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Relations and relativities: A Kantian approach to relational interpretations of quantum theory

Michel Bitbol

Published Dec 1, 2024• 0 citations
OpenAlex

Abstract

Quantum theory cannot consistently describe the use of itself », Nature Communications, 9, 3711, 2018 11 Wigner's friend's thought experiment involves two observers.The first (the friend) is locked up in a laboratory, performing a quantum measurement on a physical system whose quantum state is a superposition of two distinct eigenstates of an observable.When the friend has finished the measurement, he obtains as a result one of the two eigenvalues of the observable, and he assigns to his system a new state identical to the eigenstate corresponding to this measured eigenvalue.The second observer (Wigner) is located outside the laboratory, and he only knows one thing about what is happening inside: that his friend is performing the measurement described above.Under such conditions, he is forced to attribute to everything contained in the laboratory (including his friend) a quantum state that extends the superposition beyond the physical system, to his friend himself.The

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Quantum theory cannot consistently describe the use of itself », Nature Communications, 9, 3711, 2018 11 Wigner's friend's thought experiment involves two observers.The first (the friend) is locked up in a laboratory, performing a quantum measurement on a physical system whose quantum state is a superposition of two distinct eigenstates of an observable.When the friend has finished the measurement, he obtains as a result one of the two eigenvalues of the observable, and he assigns to his system a new state identical to the eigenstate corresponding to this measured eigenvalue.The second observer (Wigner) is located outside the laboratory, and he only knows one thing about what is happening inside: that his friend is performing the measurement described above.Under such conditions, he is forced to attribute to everything contained in the laboratory (including his friend) a quantum state that extends the superposition beyond the physical system, to his friend himself.The
This paper offers a comprehensive analysis of Wigner’s Friend paradox (1961), a foundational thought experiment in quantum mechanics that highlights the tension between the internal perspective of a measuring observer (who experiences a definite outcome) and the external perspective of a super-observer who treats the entire laboratory as a quantum system in superposition. It traces the historical lineage from Schrödinger’s cat and von Neumann’s measurement theory, provides a formal mathematical description of the state evolution and logical structure of the paradox, examines implications for major interpretations of quantum mechanics (Copenhagen, Everettian many-worlds, QBism, relational quantum mechanics, and objective collapse theories), and discusses modern extensions such as the Frauchiger–Renner paradox. The work explores profound philosophical and epistemological consequences for the nature of observation, objectivity, intersubjectivity, and the role of consciousness in quantum theory (2026).
Despite its enormous practical success, quantum theory is so contrary to intuition that, even after 45 years, the experts themselves still do not all agree what to make of it. The area of disagreement centers primarily around the problem of describing observations. Formally, the result of a measurement is a superposition of vectors, each representing the quantity being observed as having one of its possible values. The question that has to be answered is how this superposition can be reconciled with the fact that in practice we only observe one value. How is the measuring instrument prodded into making up its mind which value it has observed?
Wigner's friend scenarios expose a tension in quantum mechanics: an observer inside a laboratory obtains a definite measurement outcome, while an observer outside describes the laboratory as being in a superposition. The Frauchiger-Renner (2018) extension produces logical contradictions when agents use quantum theory to reason about each other. We show that the recursion-consistency functional K resolves these contradictions without modifying quantum mechanics. The resolution rests on a single physical fact: the friend's measurement creates ~10^20 environmental records inside the laboratory, driving K_rec to its minimum in ~10^-30 seconds. Wigner's description of the laboratory as a superposition is not wrong but incomplete: it omits the internal records that have already selected a definite outcome. The superposition description is operationally correct for Wigner (he cannot access the internal records) but ontologically incorrect (the records exist whether he accesses them or not). This distinction dissolves the Frauchiger-Renner contradiction, resolves the quantum eraser and delayed choice experiments as corollaries, and commits the framework to an ontic interpretation of the quantum state consistent with the PBR theorem.
In a joint paper Jeff Bub and Itamar Pitowski argued that the quantum state represents `the credence function of a rational agent [...] who is updating probabilities on the basis of events that occur'. In the famous thought experiment designed by Wigner, Wigner's friend performs a measurement in an isolated laboratory which in turn is measured by Wigner. Here we consider Wigner's friend as a rational agent and ask what her `credence function' is. We find experimental situations in which the friend can convince herself that updating the probabilities on the basis of events that happen solely inside her laboratory is not rational and that conditioning needs to be extended to the information that is available outside of her laboratory. Since the latter can be transmitted into her laboratory, we conclude that the friend is entitled to employ Wigner's perspective on quantum theory when making predictions about the measurements performed on the entire laboratory, in addition to her own perspective, when making predictions about the measurements performed inside the laboratory.
Despite its enormous practical success, quantum theory is so contrary to intuition that, even after 45 years, the experts themselves still do not all agree what to make of it. The area of disagreement centers primarily around the problem of describing observations. Formally, the result of a measurement is a superposition of vectors, each representing the quantity being observed as having one of its possible values. The question that has to be answered is how this superposition can be reconciled with the fact that in practice we only observe one value. How is the measuring instrument prodded into making up its mind which value it has observed?