[Paper Review] Quantum formalism to describe binocular rivalry

Efstratios Manousakis|ArXiv.org|Sep 28, 2007

Neural dynamics and brain function42 references4 citations

TL;DR

This paper proposes a quantum formalism based on orthodox quantum measurement theory to model the subjective dynamics of binocular rivalry, treating perceptual switches as quantum-like transitions. It successfully reproduces experimental dominance duration distributions and predicts increased dominance times under periodic stimulus interruption, offering a novel framework for understanding conscious perception through quantum-inspired dynamics.

ABSTRACT

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.

Motivation & Objective

• To develop a mathematical formalism based on quantum theory to describe the subjective dynamics of perception, particularly perceptual switches in binocular rivalry.
• To model the probability distribution of dominance durations in binocular rivalry using quantum measurement formalism, without requiring a physical brain model.
• To test whether quantum-inspired dynamics can explain observed psychophysical phenomena, including changes in dominance duration under altered neural conditions.
• To provide testable predictions for perceptual alternation patterns under periodic stimulus interruption.

Proposed method

• Adopts the formalism of standard quantum mechanics, particularly von Neumann's measurement theory, to model the observer's subjective experience of perceptual transitions.
• Models perceptual switches as quantum measurements occurring at discrete time intervals, with transition probabilities governed by a time-dependent Hamiltonian.
• Introduces parameters such as burst duration (δT), inter-burst interval (Tb), and firing rate (Nf) to simulate neuronal activity patterns influencing perceptual stability.
• Uses the quantum Zeno effect to explain reduced transition probability when measurements (neuronal firings) are frequent within a burst.
• Applies the transition probability formula P_Nf(t) = (cos(ω̄δT/Nf))^{2Nf} * sin²(ω̄δT/Nf) to compute dominance duration distributions.
• Compares theoretical P(t) distributions with experimental data across varying neural parameters and stimulus conditions.

Experimental results

Research questions

• RQ1 Can the formalism of quantum measurement theory accurately describe the probability distribution of dominance durations in binocular rivalry?
• RQ2 How does periodic interruption of the stimulus affect perceptual alternation dynamics according to the quantum model?
• RQ3 To what extent can changes in neuronal firing rates and burst patterns explain observed shifts in dominance duration distributions?
• RQ4 Does the model predict measurable oscillatory behavior in perceptual alternation under specific stimulus conditions?
• RQ5 Can the quantum Zeno effect explain reduced perceptual switching when neuronal activity is highly frequent?

Key findings

• The theoretical probability distribution P(t) of dominance durations matches experimental data across various stimulus conditions, showing strong quantitative agreement.
• The model successfully explains the experimentally observed increase in dominance duration when the stimulus is periodically interrupted, attributing it to reduced effective measurement frequency.
• When burst duration δT is increased beyond the inter-burst interval Tb, the dominance duration distribution exhibits oscillatory behavior with period δT, matching observed patterns.
• For small Tb/T ratios, the decay time constant of P(t) increases, consistent with the quantum Zeno effect and reduced transition probability due to frequent measurements.
• The model predicts a measurable distribution of perceptual alterations over time under periodic stimulus interruption, which can be tested in future experiments.
• The model demonstrates that changes in neuronal firing rates and burst structure—such as increased Nf or altered δT—produce distinct, analyzable shifts in P(t), aligning with empirical observations.