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Empirical verification of the violation of the temporal Bell inequality in bistable perception

Yasunori Aizawa, Naotsugu Tsuchiya, Emmanuel Pothos, Jerome R. Busemeyer, Peter Bruza, Yamada Makiko

Published Dec 8, 2021• 0 citations
OpenAlex

Abstract

Introduction The purpose of the present study is to investigate quantum-like properties of mental states in bistable perception. In order to do this, we tested whether the temporal Bell inequality applied to bistable perception experiments[1] can be violated. In the present study, we used visual stimuli [2], where we can continuously and systematically manipulate two types of ambiguities in the perceived rotation of dots. When the rotation angle is large, the stimuli induce bistable percept. When the angle is small, the direction of rotation of the stimuli becomes difficult to judge. We use the stimuli to test if the temporal Bell inequality can be violated, and if so, under what parameter regime, it can be violated. Method Two patterns were presented alternately: a visual stimulus consisting of four disks, and one in which the disks were rotated by a specific angle (5-45 degrees) in each trial [FIG. 1(A)]. When the angle of rotation was close to 45 degrees, stimuli were perceived to rotate in one of the two directions for a while with occasional reversals at random times (i.e., bistable perception). When the angle of rotation was close to 5 degrees, no rotation was perceived beyond the angle of rotation of the stimulus, and left and right rotations were perceived alternately, but the angle of rotation was so small that it was difficult to determine the direction of rotation [FIG. 1(B)]. At two time points after the beep, the participants responded by pressing a button in the direction of rotation that they saw at that time [FIG. 1(C)]. Reference 1H. Atmanspacher, and T. Filk, J. Math. Psychol. 54, 314-321 (2010). 2S. Takei and S. Nishida, J. Vision. 10, 23 (2010). 3M. M. Wilde and A. Mizel, Found. Phys. 42, 256 (2012). Acknowledgement This work was supported by JSPS KAKENHI JP20H05711 and MEXT Q-LEAP Grant Number JPMXS0120330644.

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Introduction The purpose of the present study is to investigate quantum-like properties of mental states in bistable perception. In order to do this, we tested whether the temporal Bell inequality applied to bistable perception experiments[1] can be violated. In the present study, we used visual stimuli [2], where we can continuously and systematically manipulate two types of ambiguities in the perceived rotation of dots. When the rotation angle is large, the stimuli induce bistable percept. When the angle is small, the direction of rotation of the stimuli becomes difficult to judge. We use the stimuli to test if the temporal Bell inequality can be violated, and if so, under what parameter regime, it can be violated. Method Two patterns were presented alternately: a visual stimulus consisting of four disks, and one in which the disks were rotated by a specific angle (5-45 degrees) in each trial [FIG. 1(A)]. When the angle of rotation was close to 45 degrees, stimuli were perceived to rotate in one of the two directions for a while with occasional reversals at random times (i.e., bistable perception). When the angle of rotation was close to 5 degrees, no rotation was perceived beyond the angle of rotation of the stimulus, and left and right rotations were perceived alternately, but the angle of rotation was so small that it was difficult to determine the direction of rotation [FIG. 1(B)]. At two time points after the beep, the participants responded by pressing a button in the direction of rotation that they saw at that time [FIG. 1(C)]. Reference 1H. Atmanspacher, and T. Filk, J. Math. Psychol. 54, 314-321 (2010). 2S. Takei and S. Nishida, J. Vision. 10, 23 (2010). 3M. M. Wilde and A. Mizel, Found. Phys. 42, 256 (2012). Acknowledgement This work was supported by JSPS KAKENHI JP20H05711 and MEXT Q-LEAP Grant Number JPMXS0120330644.
Binocular rivalry refers to a phenomenon in which the perceived image changes spontaneously over time when the two eyes are presented with different images. The purpose of this study is to test whether the violation of temporal Bell inequality can be experimentally observed in binocular rivalry. If the temporal Bell inequality is violated (under no-signaling in time: NSIT), it implies that the perception of the rival stimuli cannot be assumed to be definite at each point in time (i.e., “realism” in the corresponding mental representations is violated), which is a key indication of non-classical behavior (as in, for example, quantum-like systems). Here, to test the violation of the inequality, we used binocular rivalry and measured both subjective reports and electroencephalogram (EEG). With EEG, we used frequency-tagging technique to track the cortical signal driven by each eye’s stimulus, known as the steady-state visual evoked potential (SSVEP). We present the conceptual and methodological approaches to test the temporal Bell inequality.
Bipartite temporal Bell inequalities are similar to the usual Bell inequalities except that, instead of changing the direction of the polarizer at each measurement, one changes the time at which the measurement is being performed. By doing so, one is able to test for realism and locality, but relying on position measurements only. This is particularly useful in experimental setups where the momentum direction cannot be probed (such as in cosmology for instance). We study these bipartite temporal Bell inequalities for continuous systems placed in two-mode squeezed states and find some regions in parameter space where they are indeed violated. We highlight the role played by the rotation angle, which is one of the three parameters characterizing a two-mode squeezed state (the other two being the squeezing amplitude and the squeezing angle). In single-time measurements, it only determines the overall phase of the wave function and can therefore be discarded, but in multiple-time measurements, its time dynamics becomes relevant and crucially determines when bipartite temporal Bell inequalities can be violated. Our study provides an opportunity for experimental designs for the observation of Bell inequality violations.
Temporally non-local measurements – single measurements yielding information about the state of a system at different instances – may provide a way to observe non-classical behavior in mental systems. The signature for such behavior is a violation of temporal Bell inequalities. We present such inequalities applicable to scenarios with two alternating mental states, such as in the perception of ambiguous figures. We indicate empirical options for testing temporal Bell inequalities, and speculate about possible explanations in case these inequalities are indeed violated.
This paper is devoted to an experimental investigation of cognitive contextuality inspired by quantum contextuality research. This contextuality is related to, but not identical to context-sensitivity which is well-studied in cognitive psychology and decision making. This paper is a part of quantum-like modeling, i.e., exploring the methodology of quantum theory outside of physics. We examined the bistable perception of cup-like objects, which strongly depends on experimental contexts. Our experimental data confirmed the existence of cognitive hysteresis, the important role of memory, and the non-commutative structure of cognitive observables. In physics, quantum contextuality is assessed using Bell-CHSH inequalities, and their violation is incorrectly believed to imply the nonlocality of Nature. The violation of Bell-type inequalities in cognitive and social science strongly indicates that the metaphysical implications of these inequalities are quite limited. In our experiments, modified Leggett-Garg inequalities were also significantly violated, but this only means that experimental data from experiments performed in different contexts cannot be modeled by a unique set of noncontextual, jointly distributed random variables. In our experiments, we know the empirical probability distributions measured in different contexts; thus, we can obtain much more detailed and reliable information about contextuality in human cognition by performing nonparametric compatibility tests.
"According to the quantum superposition principle, quantum mechanics at the macroscopic scale predicts that a macroscopic system can be in more than one distinct state at the same time. Such an extrapolation of quantum mechanics contradicts our everyday instinct, summarized by Leggett and Garg (LG) under the heading of macrorealism (MR) [1]. To resolve the conflict and to determine whether MR or quantum mechanics is the right description of macroscopic objects, in 1985, Leggett and Garg [1] proposed the temporal Bell's inequality (TBI). If a macorealist description is possible, the inequality is satisfied - quantum mechanics, on the other hand, predicts a violation. Thereafter, people were motivated to engineer macroscopic quantum systems and to test the TBI. In the TBI, one of the most critical postulates is that of the noninvasive measurability (NIM) : it is in principle possible to determine which state the system is in with an arbitrarily small e ect on the subsequent system dynamics. To satisfy the NIM postulate in the TBI experiment, the implementation of the ""ideal negative result"" (INR) measurement was also proposed by LG [1]. In a two-state system, an INR measurement is designed to interact (in each run) with only one of two system states. Only runs where the measurement reported no outcome are kept. Although in the last few years there have been tests of the TBI on microscopic systems with the use of INR measurements [4] and on macroscopic systems using weak measurement [5], no one has ever implemented INR measurements on macroscopic systems in TBI tests so far. In addition, the NIM postulate was simply assumed, and not veri ed by an ancillary test [9, 3]. With these considerations in mind, there are two main tasks in this thesis: the rst one is to analyze the realization of an INR measurement on a macroscopic object. I propose an experiment based on coupling a flux-qubit to a dcSQUID, which mirrors the approach of Knee et al. [4], where the system of interest is coupled to another quantum system which acts as a measuring device. In order to accomplish the first task, we analyze the escape dynamics of a flux-qubit SQUID composite system in various limits and discuss the prospects of operating in a regime realizing a von Neumann (""projective"")-like measurement onto the qubit flux basis. Later in the thesis, I discuss current feasibility of the proposed experiment based on the possible measurement error (the ""venality"" [4]) of our INR measurement. The second task is to analyze experimental tests of measurement invasiveness. I propose a concrete protocol, ancillary to the main TBI experiment, which may narrow some loopholes in the test of MR [3]. I generalize the approach of Wilde and Mizel [3], using the behavior of the two-time correlator of a system as an indicator of measurement invasiveness. The measured invasivities can be used to give a improved lower bound for the TBI."
There is widespread evidence that human memory is constructive, so that recollective processes may alter the information retrieved or impact on subsequent recollections. We examine a framework for narrowing down the nature of such processes, from physics. In Physics, the Temporal Bell (TB) inequality offers a general test of the sensitivity of the context of previous measurements in sequential measurement scenarios, as predicted by quantum theory. We present an empirical memory paradigm that allows a test of the TB inequality, using a novel kind of "change judgment," whereby participants are asked to decide whether there has been a change in a question across different time points of a scenario. Across two experiments, we were able to observe evidence for the violation of a TB inequality in one case, offering evidence for quantum-like processes in memory. The present results complement other recent work purporting the relevance of quantum-like representations in memory and raise questions regarding the adaptive value of such representations.