I am not sure that I fully understand even the basic aspects of the Quantum measurement and entanglement but I just came across this thought experiment and I wish to resolve it.(adsbygoogle = window.adsbygoogle || []).push({});

In a setting of two entangled spin-1/2 particles, suppose that Alice applies a uniform magnetic field ##B_0## along ##z## direction at her location. She dose not measure the spin of her particle but because the particle passes through ##B_0## the spin should align along that direction as this is the lowest energy the particle may have. And if she is 100% sure that her unmeasured particle is spin-up, she must conclude that Bob`s particle is spin-down due to conservation of the angular momentum. Now if Bob, however, measures his particle spin and finds that it is spin-down, then he must conclude that Alice uniform magnetic field is directed up and vice versa. Then based on the outcome of his result, he knows the direction of Alice`s ##B_0## which means that Alice can encode any message in the form of 1 and 0 where 1 means ##B_0## is toward the +ve Z-direction and 0 means that ##B_0## is along the -ve Z-direction and this message can be delivered faster than light.

Now suppose a different scenario, 100 pairs of entangled particles are emitted into 2 directions. Alice measures her particles at the same time and it happens that she finds 55 out of 100 particles are spin-up and 45 are down. Bob, who does not measure anything, should have 45 up and 55 down. If Bob put a little coil near his particles, he can picks up a signal which is induced into the coil by that 10 difference in the magnetic angular momentum. So, despite that the Bob system is undisturbed, how the can the laws of angular momentum and energy conservation hold?

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# I Entanglement, magnetic field and conservation law

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