Based on her complex measurement, which can come out as either YES or NO, she can infer the result of the measurement made by Bob’s friend. Say Alice got YES for an answer. She can deduce using quantum mechanics that Bob’s friend must have found the particle’s spin to be UP, and therefore that Alice’s friend got tails in her coin toss.
This assertion by Alice necessitates another assumption about her use of quantum theory. Not only does she reason about what she knows, but she reasons about how Bob’s friend used quantum theory to arrive at his conclusion about the result of the coin toss. Alice makes that conclusion her own. This assumption of consistency argues that the predictions made by different agents using quantum theory are not contradictory.
Meanwhile, Bob can make a similarly complex measurement on his friend and his lab, placing them in a quantum superposition. The answer can again be YES or NO. If Bob gets YES, the measurement is designed to let him conclude that Alice’s friend must have seen heads in her coin toss.
It’s clear that Alice and Bob can make measurements and compare their assertions about the result of the coin toss. But this involves another assumption: If an agent’s measurement says that the coin toss came up heads, then the opposite fact — that the coin toss came up tails — cannot be simultaneously true.
The setup is now ripe for a contradiction. When Alice gets a YES for her measurement, she infers that the coin toss came up tails, and when Bob gets a YES for his measurement, he infers the coin toss came up heads. Most of the time, Alice and Bob will get opposite answers. But Frauchiger and Renner showed that in 1/12 of the cases both Alice and Bob will get a YES in the same run of the experiment, causing them to disagree about whether Alice’s friend got a heads or a tails. “So, both of them are talking about the past event, and they are both sure what it was, but their statements are exactly opposite,” Renner said. “And that’s the contradiction. That shows something must be wrong.”
This led Frauchiger and Renner to claim that one of the three assumptions that underpin the thought experiment must be incorrect.
“The science stops there. We just know one of the three is wrong, and we cannot really give a good argument [as to] which one is violated,” Renner said. “This is now a matter of interpretation and taste.”