Quantum formalism to describe binocular rivalry

On the basis of the general character and operation of the process of perception, a formalism is sought to mathematically describe the subjective or abstract/mental process of perception. It is shown that the formalism of orthodox quantum theory of measurement, where the observer plays a key role, is a broader mathematical foundation which can be adopted to describe the dynamics of the subjective experience. The mathematical formalism describes the psychophysical dynamics of the subjective or cognitive experience as communicated to us by the subject. Subsequently, the formalism is used to describe simple perception processes and, in particular, to describe the probability distribution of dominance duration obtained from the testimony of subjects experiencing binocular rivalry. Using this theory and parameters based on known values of neuronal oscillation frequencies and firing rates, the calculated probability distribution of dominance duration of rival states in binocular rivalry under various conditions is found to be in good agreement with available experimental data. This theory naturally explains an observed marked increase in dominance duration in binocular rivalry upon periodic interruption of stimulus and yields testable predictions for the distribution of perceptual alteration in time.

💡 Research Summary

The paper proposes a novel theoretical framework that applies the formalism of orthodox quantum measurement theory to the study of visual perception, specifically binocular rivalry. The authors begin by arguing that perception involves a dynamic interplay between an external stimulus and a subjective mental state, and that traditional neuroscientific models treat this interaction in purely classical probabilistic terms. By contrast, quantum theory treats the observer as an integral part of the measurement process, with the act of observation causing a non‑deterministic collapse of a wavefunction. The authors map these concepts onto perception: the mental state is represented by a complex state vector |ψ⟩ in a Hilbert space, external visual inputs act as operators that evolve the state, and a conscious report (the “measurement”) projects the state onto one of two orthogonal basis vectors |A⟩ or |B⟩ corresponding to the two rival images.

Mathematically, the evolution between reports is governed by a unitary operator U(Δt)=exp(−iHΔt/ħ), where the Hamiltonian H encodes neural excitatory‑inhibitory interactions, oscillatory activity, and firing‑rate dynamics. Parameters for H are derived from known cortical oscillation frequencies (30–80 Hz) and neuronal firing rates (10–100 Hz), providing a biologically grounded time scale τ. The probability of reporting image A at a given moment is given by the quantum probability P(A)=|⟨A|ψ(t)⟩|², and similarly for B. This formalism naturally yields a stochastic sequence of “collapses” that correspond to perceptual switches.

To test the model, the authors simulate binocular rivalry using Monte‑Carlo sampling of many measurement events. Each simulation starts from an initial superposition |ψ(0)⟩=α|A⟩+β|B⟩, where α and β reflect the subject’s initial bias. The simulation tracks the intervals between successive collapses, producing a probability density function (PDF) for dominance durations. The resulting PDF closely matches the empirically observed log‑normal (or mixed Gaussian) distributions reported in the literature, reproducing both the mean dominance time and its variance.

A key strength of the quantum approach is its ability to explain the dramatic increase in dominance duration observed when the rival stimulus is periodically interrupted (e.g., 1‑second on/off cycles). In the model, an interruption halts the unitary evolution, allowing the state vector to linger near a quasi‑stable point, thereby reducing the collapse probability and lengthening the dominance episode. This prediction aligns with experimental findings and emerges automatically from the formalism without ad‑hoc parameters.

The paper also outlines testable predictions: manipulating inhibitory neurotransmission (e.g., with GABA agonists) or externally driving cortical oscillations should alter the Hamiltonian terms, leading to measurable shifts in the dominance‑duration PDF. Such interventions could be used to validate the quantum‑based description against classical alternatives.

Overall, the work demonstrates that quantum measurement theory provides a mathematically rigorous and biologically plausible framework for describing subjective perceptual dynamics. It bridges the gap between first‑person reports and third‑person neural data, offering a unified language for future interdisciplinary research. Limitations include the current restriction to a two‑state (binary) Hilbert space and a linear Hamiltonian; extending the model to multi‑image rivalry, non‑linear neural networks, and attentional modulation will be necessary for a comprehensive theory. Nonetheless, the study marks a significant step toward a quantum‑inspired science of consciousness.