Timeless formulation of Wigner’s friend scenarios

At the heart of the quantum measurement problem lies the ambiguity about exactly when to use the unitary evolution of the quantum state and when to use the state-update in dynamics of quantum mechanical systems. In the Wigner’s friend gedankenexperiment, different observers (one of whom is observed by the other) describe one and the same interaction differently. One – the friend – uses the state-update rule and the other – Wigner – chooses unitary evolution. This can lead to paradoxical situations in which Wigner and his friend assign different probabilities to the outcomes of subsequent measurements. In my talk, I will apply the Page-Wootters mechanism (PWM) as a timeless description of the Wigner's friend-like scenario. This description assigns one timeless state to the entire experimental scenario from which it is possible to derive probabilities without the need to involve the evolution of the quantum state during – and in-between – measurements. I will consider several rules for assigning two-time conditional probabilities within the PWM. All of these reduce to standard (“textbook”) rules for non-Wigner’s friend scenarios. However, when applied to the Wigner’s friend setup, they differ. Each rule potentially resolves the probability-assignment paradox in a different way. Moreover, one rule imposes that a joint probability distribution for the measurement outcomes of Wigner and his friend is well-defined only when Wigner’s measurement does not disturb the friend’s memory, in agreement with the recent “no-go theorem for observer-independent facts

(with Veronika Baumann, Flavio Del Santo, Alexander R. H. Smith, Flaminia Giacomini, and Esteban Castro-Ruiz)