I don't understand Wigner's friend paradox The Wigner's friend experiment goes like this:
Say Wigner instructed his friend to perform Schrödinger's cat experiment in a laboratory while he work from home, his friend made the measurement and email Wigner about the result. The paradox is the state of the cat is defined for his friend since he took a peek but before the email containing the result reaches Wigner, to Wigner the state of the cat is both alive and dead at the same time. I am now confused as why would Wigner knowing the result even matters? Please help me understand this paradox because of Wigner involvement there now seems to be a contradiction of the result.
 A: The paradox is more or less a consequence of the unresolved measurement problem. How do we interpret measurements and how does an observer affect measurements. Let's assume we use the interpretation that a quantum state collapses to an eigenstate corresponding to the measured value. We can then ask when does this collapse happen and who causes the collapse ? Wigner's friend paradox is due to the fact that we can obtain two different answers to these questions.
First we have the friend who does the experiment on a superposition state in his lab. He will say that the system collapsed to an eigenstate when he did the measurement. At the same time we can take the point of view of Wigner. Wigner will model his friend and the experiment as one combined quantum system. The "measurement" for Wigner is then the process of asking his friend for the outcome and the collapse only happens when he asks his friend for the information. The "asking measurement" can happen at a different time than the friend's lab measurement.
Now we have seemingly two different answers to the question when the collapse of the superposition state took place and it also begs the question who caused the collapse ? Did the friend or Wigner cause the collapse ? And at which point in time did the unitary time evolution of the system stop ? When the friend did his measurement or when Wigner "measured" the friend-lab system.
The paradox is that both points of view, the friends view and Wigners view, are eqvivalent. There is no physical or axiomatic reason in quantum mechanics that tells us that one is favorable over the other. For some it is "common sense" to not view humans as part of quantum systems but technically there is no reason to exclude them or to treat them differently than any measurement apparatus. Wigner also thought that humans/conscious beings should be treated differently than inanimate measurement devices. But that is a subjective opinion/decision and not a fact that follows from the rules of quantum mechanics.
A: The important part of the thought experiment is the time where Wigner's friend knows the cat is dead but Wigner himself has not yet read the email.
After Wigner reads the email, he and his friend will agree that the system has collapsed and the paradox disappears.
I would say that Wigner knowing the result eventually is not important for the paradox. The fact that at one time his friend knows for sure that the cat is dead but for Wigner the cat is in a superposition is the crucial part.
While the email is on its way we have:
Wigner's friend says: $$ |\psi> = |dead> $$
Wigner says: $$|\psi> \propto (|dead> + |alive>)$$
Now who is right and when does the system collapse?
In order for this paradoxical situation to occur, you need Wigner as an observer of the system that involves his friend and the cat.
