Wigner's friend is a thought experiment in theoretical quantum physics, first published by the Hungarian-American physicist Eugene Wigner in 1961, and further developed by David Deutsch in 1985. The scenario involves an indirect observation of a quantum measurement: An observer W {\displaystyle W} observes another observer F {\displaystyle 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. 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:
All that quantum mechanics purports to provide are probability connections between subsequent impressions (also called "apperceptions") of the consciousness, and even though the dividing line between the observer, whose consciousness is being affected, and the observed physical object can be shifted towards the one or the other to a considerable degree, it cannot be eliminated.
Nature of the wave function Going into more detail, Wigner says:
Given any object, all the possible knowledge concerning that object can be given as its wave function. This is a mathematical concept the exact nature of which need not concern us here—it is composed of a (countable) infinity of numbers. If one knows these numbers, one can foresee the behavior of the object as far as it can be foreseen. More precisely, the wave function permits one to foretell with what probabilities the object will make one or another impression on us if we let it interact with us either directly, or indirectly. [...] In fact, the wave function is only a suitable language for describing the body of knowledge—gained by observations—which is relevant for predicting the future behaviour of the system. For this reason, the interactions which may create one or another sensation in us are also called observations, or measurements. One realises that all the information which the laws of physics provide consists of probability connections between subsequent impressions that a system makes on one if one interacts with it repeatedly, i.e., if one makes repeated measurements on it. The wave function is a convenient summary of that part of the past impressions which remains relevant for the probabilities of receiving the different possible impressions when interacting with the system at later times. The wave function of an object "exists" (Wigner's quotation marks) because observers can share it:
The information given by the wave function is communicable. If someone else somehow determines the wave function of a system, he can tell me about it and, according to the theory, the probabilities for the possible different impressions (or "sensations") will be equally large, no matter whether he or I interact with the system in a given fashion. 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".
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