Continuing entanglement after first measurement

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SUMMARY

In quantum mechanics, measuring an entangled particle collapses its wavefunction, thereby destroying the entanglement. Specifically, measuring both particles A and B with photons of identical energy does not create new entanglement. The Zeeman effect, which involves changing a particle's spin state through an electric field, does not affect the existing entanglement between two particles. However, altering the spin state of one particle can lead to the loss of entanglement if the particles transition into different states.

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Ok so if two particles are entangled and I choose to measure particle A, then the entanglement is finished. But what if I measure both A and B with photons of the exact same energy; is there now a new entanglement?

Additionally, if the spn is changed, can the entanglement continue? Placing a particle into an electric field to separate the spin state energy levels (this is called something called the Zeeman effect and was one of the reasons we made the mistake of calling the property spin in the first place) and then putting in sufficient energy (usually radio waves) will change the spin state of that particle. This is the basis for NMR and MRI.
 
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No, measuring both particles with photons of the same energy will not cause a new entanglement. Entanglement is a property of two particles which results from their wavefunction being in a superposition of states. Measuring one or both particles collapses the wavefunction into one of the possible states, thereby destroying the entanglement. Changing the spin state of a particle by applying an external force (e.g. electric field) does not affect the entanglement between two particles. However, if the spin state of one particle is changed, this can cause the entangled particles to move into different states, and thus the entanglement can be lost.
 

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