detectors. They couldn't possibly talk to each other over that distance and that short amount of time.
What is locality? All we're saying here is that things do not influence other things greater than the speed of light and that there must be some medium for this influence to occur. The earth can be affected by the gravitational pull of the sun because there is a gravitational field causing that interaction. Furthermore a disturbance of the sun takes the 8 minutes or so light takes to travel the distance before we on earth would feel that disturbance because that's how long it takes the influence to reach us (due to gravitons). In other words, things do not influence other things without some mechanistic interaction and they certainly do not do it instantaneously. Scientists hold onto this concept of locality more tightly than they held onto pre-relativity and pre-quantum concepts. This is a major deal breaker for everyone. And Bohr knew it. Both sides struggled with these concepts until John Bell came along.
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