Now suppose Alice is an observer for system A, and Bob is an observer for system B. If in the entangled state given above Alice makes a measurement in the eigenbasis of A, there are two possible outcomes, occurring with equal probability:
Alice measures 0, and the state of the system collapses to .
Alice measures 1, and the state of the system collapses to .
If the former occurs, then any subsequent measurement performed by Bob, in the same basis, will always return 1. If the latter occurs, (Alice measures 1) then Bob's measurement will return 0 with certainty. Thus, system B has been altered by Alice performing a local measurement on system A. This remains true even if the systems A and B are spatially separated. This is the foundation of the EPR paradox.
diliu wrote:Two spin-1/2 particles, 1 and 2, have spins in a singlet state with spin wave function
Ψ(1,2)=1/sqrt(2)[α(1) β(2) −α(2) β(1)]
where α and β refer to up and down spins, respectively, along any chosen axis.
SSM wrote:In physicsworks proof, and I think Carl's argument, you assumed that the eigenstates were chosen along the z axis, right?
CarlBrannen wrote:I agree with the answer: (B) Down with 100% probability
Are you sure that both measurements were taken to be "z"? Maybe one of them was "x".
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