Are Colors Quanta of Light for Human Vision? A Quantum Cognition Study of Visual Perception

TL;DR

The paper investigates whether colors can be regarded as quanta of light for human vision, analogous to photons as quanta for physical measurement. It develops a quantum-cognition framework and a two-color Bloch-sphere model in which the quantum measurement process, via decoherence, implements the warping characteristic of categorical perception, quantified by $d_{pure}$ and $d_{density}$. The authors show contraction within a color category and dilation across categories, then extend the approach to multi-color spaces (e.g., eleven Berlin-Kay basic colors) and connect to Rosch’s prototype theory and Sapir-Whorf language effects. They argue that this formalism links perception, language, and quantum structure, with potential experimental tests and philosophical implications about qualia and the quantization of perceptual content.

Abstract

We show that colors are light quanta for human visual perception in a similar way as photons are light quanta for physical measurements of light waves. Our result relies on the identification in the quantum measurement process itself of the warping mechanism which is characteristic of human perception. This warping mechanism makes stimuli classified into the same category perceived as more similar, while stimuli classified into different m categories are perceived as more different. In the quantum measurement process, the warping takes place between the pure states, which play the role played for human perception by the stimuli, and the density states after decoherence, which play the role played for human perception by the percepts. We use the natural metric for pure states, namely the normalized Fubini Study metric to measure distances between pure states, and the natural metric for density states, namely the normalized trace-class metric, to measure distances between density states. We then show that when pure states lie within a well-defined region surrounding an eigenstate, the quantum measurement, namely the process of decoherence, contracts the distance between these pure states, while the reverse happens for pure states lying in a well-defined region between two eigenstates, for which the quantum measurement causes a dilation. We elaborate as an example the situation of a two-dimensional quantum measurement described by the Bloch model and apply it to the situation of two colors 'Light' and 'Dark'. We argue that this analogy of warping, on the one hand in human perception and on the other hand in the quantum measurement process, makes colors to be quanta of light for human vision.

Figures (4)

• Figure 1: A three-dimensional representation of the Bloch sphere. The quantum state of the considered quantum entity represented by point $A$ moves as a consequence of decoherence during a measurement on the line orthogonally to the diameter of the sphere to end up in the density state represented by the interior point $A'$ of the Bloch sphere and then collapses to one of the two eigen states of the measurement represented by points $A_{down}$ or $A_{up}$ respectively giving outcome 'down' or 'up'.
• Figure 2: We consider a situation where there are two names for colors, which we call Light and Dark, and wish to show that the quantum measurement model, which in this case represents a 'qubit', incorporates the phenomenon of categorical perception. For this, we consider three pure states located in the Bloch representation in points $A$, $B$ and $C$, which represent stimuli associated with a quantum measurement on this qubit. With each of the three pure states corresponds a density state in which the qubit is located after the measurement, in the Bloch representation in respectively points $A'$, $B'$ and $C'$, and described by density matrices. The pure states in $A$ and $B$ belong to two different colors, Light and Dark, and lie at a distance 1/3 from each other. The density states corresponding to them, located in points $A'$ and $B'$, are at a distance 1/2 from each other. We see here the dilation mechanism of categorical reception at work, for percepts belonging to different categories, Light and Dark. The pure states in $C$ and $A$ belong to the same color, Light, and also lie at a distance 1/3 from each other. The density states corresponding to $C$ and $A$, located in points $C'$ and $A'$, are at a distance 1/4 from each other. We see here the contraction mechanism of categorical reception at work, for percepts belonging to the same category.
• Figure 3: A more detailed representation of the contraction or dilation that takes place in a quantum measurement. We have divided the $pi$ radians long circle arc connecting the North Pole with the South Pole in equal parts, each part spanning an angle of $0.05556 \cdot \pi$ radians or $10$ degrees. We thus determine $18$ points on the great circle arc connecting the North Pole and South Pole. In a region localized around the North Pole and a similar region localized around the South Pole, the decoherence of a quantum measurement causes the pure states associated with each of these points to be transformed into density states that are closer to each other and thus a contraction occurs. In the table, these cases are indicated in green. In a region located between the North Pole and the South Pole centered around the point $\frac{1}{2} \cdot \pi$ radians away from both, the decoherence of the quantum measurement causes a dilation. The pure states connecting to the points there are transformed into density states farther apart. In the table, these cases are indicated in blue.
• Figure 4: A representation of the colors of visible light corresponding to the wavelengths of that light. Light with wavelength 504 nanometer has a color right between green and blue.