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arXiv:1201.4685 · Journal of Mathematical Psychology

Order effects in sequential measurements of non-commuting psychological observables

Harald Atmanspacher A, H. Römer

Published Jul 30, 2012• 70 citations
arXivHTMLPDF
DOI
10.1016/j.jmp.2012.06.003

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Sequential weak measurements of non-commuting observables are not only fundamentally interesting in terms of quantum measurement but also show potential in various applications. Previously reported methods, however, can only make limited sequential weak measurements experimentally. In this article, we propose the realization of sequential measurements of non-commuting Pauli observables and experimentally demonstrate for the first time the measurement of sequential weak values of three non-commuting Pauli observables using genuine single photons.
Metacognition, understood as the monitoring and regulation of one's own cognitive processes, is inherently sequential: an agent evaluates an internal state, updates it, and may then re-evaluate under modified criteria. Order effects in cognition are well documented, yet it remains unclear whether such effects reflect classical state changes or reveal a deeper structural non-commutativity. We develop an operational framework that makes this distinction explicit. In our formulation, metacognitive evaluations are modeled as state-transforming operations acting on an internal state space with probabilistic readouts, thereby separating evaluation back-action from observable output. We show that order dependence prevents any faithful Boolean-commutative representation. We then address a stronger question: can observed order effects always be explained by enlarging the state space with classical latent variables? To formalize this issue, we introduce two assumptions, counterfactual definiteness and evaluation non-invasiveness, under which the existence of a joint distribution over all sequential readouts implies a family of testable constraints on pairwise sequential correlations. Violation of these constraints rules out any classical non-invasive account and certifies what we call genuine non-commutativity. We provide an explicit three-dimensional rotation model with fully worked numerical examples that exhibits such violations. We also outline a behavioral paradigm involving sequential confidence, error-likelihood, and feeling-of-knowing judgments following a perceptual decision, together with the corresponding empirical test. No claim is made regarding quantum physical substrates; the framework is purely operational and algebraic.