EPR Paradox

The Paradox is based on two things, first is locality, second is reality.

The scenario is as follows. Suppose Alice and Bob have a pair of entangled states, the locality take its effect now, saying that if Alice and Bob is very far away from each other. No matter what Alice do to her particle, the particle in Bob's side will not be influenced. So if Alice can take measurements to measure position \(x\) very precise, and since Alice's particle is entangled with Bob's particle, so Bob's particles' position \(x\) is the same as Alice's so also be measured very precisely. Alternatively, if Alice do not measure her particle's position, instead, she measure the momentum of her particle, then for the same reason, Bob's particle's momentum will also be measured as precise as she want. Reality takes its effect now, since the position and momentum of Bob's particle exist objectively, so Bob's particle's position \(x\) and momentum \(p\) can be measured as precise as possible at the same time. This conflicts with the unvertainty principle. So the paradox.