Global Distribution of Large Aether Particles and the Origin of Particle Scales: Critical Cluster Density and Mean Free Path Constraints

As a supplement to the series of papers on the dual medium model of large and small aether, this paper systematically elaborates the global distribution characteristics of large aether particles and the origin mechanism of particle scales. This paper proposes that free large aether particles are not affected by gravitational or electromagnetic forces, and are uniformly distributed throughout the universe in the form of an approximate ideal gas. Their current number density is slightly lower than the critical density for spontaneous clustering, which is a natural evolutionary result after the cluster formation process in the early universe. On this basis, this paper further demonstrates that the spatial scale of protons is directly determined by the mean free path of small aether particles, which is the critical size satisfying the binding condition of shielding pressure difference. The scale and mass of electrons are the inevitable products of the requirement of cosmic electrical neutrality and the automatic compensation mechanism of medium pressure difference, and their charge amplitude is strictly equal and opposite in phase to that of protons. The above conclusions improve the complete evolution chain from binary primitives to elementary particles, and further consolidate the theoretical self-consistency of the large-small aether model.