Trying to understand the EPR paradox So I keep reading all these articles on the EPR paradox, and I follow them pretty easily right up until it gets to the most important matter.
Assuming you are trying to measure x and y spin,
Wikipedia and others say that when you measure x-spin on the first particle, it suddenly becomes impossible to measure the y-spin on the other particle.
But no one really goes on to say what this means in a physical sense.
Let's say you have 2 actual detectors.  When the first particle hits the x-detector, now x-spin is measured for both particles.  When the second particle hits the y-detector, now y-spin is measured for both particles.  But all these articles say the second detector is unable to measure y-spin.  So what happened?  Did the detector just explode or something?!
 A: I have to think David will agree, on reflection, that his answer has failed to capture the essence of entanglement. Any stream of particles, if not specially prepared, will measure +h/2 or -h/2 at detector A; they will do with respect to the x axis, or the y axis, or any axis. Exactly the same is true at detector B. How can this very ordinary circumstance illustrate the mystery of entanglement? But that seems to be what David has said: that if you prepare the particles in the entangled state, you get this "strange result". I see nothing strange about it since it seems to be exactly the same result if you set up two detectors far apart and measured streams of particles that were totally random.
I am going to suggest that the mystery of entanglement lies in the perfect correlation (or anti-correlation) that you get when you set up both detectors along the x axis. Some people think there is nothing mysterious about this because it is exactly what you would expect if the two particles were created with equal and opposite spins. These people are very wrong. The reason they are wrong is that the experiment works the same no matter how you align the detectors with respect to the source of the particles. We can imagine an experiment where particles are created with opposite spins, but assuming the spin axis is random at the moment of creation, there is no way a pair of detectors should show 100% correlation no matter what angle you set it to. In fact, in the case of entanglement, there is 100% correlation regardless of the orientation. That is a real problem and it is really the only problem.
EDIT: I explain this issue in more detail in my blog article, "Entanglement and the Crossed Polarizers".
A: There are no problems with second detector measurements. They occur as they would without first detector. The "problem" is that if you check them with the knowledge of the results of first detector, you might notice that measurements on both ends are correlated. If you measured x components in both, you definitely got opposite results. While if you check x in one and y in another you have no correlation at all. Which may be confusing.
A: It's not a "paradox". Einstein was troubled about the objective reality of complimentary variables. Before EPR, it was thought it's not possible to measure complimentarity variables simultaneously. He argued that some property has an objective value if without in any way disturbing it, we can know what it is with certainty. If we measure the z spin of an entangled pair, we automatically know if a measurement of the other z spin is made, it will have the opposite value. By his definition, the z spin of the other particle has now an objective existence. However, we may choose to measure the x spin of the first particle instead and the z spin of the other particle. The assumption he snuck in was counterfactual definiteness. Because we're no longer measuring the z spin of the first particle, we can't argue anymore that the z spin of the other particle has an element of reality prior to measurement. His argument falls flat if there's no counterfactual definiteness.
A: In a certain way, to see the paradox in the EPR experiment you have to have absorbed quantum mechanics into your blood. Otherwise one might not see the surprise in the result. I think that a much better paradox, for someone just learning the theory, is the GHZ experiment.
You begin with three photons in a linear superposition of two pure states. In the first pure state, all the photons are horizontally polarized HHH. In the second pure state, they are all vertically polarized VVV. In this situation, measuring any one photons horizontal versus vertical polarization immediately determines the measurements for the other two.
Something interesting happens when you make a measurement at an angle. It's too long to describe here, but it is elementary and by spending a few hours reading it and working it out you will see some amazing things. My feeling is that this is more of a surprise than the EPR experiment as it is an apparent contradiction in how we are used to using probabilities. In short, quantum mechanics seems to be about waves (and therefore complex numbers which encode the phase and amplitude of a wave) more than it is just about probabilities. It makes me sort of feel that our extraction of probabilities (i.e. the Born rule) is more accidental than fundamental; or that an answer to Einstein's complaint about QM is that the dice is our playing with the world (or perhaps vice versa) rather than that God does play with dice.
A: As reading the wikipedia article, we can clearly see a way to transfer information faster than the speed of light, therefore we know there is an error in the article.
Let's say entangled particle pair has identical x-spins. We measure y-spin of one particle. The x-spin of the measured particle becomes random, the x-spin of the other particle is not affected.
Bohr debunked Einstein's, Podolsky's and Rosen's claim that, by using entangled particles, it is possible to measure both momentum and position accurately, by saying that measuring position causes the laboratory to have somewhat uncertain momentum, which cause the momentum measurement in the laboratory to be uncertain.
So don't you think Bohr's way to solve the EPR-paradox is the right way to solve the EPR-paradox?
