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Topics in Cognitive Science

A Double‐Slit Experiment for Non‐Classical Interference Effects in Decision Making

Pierfrancesco La Mura

Published Nov 21, 2013• 1 citation
Publisher

Abstract

We discuss the possible nature and role of non-physical entanglement, and the classical vs. non-classical interface, in models of human decision-making. We also introduce an experimental setting designed after the double-slit experiment in physics, and discuss how it could be used to discriminate between classical and non-classical interference effects in human decisions.

DOI
10.1111/tops.12066

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We discuss the possible nature and role of non-physical entanglement, and the classical vs. non-classical interface, in models of human decision-making. We also introduce an experimental setting designed after the double-slit experiment in physics, and discuss how it could be used to discriminate between classical and non-classical interference effects in human decisions.
Science, as it is generally described at school, starts with experimental data. Scientists then have to find some hypothesis which explains these results. Using this hypothesis, a prediction is made about what might happen in a slightly different experiment. The double-slit experiment is a modified version of the setup first used by Thomas Young in 1801. Young’s version is a classic experiment that, at the time, seemed to have settled the dispute between wave and particle views of light decisively in favour of waves. The idea that particles might display some wavelike properties dates to the mid-1920s when a young PhD student called Louis De Broglie was thinking about the dual wave/particle nature of light. A quantum mechanical description of the double-slit experiment must involve a set of amplitudes governing the passage of an electron through the slits to the far detector.
The double-slit experiment provides insights into quantum mechanics and sheds light on fundamental contradictions with classical physics, which, although predicting independent trajectories by simple random addition, reveals interference patterns even when only one particle is emitted at a time, providing direct evidence for effects of wave-particle duality and quantum superposition. Furthermore, we explore why thematic coherence and overlap in this study are essential elements of quantum computer design. Mechanisms such as phase interference (defined by the Deutsch algorithm) demonstrate the computational power provided by quantum effects. In other words, double-slit learning is not just a theoretical concept, but also a set of ideas and techniques that combine the theory of advanced quantum technology.
This article reconsiders the double-slit experiment by establishing a new type of relationship between it and the concept of entanglement. While the role of entanglement in the double-slit experiment has been considered, this particular relationship appears to have been missed in preceding discussions of the experiment, even by Bohr, who extensively used it to support his argument concerning quantum physics. The main reason for this relationship is the different roles of the diaphragm with slits in two setups, S1 and S2, defining the double-slit experiment as a quantum experiment. In S1, in each individual run of the experiment one can in principle (even if not actually) know throughout which slit the quantum object considered has passed; in S2 this knowledge is in principle impossible, which impossibility is coextensive with the appearance of the interference pattern, once a sufficient number of individual runs of the experiment have taken place. The article offers the following argument based on two new concepts, an "experimentally quantum object" and an "ontologically quantum object." In S1 the diaphragm can be treated as part of an observational arrangement and thus considered as a classical object, while the object passing through one or the other slit is considered as an "ontologically quantum object," defined as an object necessary to establish a quantum phenomenon. By contrast, in S2, the diaphragm can, via the concept of Heisenberg-von-Neumann cut, be treated as an "experimentally quantum object," defined as an object treatable by quantum theory, even while possibly being an ontologically classical object. This interaction is not an observation but a quantum entanglement between these two quantum objects, one ontologically and one experimentally quantum. This argument is grounded in a particular interpretation of quantum phenomena and quantum theory, which belongs to the class of interpretations designated here as "reality without realism" (RWR) interpretations. The article also argues that wave-particle complementarity, with which the concept of complementarity is often associated, plays little, if any, role in quantum physics, or in Bohr's thinking, and may be misleading in considering the double-slit experiment, often explained by using this complementarity.
Recently quantum probability theory started to be actively used in studies of human decision-making, in particular for the resolution of paradoxes (such as the Allais, Ellsberg, and Machina paradoxes). Previous studies were based on a cognitive metaphor of the quantum double-slit experiment - the basic quantum interference experiment. In this paper, we report on an economics experiment based on a three-slit experiment design, where the slits are menus of alternatives from which one can choose. The test of nonclassicality is based on the Sorkin equality (which was only recently tested in quantum physics). Each alternative is a voucher to buy products in one or more stores. The alternatives are obtained from all disjunctions including one, two or three stores. The participants have to reveal the amount for which they are willing to sell the chosen voucher. Interference terms are computed by comparing the willingness to sell a voucher built as a disjunction of stores and the willingness to sell the vouchers corresponding to the singleton stores. These willingness to sell amounts are used to estimate probabilities and to test both the law of total probabilities and the Born Rule. Results reject neither classical nor quantum probability. We discuss this initial experiment and our results and provide guidelines for future studies.