Wigner's friend

Wigner's friend is a thought experiment in theoretical quantum physics, proposed by the physicist Eugene Wigner in 1961.^[1] The scenario involves an indirect observation of a quantum measurement: An observer W observes another observer F who performs a quantum measurement on a physical system. The two observers then formulate a statement about the physical system's state after the measurement according to the laws of quantum theory. However, in most of the interpretations of quantum theory, the resulting statements of the two observers contradict each other. This reflects a seeming incompatibility of two laws in quantum theory: the deterministic and continuous time evolution of the state of a closed system and the probabilistic, discontinuous collapse of the state of a system upon measurement. Wigner's friend is therefore directly linked to the measurement problem in quantum mechanics with its famous Schrödinger's cat paradox.

The thought experiment

The thought experiment posits a friend of Wigner in a laboratory and lets him perform a quantum measurement on a physical system (this could be a spin system or also Schrödinger's cat). This system is assumed to be in a superposition of two distinct states, say, state 0 and state 1 (or "dead" and "alive", in the case of Schrödinger's cat). When Wigner's friend measures the system in the 0/1-basis, according to quantum mechanics, he will get one of the two possible outcomes (0 or 1) and the system collapses into the corresponding state.

Now Wigner himself models the scenario from outside the laboratory, knowing that inside, his friend will at some point perform the 0/1-measurement on the physical system. According to the linearity of the quantum mechanical equations, Wigner will assign a superposition state to the whole laboratory (i.e. the joint system of the physical system together with the friend): The superposition state of the lab is then a linear combination of "system is in state 0/ friend has measured 0" and "system is in state 1/ friend has measured 1".

Let Wigner now ask his friend what he had obtained as a measurement result: Whichever answer the friend gives (0 or 1), in each case, Wigner would then assign the state "system is in state 0/ friend has measured 0" or "system is in state 1/ friend has measured 1" to the laboratory. Therefore, it is only at the time when he learns about his friend's result that the superposition state of the laboratory collapses.

However, unless Wigner is considered in a "priviliged position as ultimate observer"^[1], the friend's point of view must be regarded as equally valid, and this is where an apparent paradox comes into play: From the point of view of the friend, the measurement result was determined long before Wigner had asked about it, and the state of the physical system has already collapsed. When now exactly did the collapse occur? Was it when the friend had finished his measurement, or when the information of its result entered Wigner's consciousness?

Mathematical description

Assume for simplicity that the physical system is a two-state spin system S with states $|0\rangle _{S}$ and $|1\rangle _{S}$ , corresponding to measurement results 0 and 1.

Initially, S is in a superposition state

\alpha |0\rangle _{S}+\beta |1\rangle _{S}

and gets measured by Wigner's friend (F) in the $\{|0\rangle _{S},|1\rangle _{S}\}$ - basis. Then, with probability $|\alpha |^{2}$ , F will measure 0 and with probability $|\beta |^{2}$ , he will measure 1.

From the friend's point of view, the spin has collapsed into one of its basis states upon his measurement, and hence, he will assign to the spin the state corresponding to his measurement result: If he got 0, he will assign the state $|0\rangle _{S}$ to the spin, if he got 1, he will assign the state $|1\rangle _{S}$ to the spin.

Wigner (W) now models the combined system of the spin together with his friend (the joint system is given by the tensor product $S\otimes F$ ). He thereby takes a viewpoint outside of F's laboratory, which is considered isolated from the environment. Hence, by the laws of quantum mechanics for isolated systems, the state of the whole laboratory evolves unitarily in time. Therefore, the correct description of the state of the joint system as seen from outside is the superposition state

\alpha (|0\rangle _{S}\otimes |0\rangle _{F})+\beta (|1\rangle _{S}\otimes |1\rangle _{F})

,

where $|0\rangle _{F}$ denotes the state of the friend when he has measured 0, and $|1\rangle _{F}$ denotes the state of the friend when he has measured 1.

For an initial state $|0\rangle _{S}$ of S, the state for $S\otimes F$ would be $|0\rangle _{S}\otimes |0\rangle _{F}$ after F's measurement, and for an initial state $|1\rangle _{S}$ , the state of $S\otimes F$ would be $|1\rangle _{S}\otimes |1\rangle _{F}$ . Now, by the linearity of Schrödinger's quantum mechanical equations of motion, an initial state $\alpha |0\rangle _{S}+\beta |1\rangle _{S}$ for S results in the superposition $\alpha (|0\rangle _{S}\otimes |0\rangle _{F})+\beta (|1\rangle _{S}\otimes |1\rangle _{F})$ for $S\otimes F$ .

Discussion

Consciousness and Wigner's Friend

E. Wigner designed the thought experiment to illustrate his belief that consciousness is necessary to the quantum mechanical measurement process (and therefore, that consciousness in general must be an "ultimate reality"^[1] according to Descartes's "Cogito ergo sum" philosophy): "All that quantum mechanics purports to provide are probability connections between subsequent impressions (also called 'apperceptions') of the consciousness"^[1].

Here, "impressions of the consciousness" are understood as specific knowledge about a (measured) system, i.e., the result of an observation. This way, the content of one's consciousness is precisely all knowledge of one’s external world and measurements are defined as the interactions which create the impressions in our consciousness. Since the knowledge about any quantum mechanical wave function is based on such impressions, the wave function of a physical system is modified once the information about the system enters our consciousness. This idea has become known as the consciousness causes collapse interpretation.

In the Wigner's Friend thought experiment, this (E. Wigner's) view comes in as follows:

The friend's consciousness gets "impressed" by his measurement of the spin, and therefore he may assign a wave function to it according to the nature of his impression. Wigner, having no access to that information, can only assign the wave function $\alpha (|0\rangle _{S}\otimes |0\rangle _{F})+\beta (|1\rangle _{S}\otimes |1\rangle _{F})$ to the joint system of spin and friend after the interaction. When he then asks his friend about the measurement outcome, Wigner's consciousness gets "impressed" by the friend's answer: As a result, Wigner will be able to assign a wave function to the spin system, i.e., he will assign to it the wave function corresponding to the friend's answer.

So far, there is no inconsistency in the theory of measurement. However, Wigner then learns (by asking his friend again) that the feelings/ thoughts of his friend about the measurement outcome had been in the friend's mind long before Wigner had asked about them in the first place. Therefore, the correct wave function for the joint system of spin and friend just after the interaction must have been either $|0\rangle _{S}\otimes |0\rangle _{F}$ or $|1\rangle _{S}\otimes |1\rangle _{F}$ , and not their linear combination. Hence, there is a contradiction.

E. Wigner then follows that "the being with a consciousness must have a different role in quantum mechanics than the inanimate measuring device":^[1] If the friend were replaced by some measuring device without a consciousness, the superposition state would describe the joint system of spin and device correctly. In addition, E. Wigner considers a superposition state for a human being to be absurd, as the friend could not have been in a state of "suspended animation"^[1] before he answered the question. This view would need the quantum mechanical equations to be non-linear. It is E. Wigner's belief that the laws of physics must be modified when allowing conscious beings to be included.

The above and other of E. Wigner's original remarks about his friend appeared in his article "Remarks on the Mind-Body Question", published in the book The Scientist Speculates (1961), edited by I. J. Good. The article is reprinted in E. Wigner's own book Symmetries and Reflections (1967).

A counterargument

A counterargument is that the superimposition of two conscious states is not paradoxical — just as there is no interaction between the multiple quantum states of a particle, so the superimposed consciousnesses need not be aware of each other.^[2]

The state of the observer's perception is considered to be entangled with the state of the cat. The perception state 'I perceive a live cat' accompanies the 'live-cat' state and the perception state 'I perceive a dead cat' accompanies the 'dead-cat' state. [..] It is then assumed that a perceiving being always finds his/her perception state to be in one of these two; accordingly, the cat is, in the perceived world, either alive or dead.[..] I wish to make clear that, as it stands, this is far from a resolution of the cat paradox. For there is nothing in the formalism of quantum mechanics that demands that a state of consciousness cannot involve the simultaneous perception of a live and a dead cat.
— Roger Penrose

Wigner's friend in Many Worlds

The various versions of the many worlds interpretation avoid the need to postulate that consciousness causes collapse — indeed, that collapse occurs at all.

Hugh Everett III's doctoral thesis "relative state formulation of quantum mechanics"^[3] serves as the foundation for today's many versions of many words interpretations. In the introductory part of his work, Everett discusses the "amusing, but extremely hypothetical drama" of the Wigner's Friend paradox. Note that there is evidence of a drawing of the scenario in an early draft of Everett's thesis^[4]. It was therefore Everett who provided the first written discussion of the problem long before it was discussed in "Remarks on the mind-body question"^[1] by Eugene Wigner, of whom it received the name and fame thereafter. However, Everett being a student of E. Wigner's, it is clear that both must have discussed about it together at some point.^[4]

In contrast to his teacher E. Wigner, who blamed the conciousness of an observer to be responsible for a collapse, Everett understands the Wigner's Friend scenario in a different way: Insisting that quantum states assignments should be objective and nonperspectival, Everett derives a straightforward logical contradiction when letting F and W reason about the laboratory's state of S together with F. Then, the Wigner's Friend scenario shows to Everett an incompatibility of the collapse postulate for describing measurements with the deterministic evolution of closed systems. ^[5] In the context of his new theory, Everett claims to solve the Wigner's Friend paradox by only allowing a continuous unitary time evolution of the wave function of the universe. Measurements are modelled as interactions between subsystems of the universe and manifest themselves as a branching of the universal state. The different branches account for the different possible measurement outcomes and are seen to exist as subjective experiences of the corresponding observers.

Objective collapse theories

According to objective collapse theories, wave function collapse occurs when a superposed system reaches a certain objective threshold of size or complexity. Objective collapse proponents would expect a system as macroscopic as a cat to have collapsed before the box was opened, so the question of observation-of-observers does not arise for them.^[6]

QBism

In the interpretation known as QBism, advocated by N. David Mermin among others, the Wigner's-friend situation does not lead to a paradox, because there is never a uniquely correct wavefunction for any system. Instead, a wavefunction is a statement of personalist Bayesian probabilities, and moreover, the probabilities that wavefunctions encode are probabilities for experiences that are also personal to the agent who experiences them.^[7] As von Baeyer puts it, "Wavefunctions are not tethered to electrons and carried along like haloes hovering over the heads of saints—they are assigned by an agent and depend on the total information available to the agent."^[8] Consequently, there is nothing wrong in principle with Wigner and his friend assigning different wavefunctions to the same system. A similar position is taken by Brukner, who uses an elaboration of the Wigner's-friend scenario to argue for it.^[6]

QBism and relational quantum mechanics have been argued to avoid the contradiction suggested by the extended Wigner's-friend scenario of Frauchiger and Renner.^[9]

An Extension of Wigner's Friend

In 2016, Frauchiger and Renner used an elaboration of the Wigner's-friend scenario to argue that "single-world" interpretations of quantum mechanics cannot be consistent with fully unitary time evolution of quantum states^[10]. They provide an information-theoretic analysis of two specifically connected pairs of "Wigner's friend" experiments, where the human observers are modelled within quantum theory. By then letting the four different agents reason about each other’s measurement results (using the laws of quantum mechanics), contradictory statements are derived.

The resulting theorem highlights an incompatibility of a number of assumptions that are usually taken for granted when modelling measurements in quantum mechanics. In the title of their published version of September 2018,^[11]^[12] the author's interpretation of their result is apparent: Quantum theory as given by the textbook and used in the numerous laboratory experiments up to date "cannot consistently describe the use of itself" in any given (hypothetical) scenario. The implications of the result are currently subject to many debates among physicists of both theoretical and experimental quantum mechanics. In particular, the various proponents of the different interpretations of quantum mechanics have challenged the validity of the Frauchiger-Renner argument.^[13] Whatever the ultimate conclusion on the Extended Wigner's friend result may be, it is expected to go beyond the implications of the simpler Wigner's friend^[2] argument.

The thought experiment

The experiment was designed using a combination of arguments by Wigner^[1] (Wigner's Friend), Deutsch^[14] and Hardy^[15] (see Hardy's paradox).

In a defined time ordering, certain quantum measurements are performed by a number of macroscopic agents (observers). The whole setup generally corresponds to two parallel pairs of "Wigners" and friends, where the friends each measure a specific spin system, and each Wigner measures “her” friend’s laboratory (which includes the friend!). For simplicity, the agents are called $F_{1}$ , $F_{2}$ , $W_1$ , $W_2$ for the two friends and the two Wigners.

Each agent measures his assigned system in a particular defined basis. Upon his measurement result, the agent starts reasoning about the results of other agents, by using logical arguments compatible with quantum theory. In the end, all the logical statements of the agents are combined and, after repeating the experiment $n$ times, a contradiction arises.

Protocol of round $n$ of the Extended Wigner’s Friend Experiment^[11]:

Initial Step at $t_{n0}$ :

F_{1}

measures a qubit state

R

of inital state

|\psi \rangle _{R}={\frac {1}{\sqrt {3}}}|h\rangle _{R}+{\sqrt {\frac {2}{3}}}|t\rangle _{R}

in the

\{h,t\}

- basis and gets

h

(“heads”) or

t

(“tails”) with probability

{\frac {1}{3}}

and

{\frac {2}{3}}

, respectively.

F_{1}

prepares a spin system

S

in a state

|\downarrow \rangle _{S}

if she got

h

and in a state

|\rightarrow \rangle _{S}={\frac {1}{\sqrt {2}}}|\uparrow \rangle _{S}+{\frac {1}{\sqrt {2}}}|\downarrow \rangle _{S}

if she got

t

. Then she sends the newly prepared spin state

|\psi \rangle _{S}

(the corresponding one of the two) to

F_{2}

.

Step at $t_{n1}$ :

F_{2}

measures

S

in the

\{\uparrow ,\downarrow \}

- basis.

Step at $t_{n2}$ :

W_1

measures

L_{1}=R\otimes F_{1}

in the

\{|+\rangle _{L_{1}},|-\rangle _{L_{1}}\}

- basis where

|+\rangle _{L_{1}}={\frac {1}{\sqrt {2}}}|h\rangle _{R}|h\rangle _{F_{1}}+{\frac {1}{\sqrt {2}}}|t\rangle _{R}|t\rangle _{F_{1}}

and

|-\rangle _{L_{1}}={\frac {1}{\sqrt {2}}}|h\rangle _{R}|h\rangle _{F_{1}}-{\frac {1}{\sqrt {2}}}|t\rangle _{R}|t\rangle _{F_{1}}

.

Step at $t_{n3}$ :

W_2

measures

L_{2}=S\otimes F_{2}

in the

\{|+\rangle _{L_{2}},|-\rangle _{L_{2}}\}

- basis where

|+\rangle _{L_{2}}={\frac {1}{\sqrt {2}}}|\downarrow \rangle _{S}|\downarrow \rangle _{F_{2}}+{\frac {1}{\sqrt {2}}}|\uparrow \rangle _{S}|\uparrow \rangle _{F_{2}}

and

|-\rangle _{L_{2}}={\frac {1}{\sqrt {2}}}|\downarrow \rangle _{S}|\downarrow \rangle _{F_{2}}-{\frac {1}{\sqrt {2}}}|\uparrow \rangle _{S}|\uparrow \rangle _{F_{2}}

.

Step at $t_{n4}$ :

The measurement outcomes of

W_1

and

W_2

are compared: If both got "minus" the experiment is halted. Otherwise, the protocol starts at the initial step again.

Note that $W_1$ and $W_2$ look at their lab from the outside, i.e., they are assumed to see the lab as perfectly isolated. Hence, they model it as a pure state superposition up to the time they themselves have measured their lab. However, even though $L_{2}$ stays isolated as a system, the Extended Wigner’s Friend experiment is constructed such that some information about the state of $S$ is accessible to outsiders. This is achieved by letting the state of $S$ depend on the outcome of $F_{1}$ 's measurement.

Furthermore, it is assumed that all agents know about the experimental protocol and they all know quantum theory. This means that, upon having received a particular measurement outcome, each agent may predict some of the measurement results of the other agents.The analysis of the thought experiment is set in an information-theoretic context: The individual agents make logical conclusions that are based on their measurement result.

In fiction

Stephen Baxter's novel Timelike Infinity (1992) discusses a variation of Wigner's friend thought experiment through a refugee group of humans self-named "The Friends of Wigner". They believe that an ultimate observer at the end of time may collapse all possible entangled wave-functions generated since the beginning of the universe, hence choosing a reality without oppression.

References

1 2 3 4 5 6 7 8 E.P. Wigner (1961), "Remarks on the mind-body question", in: I.J. Good, "The Scientist Speculates", London, Heinemann
↑ R. Penrose, The Road to Reality, section 29.8.
↑ Everett, Hugh III. (1957). "'Relative State' Formulation of Quantum Mechanics". Reviews of Modern Physics. 29 (3): 454&ndash, 462. Bibcode:1957RvMP...29..454E. doi:10.1103/RevModPhys.29.454.
1 2 Barrett, J. A., & Byrne, P. (Eds.). (2012). The Everett interpretation of quantum mechanics: Collected works 1955-1980 with commentary. Princeton University Press.
↑ Barrett, Jeffrey (2016-10-10). "Everett's Relative-State Formulation of Quantum Mechanics". Stanford Encyclopedia of Philosophy.
1 2 Brukner, Caslav (2017). "On the quantum measurement problem". Quantum [Un]Speakables II: 50 Years of Bell’s Theorem. Springer. arXiv:1507.05255. doi:10.1007/978-3-319-38987-5. ISBN 978-3-319-38985-1. OCLC 1042356376.
↑ Healey, Richard (2016-12-22). "Quantum-Bayesian and Pragmatist Views of Quantum Theory". Stanford Encyclopedia of Philosophy.
↑ von Baeyer, Hans Christian (2016). QBism: The Future of Quantum Physics. Harvard University Press. ISBN 9780674504646. OCLC 946907398.
↑ Pusey, Matthew F. (2018-09-18). "An inconsistent friend". Nature Physics. 14 (10): 977–978. doi:10.1038/s41567-018-0293-7. ISSN 1745-2473.
↑ "Single-world interpretations of quantum theory cannot be self-consistent".
1 2 Frauchiger, Daniela; Renner, Renato (Sep 2018). "Quantum theory cannot consistently describe the use of itself". Nature communications. 9: 3711.
↑ Frauchiger, Daniela; Renner, Renato (2018). "Single-world interpretations of quantum theory cannot be self-consistent". Nature Communications. 9 (1): 3711. arXiv:1604.07422. Bibcode:2016arXiv160407422F. doi:10.1038/s41467-018-05739-8. PMC 6143649. PMID 30228272.
↑
Responses taking various positions include the following:
- Baumann, Veronika; Hansen, Arne; Wolf, Stefan (2016-11-03). "The measurement problem is the measurement problem is the measurement problem". arXiv:1611.01111 [quant-ph].
- Sudbery, Anthony (2017-05-01). "Single-World Theory of the Extended Wigner's Friend Experiment". Foundations of Physics. 47 (5): 658–669. arXiv:1608.05873. Bibcode:2017FoPh..tmp...27S. doi:10.1007/s10701-017-0082-7. ISSN 0015-9018.
- Fuchs, Christopher (2017). "Notwithstanding Bohr, the Reasons for QBism". Mind and Matter. 15 (2): 245&ndash, 300. arXiv:1705.03483. Bibcode:2017arXiv170503483F.
- Łukaszyk, Szymon (2018-01-23). "Making Mistakes Saves the Single World of the Extended Wigner's Friend Experiment". arXiv:1801.08537 [quant-ph].
- Laloë, Franck (2018-02-18). "Can quantum mechanics be considered consistent? a discussion of Frauchinger and Renner's argument". arXiv:1802.06396 [quant-ph].
- Bub, Jeffrey (2018-04-27). "In Defense of a "Single-World" Interpretation of Quantum Mechanics". Studies in History and Philosophy of Modern Physics. arXiv:1804.03267. doi:10.1016/j.shpsb.2018.03.002.
- Łukaszyk, Szymon (2018-05-13). "Life as an Explanation of the Measurement Problem". arXiv:1805.05774. Bibcode:2018arXiv180505774L. doi:10.13140/RG.2.2.24517.91368.
- Fuchs, Christopher (presenter); Stacey, Blake (editor); Thisdell, Bill (editor) (2018-04-25). Some Tenets of QBism. YouTube. Retrieved 2018-05-16.
↑ Deutsch, D. (1985). Quantum theory as a universal physical theory. International Journal of Theoretical Physics, 24(1), 1-41.
↑ Hardy, L. (1992). Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories. Physical Review Letters, 68(20), 2981.

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[:0-1] 1 2 3 4 5 6 7 8 E.P. Wigner (1961), "Remarks on the mind-body question", in: I.J. Good, "The Scientist Speculates", London, Heinemann

[2] R. Penrose, The Road to Reality, section 29.8.

[3] Everett, Hugh III. (1957). "'Relative State' Formulation of Quantum Mechanics". Reviews of Modern Physics. 29 (3): 454&ndash, 462. Bibcode:1957RvMP...29..454E. doi:10.1103/RevModPhys.29.454.

[:1-4] 1 2 Barrett, J. A., & Byrne, P. (Eds.). (2012). The Everett interpretation of quantum mechanics: Collected works 1955-1980 with commentary. Princeton University Press.

[barrett-5] Barrett, Jeffrey (2016-10-10). "Everett's Relative-State Formulation of Quantum Mechanics". Stanford Encyclopedia of Philosophy.

[brukner-6] 1 2 Brukner, Caslav (2017). "On the quantum measurement problem". Quantum [Un]Speakables II: 50 Years of Bell’s Theorem. Springer. arXiv:1507.05255. doi:10.1007/978-3-319-38987-5. ISBN 978-3-319-38985-1. OCLC 1042356376.

[healey-7] Healey, Richard (2016-12-22). "Quantum-Bayesian and Pragmatist Views of Quantum Theory". Stanford Encyclopedia of Philosophy.

[8] von Baeyer, Hans Christian (2016). QBism: The Future of Quantum Physics. Harvard University Press. ISBN 9780674504646. OCLC 946907398.

[9] Pusey, Matthew F. (2018-09-18). "An inconsistent friend". Nature Physics. 14 (10): 977–978. doi:10.1038/s41567-018-0293-7. ISSN 1745-2473.

[10] "Single-world interpretations of quantum theory cannot be self-consistent".

[:2-11] 1 2 Frauchiger, Daniela; Renner, Renato (Sep 2018). "Quantum theory cannot consistently describe the use of itself". Nature communications. 9: 3711.

[12] Frauchiger, Daniela; Renner, Renato (2018). "Single-world interpretations of quantum theory cannot be self-consistent". Nature Communications. 9 (1): 3711. arXiv:1604.07422. Bibcode:2016arXiv160407422F. doi:10.1038/s41467-018-05739-8. PMC 6143649. PMID 30228272.

[13] Responses taking various positions include the following:
Baumann, Veronika; Hansen, Arne; Wolf, Stefan (2016-11-03). "The measurement problem is the measurement problem is the measurement problem". arXiv:1611.01111 [quant-ph].

Sudbery, Anthony (2017-05-01). "Single-World Theory of the Extended Wigner's Friend Experiment". Foundations of Physics. 47 (5): 658–669. arXiv:1608.05873. Bibcode:2017FoPh..tmp...27S. doi:10.1007/s10701-017-0082-7. ISSN 0015-9018.

Fuchs, Christopher (2017). "Notwithstanding Bohr, the Reasons for QBism". Mind and Matter. 15 (2): 245&ndash, 300. arXiv:1705.03483. Bibcode:2017arXiv170503483F.

Łukaszyk, Szymon (2018-01-23). "Making Mistakes Saves the Single World of the Extended Wigner's Friend Experiment". arXiv:1801.08537 [quant-ph].

Laloë, Franck (2018-02-18). "Can quantum mechanics be considered consistent? a discussion of Frauchinger and Renner's argument". arXiv:1802.06396 [quant-ph].

Bub, Jeffrey (2018-04-27). "In Defense of a "Single-World" Interpretation of Quantum Mechanics". Studies in History and Philosophy of Modern Physics. arXiv:1804.03267. doi:10.1016/j.shpsb.2018.03.002.

Łukaszyk, Szymon (2018-05-13). "Life as an Explanation of the Measurement Problem". arXiv:1805.05774. Bibcode:2018arXiv180505774L. doi:10.13140/RG.2.2.24517.91368.

Fuchs, Christopher (presenter); Stacey, Blake (editor); Thisdell, Bill (editor) (2018-04-25). Some Tenets of QBism. YouTube. Retrieved 2018-05-16.

[mwAYM] Baumann, Veronika; Hansen, Arne; Wolf, Stefan (2016-11-03). "The measurement problem is the measurement problem is the measurement problem". arXiv:1611.01111 [quant-ph].

[mwAYw] Sudbery, Anthony (2017-05-01). "Single-World Theory of the Extended Wigner's Friend Experiment". Foundations of Physics. 47 (5): 658–669. arXiv:1608.05873. Bibcode:2017FoPh..tmp...27S. doi:10.1007/s10701-017-0082-7. ISSN 0015-9018.

[mwAZ4] Fuchs, Christopher (2017). "Notwithstanding Bohr, the Reasons for QBism". Mind and Matter. 15 (2): 245&ndash, 300. arXiv:1705.03483. Bibcode:2017arXiv170503483F.

[mwAas] Łukaszyk, Szymon (2018-01-23). "Making Mistakes Saves the Single World of the Extended Wigner's Friend Experiment". arXiv:1801.08537 [quant-ph].

[mwAbQ] Laloë, Franck (2018-02-18). "Can quantum mechanics be considered consistent? a discussion of Frauchinger and Renner's argument". arXiv:1802.06396 [quant-ph].

[mwAb0] Bub, Jeffrey (2018-04-27). "In Defense of a "Single-World" Interpretation of Quantum Mechanics". Studies in History and Philosophy of Modern Physics. arXiv:1804.03267. doi:10.1016/j.shpsb.2018.03.002.

[mwAco] Łukaszyk, Szymon (2018-05-13). "Life as an Explanation of the Measurement Problem". arXiv:1805.05774. Bibcode:2018arXiv180505774L. doi:10.13140/RG.2.2.24517.91368.

[mwAdY] Fuchs, Christopher (presenter); Stacey, Blake (editor); Thisdell, Bill (editor) (2018-04-25). Some Tenets of QBism. YouTube. Retrieved 2018-05-16.

[14] Deutsch, D. (1985). Quantum theory as a universal physical theory. International Journal of Theoretical Physics, 24(1), 1-41.

[15] Hardy, L. (1992). Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories. Physical Review Letters, 68(20), 2981.

Wigner's friend

The thought experiment

Mathematical description

Discussion

Consciousness and Wigner's Friend

A counterargument

Wigner's friend in Many Worlds

Objective collapse theories

QBism

An Extension of Wigner's Friend

The thought experiment

In fiction

See also

References