Wigner's convoluted friends

Abstract

Considering a complicated extension of a Wigner's friend scenario, Frauchiger and Renner (FR) allegedly showed that "quantum theory cannot consistently describe the use of itself". However, such a result has been under severe criticism, as it has been convincingly argued to crucially depend on an implicit, non-trivial assumption regarding details of the collapse mechanism. In consequence, the result is not as robust or general as intended. On top of all this, in this work we show that a much simpler arrangement-basically an EPR setting-is sufficient to derive a result fully analogous to that of FR. Moreover, we claim that all lessons learned from FR's result are essentially contained within the original EPR paper. We conclude that FR's result does not offer any novel insights into the conceptual problems of quantum theory.

Understanding the Frauchiger-Renner Argument

“…A further unitary, implementing an inference via rule C from F 's inference about w at n ∶ 31 to F 's certainty that w = fail at n ∶ 31 or a null inference to 'no conclusion drawn,' results in the state ψ⟩ n∶14 = 1 3 tails⟩ R "r = tails, so I am certain that w = fail at n ∶ 31"⟩ F ↑⟩ S "z = + 1 2 , so I am certain that w = fail at n ∶ 31"⟩ F + 1 3 tails⟩ R "r = tails, so I am certain that w = fail at n ∶ 31"⟩ F ↓⟩ S "I observed z = − 1 2 ; no conclusion drawn"⟩ F + 1 3 heads⟩ R "r = heads, so no conclusion drawn"⟩ F ↓⟩ S "I observed z = − 1 2 ; no conclusion drawn"⟩ F (7) Continuing in this way, and transforming to the basis { ok⟩, fail⟩} of L defined in the experimental protocol above, we find that after W 's measurement and inferences from the outcome of his measurement (to F 's certainty about z via rule Q, and hence from F 's certainty about w at n ∶ 31 to W 's certainty about w at n ∶ 31 via rule C, or to 'no conclusion drawn'), the global state has the form Ψ⟩ n∶24 = 1 6 fail⟩ L "w = fail; no conclusion drawn"⟩ W ↑⟩ S "z = + 1 2 , so I am certain that w = fail at n ∶ 31"⟩ F − 1 6 ok⟩ L "w = ok, so I am certain that w = fail at n ∶ 31"⟩ W ↑⟩ S "z = + 1 2 , so I am certain that w = fail at n ∶ 31"⟩ F + 2 3 fail⟩ L "w = ok; no conclusion drawn"⟩ W ↓⟩ S "z = − 1 2 ; no conclusion drawn"⟩ F…”

“…What comes to much the same thing is the claim that the argument assumes that when an agent in an isolated laboratory performs a measurement, the state collapses inside the laboratory, but not outside. Muciño and Okon [7] argue that, in addition to the three rules, Frauchiger and Renner implicitly invoke the assumption:…”

Comment on "Understanding the Frauchiger-Renner argument" by Jeffrey Bub

“…Several authors (e.g. [5]) have pointed out that the argument relies on more assumptions than the three rules Q, C and S; in particular, that a measurement leads to projection of the quantum state to an eigenstate of the measured observable, at least for some observers [3]. Bub denies this.…”