# A No-Go Theorem for Observer-Independent Facts

^{1}

^{2}

## Abstract

**:**

## 1. Introduction

## 2. Deutsch’s Version of Wigner’s Friend Experiment

## 3. The No-Go Theorem

**Postulate**

**1.**

**Theorem**

**1.**

- 1.
- “Universal validity of quantum theory”. Quantum predictions hold at any scale, even if the measured system contains objects as large as an “observer“ (including her laboratory, memory etc.).
- 2.
- “Locality”. The choice of the measurement settings of one observer has no influence on the outcomes of the other distant observer(s).
- 3.
- “Freedom of choice”. The choice of measurement settings is statistically independent from the rest of the experiment.
- 4.
- “Observer-independent facts”. One can jointly assign truth values to the propositions about observed outcomes (“facts”) of different observers (as specified in the postulate above).

**Proof.**

## 4. Relation to the Paper by Frauchiger and Renner, arXiv: 1604.07422

**(QT)**- “Compliance with quantum theory: T forbids all measurement results that are forbidden by standard quantum theory (and this condition holds even if the measured system is large enough to contain itself an experimenter).”
**(SW)**- “Single-world: T rules out the occurrence of more than one single outcome if an experimenter measures a system once.”
**(SC)**- “Self-consistency: T’s statements about measurement outcomes are logically consistent (even if they are obtained by considering the perspectives of different experimenters).”

**S**${}_{1}$- If F${}_{1}$ sees $r=t$, then W sees $w\ne ok$.
**S**${}_{2}$- If F${}_{2}$ sees $z=+$, then F${}_{1}$ sees $r=t$.
**S**${}_{3}$- If A sees $x=ok$, then F${}_{2}$ sees $z=+$.
**S**${}_{4}$- W sees $w=ok$ and is told by A that $x=ok$.

**S**${}_{a}$- Observer W assigns the truth value “true” to the statement: “A sees $x=ok$”;
**S**${}_{b}$- Observer A assigns the truth value “true” to the statement: “If $x=ok$, then F${}_{2}$ sees $z=+$”;
**S**${}_{c}$- Observer W assigns the truth value “true” to the statement: “A concludes that F${}_{2}$ sees $z=+$”.

**T**- Observer W concludes that A concludes that F${}_{2}$ concludes that F${}_{1}$ concludes that $w\ne ok$.

**S**- Observer W concludes that $w\ne ok$,

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**Deutsch’s version of the Wigner-friend thought experiment. An observer (Wigner’s friend) performs a Stern–Gerlach experiment on a spin 1/2 particle in a sealed laboratory. The outcome, either “spin up” or “spin down”, is recorded in the friend’s laboratory, including her memory. A super-observer (Wigner) describes the entire experiment as a unitary transformation resulting in an encompassing entangled state between the system and the friend’s laboratory. The friend is allowed to communicate a message, which only reports whether she sees a definite outcome or not, without in any way revealing the actual outcome she observes.

**Figure 2.**A Bell experiment on two entangled observers in a Wigner-friend scenario. The super-observers Alice and Bob perform their respective measurements on laboratories containing the observers Charlie and Debbie, who both perform a Stern–Gerlach measurement on their respective spin-1/2 particles.

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Brukner, Č. A No-Go Theorem for Observer-Independent Facts. *Entropy* **2018**, *20*, 350.
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Brukner Č. A No-Go Theorem for Observer-Independent Facts. *Entropy*. 2018; 20(5):350.
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**Chicago/Turabian Style**

Brukner, Časlav. 2018. "A No-Go Theorem for Observer-Independent Facts" *Entropy* 20, no. 5: 350.
https://doi.org/10.3390/e20050350