Towards a Relativistic Quantum Theory for Color Perception
The presentation will deal with a modern program of refoundation of the theory of color perception headed by Michel Berthier et Edoardo Provenzi. This theory is based on the classical Schrödinger's axioms of color perception fused with the remarkable, but strongly underestimated, works of H. Yilmaz (1962) and H.L. Resnikoff (1974). It will be shown that Yilmaz's ideas recast color perception into a (special) relativistic framework, while Resnikoff's one leads to a quantum-like setting for color perception; together, they imply that a relativistic quantum model is necessary to understand how the human visual system senses colors. Mathematically speaking, the key to understanding how to deal with this framework is represented by the so-called Jordan algebras, which are commutative, but not associative, algebras used as an alternative for quantization with respect to the classical procedure based on the associative, but not commutative, algebra of self-adjoint operators over a Hilbert space. It will be shown how the properties of Jordan algebras turn out to match exactly with Resnikoff's results and to allow us integrating Yilmaz's findings in a single, coherent, framework. As a major result of this model, it will be discussed how the achromatic plus opponent codification of color is naturally contained in this theory, without the need of resorting to a-posteriori statistical analysis.