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There are two particular scenarios involving entanglement that are confusing me. For both of these, assume we have an electron-positron pair created from a spin-0 particle, in which all components of spin must be opposite in order to conserve angular momentum. The electron and positron are a considerable distance apart.

1. The x-component of the electron's spin is measured to be, say, up, which would mean the x-component of the positron's spin is down. At the exact same instance, the y-component of the positron's spin is measured to be down, which would mean that the y-component of the electron's spin is up. At that exact moment, why is the HUP not violated? If, shortly after, we measure either quantity again, will we be guaranteed to get the same result, or does the previous "double measurement" randomize the results?

2. The scientist with the positron asks the scientist with the electron a yes-or-no question. They then get their watches completely synchronized and each travel a lightyear in opposite directions with the same speeds and accelerations, so their watches are still synchronized. After they both simultaneously arrive at their final destinations, the scientist with the electron has exactly one hour to repeatedly measure x-spin and y-spin over and over again until he/she gets the desired result; y-spin up for yes, y-spin down for no (the x-spin is measured to randomize the y-spin results). After the hour, which, especially if the scientist can perform a spin measurement every few seconds, would be far more than enough time to surely get the desired answer, the scientist with the positron measures its y-spin and finds the answer to the question, at most an hour after the answer was sent. Is this not information traveling at the speed of light? Now, I do understand that if, say, an hour is enough time for 60 x-spin-y-spin measurements, the scientist with the positron has a 1/2^60 chance of not having the correct answer (that is the probability that all y-measurements will end up with the wrong answer), so definite information was not really sent. But, take the limit of this situation. Say the scientists are x light years apart, and the scientist has x/2 years to answer the question, and then let x tend towards infinity. Wouldn't an answer to the question that has a probability of being correct approaching 100% travel at double the speed of light?

Thanks in advance!

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# B Two Confusing Entanglement Scenarios

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