Symétrisation de la longueur et du temps dans un espace de Lorentz <i>C</i>³ en algèbre lineaire, pouvant servir en théorie trichromatique des couleurs

Abstract

It is proposed to express time as a composition of three auxiliary variables t x , t y , t z . which will be named components of vector t. Event P is expressed as a composition of six variables x, y, z, t x , t y , t z in R 6 or of three coordinates ξ = x + it x , η = y + it y , and ζ = z + it z in C 3 . A quadratic function is defined, called 'carré simple', of P, which comes to the same as taking the square of the Lorentzian form of P in R 4 , equalling.s 2 . In this formalism, length r(x, y, z) and time t (t x , t y , t z ) play roles exactly symmetrical and are exchangeable one for the other. This formalism will be applied to trichromatic theory.