Wigner's friend is a thought experiment in theoretical quantum physics, first published by the Hungarian-American physicist Eugene Wigner in 1961, Reprinted in and further developed by David Deutsch in 1985. The scenario involves an indirect observation of a quantum measurement: An observer observes another observer 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. In the Copenhagen interpretation, the resulting statements of the two observers contradict each other. This reflects a seeming incompatibility of two laws in the Copenhagen interpretation: the deterministic and continuous time evolution of the state of a closed system and the nondeterministic, 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.
Generalizations and extensions of Wigner's friend have been proposed. Two such scenarios involving multiple friends have been implemented in a laboratory, using photons to stand in for the friends. However, the use of photons as observers has been criticized by quantum physicist Lev Vaidman of Tel Aviv University as "ridiculous; the friend has to be macroscopic". Philosopher of physics Tim Maudlin of New York University says that "Nobody thinks a photon is an observer".
Original paradox Wigner introduced the thought experiment in a 1961 article "Remarks on the Mind-Body Question". He begins by noting that most physicists in the then-recent past had been thoroughgoing materialists who would insist that "mind" or "soul" are illusory, and that nature is fundamentally deterministic. He argues that quantum physics has changed this situation:
Nature of the wave function Going into more detail, Wigner says:
The wave function of an object "exists" (Wigner's quotation marks) because observers can share it:
Observing a system causes its wave functions to change indeterministically, because "the entering of an impression into our consciousness" implies a revision of "the probabilities for different impressions which we expect to receive in the future".
The observer observed Wigner presents two arguments for the thesis that the mind influences the body, i.e., that a human body can "deviate from the laws of physics" as deduced from experimenting upon inanimate objects. The argument that he personally finds less persuasive is the one that has become known as "Wigner's friend". In this thought experiment, Wigner posits that his friend is in a laboratory, and Wigner lets the friend perform a quantum measurement on a physical system (this could be a spin system). This system is assumed to be in a superposition of two distinct states, say, state 0 and state 1 (or and in Dirac notation). When Wigner's friend measures the system in the {0,1}-basis, according to quantum mechanics, they will get one of the two possible outcomes (0 or 1) and the system will collapse 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 for the result of the measurement. Whichever answer the friend gives (0 or 1), 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 "privileged position as ultimate observer", 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 exactly did the collapse occur? Was it when the friend had finished their measurement, or when the information of its result entered Wigner's consciousness? As Wigner says, he could ask his friend, "What did you feel about the [measurement result] before I asked you?" The question of what result the friend has seen is surely "already decided in his mind", Wigner writes, which implies that the friend–system joint state must already be one of the collapsed options, not a superposition of them. Wigner concludes that the linear time evolution of quantum states according to the Schrödinger equation cannot apply when the physical entity involved is a conscious being.
Wigner presents his second argument, which he finds more persuasive, much more briefly:
As a reductio ad absurdum According to physicist Leslie Ballentine, by 1987 Wigner had decided that consciousness does not cause a physical collapse of the wavefunction, although he still believed that his chain of inferences leading up to that conclusion were correct. As Ballentine recounts, Wigner regarded his 1961 argument as a , indicating that the postulates of quantum mechanics need to be revised in some way.
Responses in different interpretations of quantum mechanics
Many-worlds interpretations 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" serves as the foundation for today's many versions of many-worlds 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.Barrett, J. A., and Byrne, P. (eds.). (2012). The Everett interpretation of quantum mechanics: Collected works 1955–1980 with commentary. Princeton University Press. It was therefore Everett who provided the first written discussion of the problem four or five years before it was discussed in "Remarks on the mind-body question" by Wigner, of whom it received the name and fame thereafter. However, Everett being a student of Wigner, it is clear that they must have discussed it together at some point.
In contrast to his teacher Wigner, who held the consciousness 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 non-perspectival, Everett derives a straightforward logical contradiction when letting and reason about the laboratory's state of together with . 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. 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. However, there is no evidence of any written argument of Everett's on the topic.
In many-worlds interpretations, 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. In this view, the friend's measurement of the spin results in a branching of the world into two parallel worlds, one, in which the friend has measured the spin to be 1, and another, in which the friend has received the measurement outcome 0. If then Wigner measures at a later time the combined system of friend and spin system, the world again splits into two parallel parts.
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. If the measured system were much simpler (such as a single spin state), then once the observation was made, the system would be expected to collapse, since the larger system of the scientist, equipment, and room would be considered far too complex to become entangled in the superposition.
Relational quantum mechanics Relational quantum mechanics (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 paradoxical situation in Wigner's friend scenario: The state that the friend assigns to the 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 physical variable that is measured of the spin system is denoted by , where takes the possible outcome values 0 or 1, the above Wigner's friend situation is modelled in the RQM context as follows: models the situation as the before-after-transition
of the state of relative to him (here it was assumed that received the outcome in his measurement of ).
In RQM language, the fact for the spin of actualized itself relative to 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 () of another () 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 () has the information that the physical variable of is being measured by , but not knowing what received as result, must model the situation as
where is considered the state of before the measurement, and and are the states corresponding to 's state when he has measured 1 or 0 respectively. This model is depicting the situation as relative to , so the assigned states are relative states with respect to the Wigner system. In contrast, there is no value for the outcome that actualizes with respect to , 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 on the system by ) 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.
QBism and Bayesian interpretations