Obviously you can't measure the particle simultaneously in the up and down state. Nobody believes that. Nobody is arguing it. Honestly it's hard to understand why you have such an agitated bee in your bonnet about superpositions. The mathematical expression of the photon polarised at 45 degrees to the measurement apparatus is a normalised vector spanning the space of both up and down. I guess what you interpret that to mean is up to you since the mathematical predictions that arise from it are the same: 50% chance of up or down. Once again, you're simply arguing at cross purposes with Bruno, who clearly understands QM perfectly well. He's not saying the photon can be measured as up and down at the same time. He's just saying that any superposition of up and down is an eigenvector in some other orientation of the apparatus.

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