Neo-Cartesian Unified Fluid Theory: From the Classical Wave Equation to De Broglie’s Lorentzian Quantized Mechanics and Quantized Gravity

Abstract

This paper introduces a fluid aether formed by discrete, 3D-extended energy-like sagions obeying three conservation principles of classical mechanics: total energy, linear momentum, and angular momentum. In contrast to Newtonian mechanics, neither mass, nor force are primitive notions (hence, the Cartesian”), but the theory is atomistic (hence the “neo”). Firstly, the notions of field, continuity, discreteness, extension, and philosophical and empirical reasons leading to reinstating aether are clarified. The collective fluid behaviour is described by the classical wave equation, also known as the homogeneous Klein-Gordon equation (HKGE). Connections of electromagnetism (EM), gravity and quantum mechanics (QM) to the theory of fluids are noted. The goal is to attain a unified field theory that contain as special cases the other “forces”. In particular, QM must be relativistic ab initio for consistency with Einstein’s general theory of relativity (GTR), while GTR must be extended to allow for permanent violation of the principle of equivalence, in the sense that gravity interactions depend upon composition of matter, as effectively observed in the original Eotvos experiment, and in the outstanding, but neglected, experiments of Quirino Majorana. Of particular interest are three families of nonharmonic solutions to the HKGE discovered by this author in the 1990s. The minimum angular momentum in sagion-sagion interactions is identified as Planck constant, thus introducing quantum features in classical mechanics. Coalescence of sagions leads to a kinematic theory of photons and fundamental particles, whose simplest object is a rotating dumbbell, which forms a torus in 3D-space. Acceleration produced by successive pushes of a small projectile (say, a sagion) generates an acceleration curve resembling Einstein’s mass increase, thus giving a different interpretation to some claims of special theory of relativity (STR); in particular, Bertozzi experiment is explained as an inefficient transfer of linear momentum, and the fitting of Bertozzi data by neo-Cartesian predictions is superior to STR’s predictions.