Wigner's friend

Wigner's friend is therefore directly linked to the measurement problem in quantum mechanics with its famous Schrödinger's cat paradox.

[1] 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: 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".

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.

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.

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.

As Ballentine recounts, Wigner regarded his 1961 argument as a reductio ad absurdum, indicating that the postulates of quantum mechanics need to be revised in some way.

Hugh Everett III's doctoral thesis "'Relative state' formulation of quantum mechanics"[8] 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.

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.

[10] 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.

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 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:

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.

[14] Jaynes expresses this as follows: “There is a paradox only if we suppose that a density matrix (i.e. a probability distribution) is something ‘physically real’ and ‘absolute’.

There is, however, a concept of effective collapse, based on the fact that, in many situations, "empty branches" of the wave function, which do not guide the actual particle configuration, can be ignored for all practical purposes.

[18] 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,[18] the authors' interpretation of their result is apparent: Quantum theory as given by the textbook and used in the numerous laboratory experiments to date "cannot consistently describe the use of itself" in any given (hypothetical) scenario.

The setup involves a number of macroscopic agents (observers) performing predefined quantum measurements in a given time order.

Those agents are assumed to all be aware of the whole experiment and to be able to use quantum theory to make statements about other people's measurement results.

The design of the thought experiment is such that the different agents' observations along with their logical conclusions drawn from a quantum-theoretical analysis yields inconsistent statements.

This means that an agent is allowed to trust this rule being correct in assigning probabilities to other outcomes conditioned on his own measurement result.

It is, however, sufficient for the extended Wigner's friend experiment to assume the validity of the Born rule for probability-1 cases, i.e., if the prediction can be made with certainty.

[18] On the other hand, one presentation of the experiment as a quantum circuit models the agents as single qubits and their reasoning as simple conditional operations.

[21] QBism, relational quantum mechanics and the De Broglie–Bohm theory have been argued to avoid the contradiction suggested by the extended Wigner's-friend scenario of Frauchiger and Renner.

[26] 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.