Quantum theory cannot consistently describe the use of itself

by avturchin 1 min read20th Sep 201816 comments


As I understand it, the new thought experiment in QM demonstrates that all currently known interpretations of QM are wrong, if we extrapolate Winger friend thought experiment to next level, where different friends are using different theories to interpret each other actions. This may have implication for agent foundations.

Short description of the experiment from Scientific American: "Frauchiger and Renner have a yet more sophisticated version (see ‘New cats in town’). They have two Wigners, each doing an experiment on a physicist friend whom they keep in a box. One of the two friends (call her Alice) can toss a coin and—using her knowledge of quantum physics—prepare a quantum message to send to the other friend (call him Bob). Using his knowledge of quantum theory, Bob can detect Alice’s message and guess the result of her coin toss. When the two Wigners open their boxes, in some situations they can conclude with certainty which side the coin landed on, Renner says—but occasionally their conclusions are inconsistent. “One says, ‘I’m sure it’s tails,’ and the other one says, ‘I’m sure it’s heads,’” Renner says."

Couple of quotes from the article which are related to agents:

"Suppose that a casino offers the following gambling game. One round of the experiment is played, with the gambler in the role of W, and the roles of F¯, F, and W¯ taken by employees of the casino. The casino promises to pay $ 1.000 to the gambler if F¯’s random value was r = heads. Conversely, if r = tails, the gambler must pay $ 500 to the casino. It could now happen that, at the end of the game, w = ok and ¯w = ok, and that a judge can convince herself of this outcome. The gambler and the casino are then likely to end up in a dispute, putting forward arguments taken from Table II.

Gambler: “The outcome w = ok implies, due to s ¯F Q, that r = heads, so the casino must pay me $ 1.000.”

Casino: “The outcome ¯w = ok proves, by virtue of s W¯ Q, that our employee observed z = +1 2 . This in turn proves, by virtue of s F Q, that r = tails, so the gambler must pay us $ 500.”

"Theorem 1 now asserts that (Q) and (S) are already in conflict with the idea that agents can consistently reason about each other, in the sense of (C)."