Editing Wigner's friend (section)

===Relational quantum mechanics===
[[Relational quantum mechanics]]<ref>{{Cite journal |last=Rovelli |first=Carlo |date=1996–2008 |title=Relational quantum mechanics |journal=International Journal of Theoretical Physics |volume=35 |issue=8 |pages=1637–1678 |doi=10.1007/bf02302261 |arxiv=quant-ph/9609002 |bibcode=1996IJTP...35.1637R |s2cid=16325959 |issn=0020-7748}}</ref> (RQM) was developed in 1996 by [[Carlo Rovelli]] and is one of the more recent [[interpretations of quantum mechanics]]. In RQM, any [[physical system]] can play the role of an observing system, to which any other system may display "facts" about physical variables. This inherent relativity of facts in RQM provides a straightforward "solution" to the seemingly [[paradox]]ical situation in Wigner's friend scenario: The state that the friend assigns to the [[Spin (physics)|spin]] is a state relative to himself as friend, whereas the state that Wigner assigns to the combined system of friend and spin is a state relative to himself as Wigner. By construction of the theory, these two descriptions do not have to match, because both are correct assignments of states relative to their respective system.

If the [[Observable (physics)|physical variable]] that is measured of the spin system is denoted by ''z'', where ''z'' takes the possible outcome values 0 or 1, the above Wigner's friend situation is modelled in the RQM context as follows: <math>F</math> models the situation as the before-after-transition
<math display="block">\alpha|0\rangle_S + \beta|1\rangle_S \to |1\rangle_S</math>
of the state of <math>S</math> relative to him (here it was assumed that <math>F</math> received the outcome ''z''&nbsp;=&nbsp;1 in his measurement of <math>S</math>).

In RQM language, the fact ''z'' = 1 for the spin of <math>S</math> actualized itself relative to <math>F</math> during the interaction of the two systems.

A different way to model the same situation is again an outside (Wigner's) perspective. From that viewpoint, a measurement by one system (<math>F</math>) of another (<math>S</math>) results in a correlation of the two systems. The state displaying such a correlation is equally valid for modelling the measurement process. However, the system with respect to which this correlated state is valid changes. Assuming that Wigner (<math>W</math>) has the information that the physical variable ''z'' of <math>S</math> is being measured by <math>F</math>, but not knowing what <math>F</math> received as result, <math>W</math> must model the situation as
<math display="block">\big(\alpha|0\rangle_S + \beta|1\rangle_S\big) |\bot\rangle_F \to \alpha\big(|0\rangle_S \otimes |0\rangle_F\big) + \beta\big(|1\rangle_S \otimes |1\rangle_F\big),</math>
where <math>|\bot\rangle_F</math> is considered the state of <math>F</math> before the measurement, and <math>|1\rangle_F</math> and <math>|0\rangle_F</math> are the states corresponding to <math>F</math>'s state when he has measured 1 or 0 respectively. This model is depicting the situation as relative to <math>W</math>, so the assigned states are relative states with respect to the Wigner system. In contrast, there is no value for the ''z'' outcome that actualizes with respect to <math>W</math>, as he is not involved in the measurement.

In this sense, two accounts of the same situation (process of the measurement of the physical variable ''z'' on the system <math>S</math> by <math>F</math>) are accepted within RQM to exist side by side. Only when deciding for a reference system, a statement for the "correct" account of the situation can be made.