Ray-Tracing as Cellular Computation

Key Result

Abstract

We prove from first principles that a single ray marching through cellular cytoplasm simultaneously computes three physically distinct observations at every integration step: optical absorption (light transport via Beer-Lambert attenuation), chromatographic retention (molecular interaction via categorical distance), and circuit current flow (biochemical reaction network via Kirchhoff's laws). The Triple Observation Identity establishes these three computations are not independent processes but a single partition observation expressed in three equivalent representations. The cytoplasm functions as a three-dimensional chromatographic column whose local retention properties are encoded by partition coordinates (n, l, m, s) at each spatial position. The intracellular reaction network is isomorphic to an electrical circuit whose node potentials are chemical potentials and whose conductances are reaction rate constants. Interference between multiple rays yields a visibility parameter identical to the cellular coherence index: high visibility indicates healthy cells, low visibility indicates pathology.

Key Theorems

• 1Triple Observation Identity: optical absorption, chromatographic retention, and circuit current are one partition observation in three representations
• 2Cellular Chromatography Theorem: cytoplasm is a 3D chromatographic column with partition coordinates at each voxel
• 3Circuit-Reaction Isomorphism: biochemical network maps to electrical circuit — potentials are chemical potentials, conductances are rate constants
• 4Coherence Diagnostic: ray interference visibility = cellular health index — synchronized oscillators indicate viability

Validation Results

Figure Panels