Neo-Cartesian unified fluid and field theory: from Klein-Gordon equation to de Broglie’s Lorentz invariant mechanics

Abstract

A unified fluid and field theory containing all forces as special cases postulates that primordial fluid is formed by discrete, 3D-extended energy-like sagions obeying usual energy-momentum conservation laws. Contrary to Newtonian mechanics, mass and force are not primitive notions (hence, “Cartesian”), but the theory is atomistic (hence “neo”). Collective fluid behaviour obeys the homogeneous Klein-Gordon equation, or homogeneous 3D-wave equation, which besides usual harmonic periodic solutions has three families of quantized, Galilean-Lorentz isomorph, nonperiodic solutions discovered around 1995. Here, quantum mechanics is relativistic ab initio thus ensuring consistency with Einstein’s general theory of relativity, which is extended to include effects upon gravity of chemical and nuclear composition, as indeed observed by Eötvös (1890s), and Majorana (1919). Planck constant is identified with the bit of minimum angular momentum in sagion-sagion interactions, thus introducing quantum features at the root of classical mechanics. Acceleration produced by successive pushes of a small projectile (say, a sagion, disagion, trisagion, 4-sagion) leads to a curve resembling Einstein’s mass increase. This reinterprets one aspect of the restricted theory of relativity: rather than mass increase, Bertozzi experiment demonstrates inefficient transfer of linear momentum. The lower branch in our background universal acceleration curve is associated to static friction.