I had a discussion about this today with a group of friends at my University while we were studying for our Quantum 2 final. Unfortunately our textbook doesn't really address the problem (Bransden and Joachain) so we weren't sure if our consensus was correct, hence I turn to you.

The issue at hand is trying to measure the spin of an electron in neutral Hydrogen.

Suppose we entangle two electrons (independent of the electrons) and measure the spin of one using a Stern-Gerlach apparatus. Hence by doing this we know the spin of the other electron. Now, suppose we allow this electron to be absorbed by the Hydrogen. If its spin is opposite to the electron in the Hydrogen it should be absorbed into the ground state and a photon of energy 13.6 eV should be emitted (or a cascade of photons totaling this energy). If it has the same spin then our electron won't be allowed into the ground state (Pauli exclusion) and overall a photon (or photons) of lesser energy will be emitted.

This then raises the following questions. Is the electron in the Hydrogen in an indeterminate spin state? Will it just assume the opposite spin when the electron we entangled earlier is introduced to the system? Or does the electron we introduce to the system no longer have the spin we determined from the entanglement process since it's being affected by an entirely different system.

We think that the electron in the Hydrogen is in an indeterminate state and will assume the opposite spin of the electron being introduced. However I am not confident enough in that answer to say I'm sure it's correct.

Thoughts?